Tree traversal
Implement a binary tree where each node carries an integer, and implement:
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
- pre-order,
- in-order,
- post-order, and
- level-order traversal.
Use those traversals to output the following tree:
1
/ \
/ \
/ \
2 3
/ \ /
4 5 6
/ / \
7 8 9
The correct output should look like this:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
- See also
- Wikipedia article: Tree traversal.
11l
<lang 11l>T Node
Int data Node? left Node? right
F (data, Node? left = N, Node? right = N)
.data = data
.left = left
.right = right
F preorder(visitor) -> N
visitor(.data)
I .left != N
.left.preorder(visitor)
I .right != N
.right.preorder(visitor)
F inorder(visitor) -> N
I .left != N
.left.inorder(visitor)
visitor(.data)
I .right != N
.right.inorder(visitor)
F postorder(visitor) -> N
I .left != N
.left.postorder(visitor)
I .right != N
.right.postorder(visitor)
visitor(.data)
F preorder2(&d, level = 0) -> N
d[level].append(.data)
I .left != N
.left.preorder2(d, level + 1)
I .right != N
.right.preorder2(d, level + 1)
F levelorder(visitor)
DefaultDict[Int, [Int]] d
.preorder2(&d)
L(k) sorted(d.keys())
L(v) d[k]
visitor(v)
V tree = Node(1,
Node(2,
Node(4,
Node(7, N, N),
N),
Node(5, N, N)),
Node(3,
Node(6,
Node(8, N, N),
Node(9, N, N)),
N))
F printwithspace(Int i)
print(‘#. ’.format(i), end' ‘’)
print(‘ preorder: ’, end' ‘’) tree.preorder(printwithspace) print() print(‘ inorder: ’, end' ‘’) tree.inorder(printwithspace) print() print(‘ postorder: ’, end' ‘’) tree.postorder(printwithspace) print() print(‘levelorder: ’, end' ‘’) tree.levelorder(printwithspace) print()</lang>
- Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
AArch64 Assembly
<lang AArch64 Assembly> /* ARM assembly AARCH64 Raspberry PI 3B */ /* program deftree64.s */
/*******************************************/ /* Constantes file */ /*******************************************/ /* for this file see task include a file in language AArch64 assembly*/ .include "../includeConstantesARM64.inc"
.equ NBVAL, 9
/*******************************************/ /* Structures */ /********************************************/ /* structure tree */
.struct 0
tree_root: // root pointer
.struct tree_root + 8
tree_size: // number of element of tree
.struct tree_size + 8
tree_fin: /* structure node tree */
.struct 0
node_left: // left pointer
.struct node_left + 8
node_right: // right pointer
.struct node_right + 8
node_value: // element value
.struct node_value + 8
node_fin: /* structure queue*/
.struct 0
queue_begin: // next pointer
.struct queue_begin + 8
queue_end: // element value
.struct queue_end + 8
queue_fin: /* structure node queue */
.struct 0
queue_node_next: // next pointer
.struct queue_node_next + 8
queue_node_value: // element value
.struct queue_node_value + 8
queue_node_fin: /*******************************************/ /* Initialized data */ /*******************************************/ .data szMessInOrder: .asciz "inOrder :\n" szMessPreOrder: .asciz "PreOrder :\n" szMessPostOrder: .asciz "PostOrder :\n" szMessLevelOrder: .asciz "LevelOrder :\n" szCarriageReturn: .asciz "\n" /* datas error display */ szMessErreur: .asciz "Error detected.\n" /* datas message display */ szMessResult: .ascii "Element value : @ \n"
/*******************************************/ /* UnInitialized data */ /*******************************************/ .bss .align 4 sZoneConv: .skip 24 stTree: .skip tree_fin // place to structure tree stQueue: .skip queue_fin // place to structure queue /*******************************************/ /* code section */ /*******************************************/ .text .global main main:
mov x1,1 // node tree value
1:
ldr x0,qAdrstTree // structure tree address bl insertElement // add element value x1 cmp x0,-1 beq 99f add x1,x1,1 // increment value cmp x1,NBVAL // end ? ble 1b // no -> loop ldr x0,qAdrszMessPreOrder bl affichageMess ldr x3,qAdrstTree // tree root address (begin structure) ldr x0,[x3,#tree_root] ldr x1,qAdrdisplayElement // function to execute bl preOrder ldr x0,qAdrszMessInOrder bl affichageMess ldr x3,qAdrstTree ldr x0,[x3,#tree_root] ldr x1,qAdrdisplayElement // function to execute bl inOrder ldr x0,qAdrszMessPostOrder bl affichageMess ldr x3,qAdrstTree ldr x0,[x3,#tree_root] ldr x1,qAdrdisplayElement // function to execute bl postOrder ldr x0,qAdrszMessLevelOrder bl affichageMess ldr x3,qAdrstTree ldr x0,[x3,#tree_root] ldr x1,qAdrdisplayElement // function to execute bl levelOrder b 100f
99: // display error
ldr x0,qAdrszMessErreur bl affichageMess
100: // standard end of the program
mov x8,EXIT // request to exit program svc 0 // perform system call
qAdrszMessInOrder: .quad szMessInOrder qAdrszMessPreOrder: .quad szMessPreOrder qAdrszMessPostOrder: .quad szMessPostOrder qAdrszMessLevelOrder: .quad szMessLevelOrder qAdrszMessErreur: .quad szMessErreur qAdrszCarriageReturn: .quad szCarriageReturn qAdrstTree: .quad stTree qAdrstQueue: .quad stQueue qAdrdisplayElement: .quad displayElement /******************************************************************/ /* insert element in the tree */ /******************************************************************/ /* x0 contains the address of the tree structure */ /* x1 contains the value of element */ /* x0 returns address of element or - 1 if error */ insertElement:
stp x1,lr,[sp,-16]! // save registers mov x4,x0 mov x0,node_fin // reservation place one element bl allocHeap cmp x0,-1 // allocation error beq 100f mov x5,x0 str x1,[x5,node_value] // store value in address heap mov x1,0 str x1,[x5,node_left] // init left pointer with zero str x1,[x5,node_right] // init right pointer with zero ldr x2,[x4,tree_size] // load tree size cbnz x2,1f // 0 element ? str x5,[x4,tree_root] // yes -> store in root b 6f
1: // else search free address in tree
ldr x3,[x4,tree_root] // start with address root add x6,x2,1 // increment tree size clz x7,x6 // compute zeroes left bits add x7,x7,1 // for sustract the first left bit lsl x6,x6,x7 // shift number in left
2:
tst x6,1<<63 // test left bit lsl x6,x6,1 // shift left bit bne 3f // bit at one ldr x1,[x3,node_left] // no store node address in left pointer cbz x1,4f // if equal zero mov x3,x1 // else loop with next node b 2b
3: // yes
ldr x1,[x3,node_right] // store node address in right pointer cbz x1,5f // if equal zero mov x3,x1 // else loop with next node b 2b
4:
str x5,[x3,node_left] b 6f
5:
str x5,[x3,node_right]
6:
add x2,x2,1 // increment tree size str x2,[x4,tree_size]
100:
ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* preOrder */ /******************************************************************/ /* x0 contains the address of the node */ /* x1 function address */ preOrder:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers cmp x0,#0 beq 100f mov x2,x0 blr x1 // call function ldr x0,[x2,#node_left] bl preOrder ldr x0,[x2,#node_right] bl preOrder
100:
ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* inOrder */ /******************************************************************/ /* x0 contains the address of the node */ /* x1 function address */ inOrder:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers cbz x0,100f mov x3,x0 mov x2,x1 ldr x0,[x3,node_left] bl inOrder mov x0,x3 blr x2 // call function ldr x0,[x3,node_right] mov x1,x2 bl inOrder
100:
ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* postOrder */ /******************************************************************/ /* x0 contains the address of the node */ /* x1 function address */ postOrder:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers cbz x0,100f mov x3,x0 mov x2,x1 ldr x0,[x3,#node_left] bl postOrder ldr x0,[x3,#node_right] mov x1,x2 bl postOrder mov x0,x3 blr x2 // call function
100:
ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* levelOrder */ /******************************************************************/ /* x0 contains the address of the node */ /* x1 function address */ levelOrder:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers cbz x0,100f mov x2,x1 mov x1,x0 ldr x0,qAdrstQueue // adresse queue bl enqueueNode // queue the node
1: // begin loop
ldr x0,qAdrstQueue bl isEmptyQueue // is queue empty cbz x0,100f // yes -> end ldr x0,qAdrstQueue bl dequeueNode mov x3,x0 // save node blr x2 // call function ldr x14,[x3,#node_left] // left node ok ? cbz x14,2f ldr x0,qAdrstQueue // yes -> enqueue mov x1,x14 bl enqueueNode
2:
ldr x14,[x3,#node_right] // right node ok ? cbz x14,3f ldr x0,qAdrstQueue // yes -> enqueue mov x1,x14 bl enqueueNode
3:
b 1b // and loop
100:
ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* display node */ /******************************************************************/ /* x0 contains node address */ displayElement:
stp x1,lr,[sp,-16]! // save registers ldr x0,[x0,#node_value] ldr x1,qAdrsZoneConv bl conversion10S ldr x0,qAdrszMessResult ldr x1,qAdrsZoneConv bl strInsertAtCharInc // insert result at @ character bl affichageMess
100:
ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
qAdrszMessResult: .quad szMessResult qAdrsZoneConv: .quad sZoneConv /******************************************************************/ /* enqueue node */ /******************************************************************/ /* x0 contains the address of the queue */ /* x1 contains the value of element */ /* x0 returns address of element or - 1 if error */ enqueueNode:
stp x1,lr,[sp,-16]! // save registers stp x2,x3,[sp,-16]! // save registers mov x14,x0 mov x0,#queue_node_fin // allocation place heap bl allocHeap cmp x0,#-1 // allocation error beq 100f mov x15,x0 // save heap address str x1,[x15,#queue_node_value] // store node value mov x1,#0 str x1,[x15,#queue_node_next] // init pointer next ldr x0,[x14,#queue_end] cbz x0,1f str x15,[x0,#queue_node_next] b 2f
1:
str x15,[x14,#queue_begin]
2:
str x15,[x14,#queue_end] mov x0,#0
100:
ldp x2,x3,[sp],16 // restaur 2 registers ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* dequeue node */ /******************************************************************/ /* x0 contains the address of the queue */ /* x0 returns address of element or - 1 if error */ dequeueNode:
stp x1,lr,[sp,-16]! // save registers ldr x14,[x0,#queue_begin] ldr x15,[x14,#queue_node_value] ldr x16,[x14,#queue_node_next] str x16,[x0,#queue_begin] cbnz x16,1f str x16,[x0,#queue_end]
1:
mov x0,x15
100:
ldp x1,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/******************************************************************/ /* dequeue node */ /******************************************************************/ /* x0 contains the address of the queue */ /* x0 returns 0 if empty else 1 */ isEmptyQueue:
ldr x0,[x0,#queue_begin] cmp x0,#0 cset x0,ne ret // return
/******************************************************************/ /* memory allocation on the heap */ /******************************************************************/ /* x0 contains the size to allocate */ /* x0 returns address of memory heap or - 1 if error */ /* CAUTION : The size of the allowance must be a multiple of 4 */ allocHeap:
stp x8,lr,[sp,-16]! // save registers
// allocation
mov x16,x0 // save size
mov x0,0 // read address start heap
mov x8,BRK // call system 'brk'
svc 0
mov x15,x0 // save address heap for return
add x0,x0,x16 // reservation place for size
mov x8,BRK // call system 'brk'
svc 0
cmp x0,-1 // allocation error
beq 100f
mov x0,x15 // return address memory heap
100:
ldp x8,lr,[sp],16 // restaur 2 registers ret // return to address lr x30
/***********************************************/ /* File Include fonctions */ /********************************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeARM64.inc" </lang>
ACL2
<lang lisp>(defun flatten-preorder (tree)
(if (endp tree)
nil
(append (list (first tree))
(flatten-preorder (second tree))
(flatten-preorder (third tree)))))
(defun flatten-inorder (tree)
(if (endp tree)
nil
(append (flatten-inorder (second tree))
(list (first tree))
(flatten-inorder (third tree)))))
(defun flatten-postorder (tree)
(if (endp tree)
nil
(append (flatten-postorder (second tree))
(flatten-postorder (third tree))
(list (first tree)))))
(defun flatten-level-r1 (tree level levels)
(if (endp tree)
levels
(let ((curr (cdr (assoc level levels))))
(flatten-level-r1
(second tree)
(1+ level)
(flatten-level-r1
(third tree)
(1+ level)
(put-assoc level
(append curr (list (first tree)))
levels))))))
(defun flatten-level-r2 (levels max-level)
(declare (xargs :measure (nfix (1+ max-level))))
(if (zp (1+ max-level))
nil
(append (flatten-level-r2 levels
(1- max-level))
(reverse (cdr (assoc max-level levels))))))
(defun flatten-level (tree)
(let ((levels (flatten-level-r1 tree 0 nil)))
(flatten-level-r2 levels (len levels))))</lang>
Ada
<lang Ada>with Ada.Text_Io; use Ada.Text_Io; with Ada.Unchecked_Deallocation; with Ada.Containers.Doubly_Linked_Lists;
procedure Tree_Traversal is
type Node;
type Node_Access is access Node;
type Node is record
Left : Node_Access := null;
Right : Node_Access := null;
Data : Integer;
end record;
procedure Destroy_Tree(N : in out Node_Access) is
procedure free is new Ada.Unchecked_Deallocation(Node, Node_Access);
begin
if N.Left /= null then
Destroy_Tree(N.Left);
end if;
if N.Right /= null then
Destroy_Tree(N.Right);
end if;
Free(N);
end Destroy_Tree;
function Tree(Value : Integer; Left : Node_Access; Right : Node_Access) return Node_Access is
Temp : Node_Access := new Node;
begin
Temp.Data := Value;
Temp.Left := Left;
Temp.Right := Right;
return Temp;
end Tree;
procedure Preorder(N : Node_Access) is
begin
Put(Integer'Image(N.Data));
if N.Left /= null then
Preorder(N.Left);
end if;
if N.Right /= null then
Preorder(N.Right);
end if;
end Preorder;
procedure Inorder(N : Node_Access) is
begin
if N.Left /= null then
Inorder(N.Left);
end if;
Put(Integer'Image(N.Data));
if N.Right /= null then
Inorder(N.Right);
end if;
end Inorder;
procedure Postorder(N : Node_Access) is
begin
if N.Left /= null then
Postorder(N.Left);
end if;
if N.Right /= null then
Postorder(N.Right);
end if;
Put(Integer'Image(N.Data));
end Postorder;
procedure Levelorder(N : Node_Access) is
package Queues is new Ada.Containers.Doubly_Linked_Lists(Node_Access);
use Queues;
Node_Queue : List;
Next : Node_Access;
begin
Node_Queue.Append(N);
while not Is_Empty(Node_Queue) loop
Next := First_Element(Node_Queue);
Delete_First(Node_Queue);
Put(Integer'Image(Next.Data));
if Next.Left /= null then
Node_Queue.Append(Next.Left);
end if;
if Next.Right /= null then
Node_Queue.Append(Next.Right);
end if;
end loop;
end Levelorder;
N : Node_Access;
begin
N := Tree(1,
Tree(2,
Tree(4,
Tree(7, null, null),
null),
Tree(5, null, null)),
Tree(3,
Tree(6,
Tree(8, null, null),
Tree(9, null, null)),
null));
Put("preorder: ");
Preorder(N);
New_Line;
Put("inorder: ");
Inorder(N);
New_Line;
Put("postorder: ");
Postorder(N);
New_Line;
Put("level order: ");
Levelorder(N);
New_Line;
Destroy_Tree(N);
end Tree_traversal;</lang>
Agda
<lang Agda>open import Data.List using (List; _∷_; []; concat) open import Data.Nat using (ℕ; suc; zero) open import Level using (Level) open import Relation.Binary.PropositionalEquality using (_≡_; refl)
data Tree {a} (A : Set a) : Set a where
leaf : Tree A node : A → Tree A → Tree A → Tree A
variable
a : Level A : Set a
preorder : Tree A → List A preorder tr = go tr []
where go : Tree A → List A → List A go leaf ys = ys go (node x ls rs) ys = x ∷ go ls (go rs ys)
inorder : Tree A → List A inorder tr = go tr []
where go : Tree A → List A → List A go leaf ys = ys go (node x ls rs) ys = go ls (x ∷ go rs ys)
postorder : Tree A → List A postorder tr = go tr []
where go : Tree A → List A → List A go leaf ys = ys go (node x ls rs) ys = go ls (go rs (x ∷ ys))
level-order : Tree A → List A level-order tr = concat (go tr [])
where go : Tree A → List (List A) → List (List A) go leaf qs = qs go (node x ls rs) [] = (x ∷ []) ∷ go ls (go rs []) go (node x ls rs) (q ∷ qs) = (x ∷ q ) ∷ go ls (go rs qs)
example-tree : Tree ℕ example-tree =
node 1
(node 2
(node 4
(node 7
leaf
leaf)
leaf)
(node 5
leaf
leaf))
(node 3
(node 6
(node 8
leaf
leaf)
(node 9
leaf
leaf))
leaf)
_ : preorder example-tree ≡ 1 ∷ 2 ∷ 4 ∷ 7 ∷ 5 ∷ 3 ∷ 6 ∷ 8 ∷ 9 ∷ [] _ = refl
_ : inorder example-tree ≡ 7 ∷ 4 ∷ 2 ∷ 5 ∷ 1 ∷ 8 ∷ 6 ∷ 9 ∷ 3 ∷ [] _ = refl
_ : postorder example-tree ≡ 7 ∷ 4 ∷ 5 ∷ 2 ∷ 8 ∷ 9 ∷ 6 ∷ 3 ∷ 1 ∷ [] _ = refl
_ : level-order example-tree ≡ 1 ∷ 2 ∷ 3 ∷ 4 ∷ 5 ∷ 6 ∷ 7 ∷ 8 ∷ 9 ∷ [] _ = refl</lang>
ALGOL 68
- note the strong code structural similarities with C.
Note the changes from the original translation from C in this diff. It contains examples of syntactic sugar available in ALGOL 68.
<lang algol68>MODE VALUE = INT; PROC value repr = (VALUE value)STRING: whole(value, 0);
MODE NODES = STRUCT ( VALUE value, REF NODES left, right); MODE NODE = REF NODES;
PROC tree = (VALUE value, NODE left, right)NODE:
HEAP NODES := (value, left, right);
PROC preorder = (NODE node, PROC (VALUE)VOID action)VOID:
IF node ISNT NODE(NIL) THEN action(value OF node); preorder(left OF node, action); preorder(right OF node, action) FI;
PROC inorder = (NODE node, PROC (VALUE)VOID action)VOID:
IF node ISNT NODE(NIL) THEN inorder(left OF node, action); action(value OF node); inorder(right OF node, action) FI;
PROC postorder = (NODE node, PROC (VALUE)VOID action)VOID:
IF node ISNT NODE(NIL) THEN postorder(left OF node, action); postorder(right OF node, action); action(value OF node) FI;
PROC destroy tree = (NODE node)VOID:
postorder(node, (VALUE skip)VOID: # free(node) - PR garbage collect hint PR # node := (SKIP, NIL, NIL) );
- helper queue for level order #
MODE QNODES = STRUCT (REF QNODES next, NODE value); MODE QNODE = REF QNODES;
MODE QUEUES = STRUCT (QNODE begin, end);
MODE QUEUE = REF QUEUES;
PROC enqueue = (QUEUE queue, NODE node)VOID: (
HEAP QNODES qnode := (NIL, node); IF end OF queue ISNT QNODE(NIL) THEN next OF end OF queue ELSE begin OF queue FI := end OF queue := qnode
);
PROC queue empty = (QUEUE queue)BOOL:
begin OF queue IS QNODE(NIL);
PROC dequeue = (QUEUE queue)NODE: (
NODE out := value OF begin OF queue; QNODE second := next OF begin OF queue;
- free(begin OF queue); PR garbage collect hint PR #
QNODE(begin OF queue) := (NIL, NIL); begin OF queue := second; IF queue empty(queue) THEN end OF queue := begin OF queue FI; out
);
PROC level order = (NODE node, PROC (VALUE)VOID action)VOID: (
HEAP QUEUES queue := (QNODE(NIL), QNODE(NIL));
enqueue(queue, node);
WHILE NOT queue empty(queue)
DO
NODE next := dequeue(queue);
IF next ISNT NODE(NIL) THEN
action(value OF next);
enqueue(queue, left OF next);
enqueue(queue, right OF next)
FI
OD
);
PROC print node = (VALUE value)VOID:
print((" ",value repr(value)));
main: (
NODE node := tree(1,
tree(2,
tree(4,
tree(7, NIL, NIL),
NIL),
tree(5, NIL, NIL)),
tree(3,
tree(6,
tree(8, NIL, NIL),
tree(9, NIL, NIL)),
NIL));
MODE TEST = STRUCT( STRING name, PROC(NODE,PROC(VALUE)VOID)VOID order );
PROC test = (TEST test)VOID:(
STRING pad=" "*(12-UPB name OF test);
print((name OF test,pad,": "));
(order OF test)(node, print node);
print(new line)
);
[]TEST test list = (
("preorder",preorder),
("inorder",inorder),
("postorder",postorder),
("level order",level order)
);
FOR i TO UPB test list DO test(test list[i]) OD;
destroy tree(node)
)</lang> Output:
preorder : 1 2 4 7 5 3 6 8 9 inorder : 7 4 2 5 1 8 6 9 3 postorder : 7 4 5 2 8 9 6 3 1 level-order : 1 2 3 4 5 6 7 8 9
APL
Written in Dyalog APL with dfns. <lang APL>preorder ← {l r←⍺ ⍵⍵ ⍵ ⋄ (⊃r)∇⍨⍣(×≢r)⊢(⊃l)∇⍨⍣(×≢l)⊢⍺ ⍺⍺ ⍵} inorder ← {l r←⍺ ⍵⍵ ⍵ ⋄ (⊃r)∇⍨⍣(×≢r)⊢⍵ ⍺⍺⍨(⊃l)∇⍨⍣(×≢l)⊢⍺} postorder← {l r←⍺ ⍵⍵ ⍵ ⋄ ⍵ ⍺⍺⍨(⊃r)∇⍨⍣(×≢r)⊢(⊃l)∇⍨⍣(×≢l)⊢⍺} lvlorder ← {0=⍴⍵:⍺ ⋄ (⊃⍺⍺⍨/(⌽⍵),⊂⍺)∇⊃∘(,/)⍣2⊢⍺∘⍵⍵¨⍵}</lang> These accept four arguments (they are operators, a.k.a. higher-order functions):
acc visit ___order children bintree
returns the accumulator after visiting each node in the order specified by the function.
"acc" is the initial value for the accumulator, and "bintree" is usually the tree to be searched (it is actually the the initial argument fed to visit and children, which in most cases corresponds to the root node and the rest of the tree).
"visit" and "children" are two functions which allow these operators to work on any representation of a tree you can cook up.
"visit" takes the accumulator on the left and the current node data on the right, and returns the modified accumulator (it visits the node).
"children" generates the children of the current node from the current node's data on the right, and the current state of the accumulator on the left if needed.
"pre-", "in-", and "postorder" all work in the same way. First "children" returns the left and right children in "l" and "r", both in a "wrapper" (sort of like the Maybe type in Haskell from the little I know of it). Then the whole function is recursively applied to the left and right children if they're there, and visit is run on the current node. The order of those three operations is what differs in the three operators. Therefor if the current node possesses neither child, then the recursion ends for that branch.
"lvlorder" is a little different. The right argument is actually a list of initial nodes considered at the top level (usually this will just be a list of one element which is the tree). First all the nodes in this list are visited, then the children of each of these nodes are generated and assembled into a single list. The accumulator and this list are passed to the same function recursively, until the list of children nodes to visit is empty. This function is tail-recursive.
Time for an example to clarify all this.
I chose to represent the description's tree using nested arrays (rectangular arrays whose elements can also be rectangular arrays). Each node is of the form
value childL childR
and empty childL or childR mean and absence of the corresponding child node.
<lang APL>tree←1(2(4(7⍬⍬)⍬)(5⍬⍬))(3(6(8⍬⍬)(9⍬⍬))⍬)
visit←{⍺,(×≢⍵)⍴⊃⍵}
children←{⊂¨@(×∘≢¨)1↓⍵}</lang>
Each time the accumulator is initialised as an empty list. Visiting a node means to append its data to the accumulator, and generating children is fetching the two corresponding sublists in the nested array if they're non-empty.
My input into the interactive APL session is indented by 6 spaces.
⍬ visit preorder children tree
1 2 4 7 5 3 6 8 9
⍬ visit inorder children tree
7 4 2 5 1 8 6 9 3
⍬ visit postorder children tree
7 4 5 2 8 9 6 3 1
⍬ visit lvlorder children ,⊂tree
1 2 3 4 5 6 7 8 9
These solutions were inspired by the DFS lesson on www.TryApl.org
You should go check it out, as in the lesson it is explained how to implement a DFS operator taking the same two functions as the operators here. What is remarkable is that these same searching operators can be used both on an actual tree data structure, and on an "imaginary" one as well such as the tree of solutions to the N-Queens problem. This is the example used on TryApl.org.
AppleScript
(ES6)
<lang AppleScript>on run
-- Sample tree of integers
set tree to node(1, ¬
{node(2, ¬
{node(4, {node(7, {})}), ¬
node(5, {})}), ¬
node(3, ¬
{node(6, {node(8, {}), ¬
node(9, {})})})})
-- Output of AppleScript code at Rosetta Code task
-- 'Visualize a Tree':
set strTree to unlines({¬
" ┌ 4 ─ 7", ¬
" ┌ 2 ┤", ¬
" │ └ 5", ¬
" 1 ┤", ¬
" │ ┌ 8", ¬
" └ 3 ─ 6 ┤", ¬
" └ 9"})
script tabulate
on |λ|(s, xs)
justifyRight(14, space, s & ": ") & unwords(xs)
end |λ|
end script
set strResult to strTree & linefeed & unlines(zipWith(tabulate, ¬
["preorder", "inorder", "postorder", "level-order"], ¬
apList([¬
foldTree(preorder), ¬
foldTree(inorder), ¬
foldTree(postorder), ¬
levelOrder], [tree])))
set the clipboard to strResult
return strResult
end run
TREE TRAVERSAL ----------------------
-- preorder :: a -> a -> [a] on preorder(x, xs)
{x} & concat(xs)
end preorder
-- inorder :: a -> a -> [a]
on inorder(x, xs)
if {} ≠ xs then
item 1 of xs & x & concat(rest of xs)
else
{x}
end if
end inorder
-- postorder :: a -> a -> [a]
on postorder(x, xs)
concat(xs) & {x}
end postorder
-- levelOrder :: Tree a -> [a]
on levelOrder(tree)
concat(levels(tree))
end levelOrder
-- foldTree :: (a -> [b] -> b) -> Tree a -> b
on foldTree(f)
script
on |λ|(tree)
script go
property g : |λ| of mReturn(f)
on |λ|(oNode)
g(root of oNode, |λ|(nest of oNode) ¬
of map(go))
end |λ|
end script
|λ|(tree) of go
end |λ|
end script
end foldTree
GENERIC --------------------------
-- Node :: a -> [Tree a] -> Tree a on node(v, xs)
{type:"Node", root:v, nest:xs}
end node
-- e.g. [(*2),(/2), sqrt] <*> [1,2,3]
-- --> ap([dbl, hlf, root], [1, 2, 3])
-- --> [2,4,6,0.5,1,1.5,1,1.4142135623730951,1.7320508075688772]
-- Each member of a list of functions applied to -- each of a list of arguments, deriving a list of new values -- apList (<*>) :: [(a -> b)] -> [a] -> [b] on apList(fs, xs)
set lst to {}
repeat with f in fs
tell mReturn(contents of f)
repeat with x in xs
set end of lst to |λ|(contents of x)
end repeat
end tell
end repeat
return lst
end apList
-- concat :: a -> [a]
-- concat :: [String] -> String
on concat(xs)
set lng to length of xs
if 0 < lng and string is class of (item 1 of xs) then
set acc to ""
else
set acc to {}
end if
repeat with i from 1 to lng
set acc to acc & item i of xs
end repeat
acc
end concat
-- foldr :: (a -> b -> b) -> b -> [a] -> b
on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(item i of xs, v, i, xs)
end repeat
return v
end tell
end foldr
-- justifyRight :: Int -> Char -> String -> String
on justifyRight(n, cFiller, strText)
if n > length of strText then
text -n thru -1 of ((replicate(n, cFiller) as text) & strText)
else
strText
end if
end justifyRight
-- length :: [a] -> Int
on |length|(xs)
set c to class of xs
if list is c or string is c then
length of xs
else
(2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite)
end if
end |length|
-- levels :: Tree a -> a
on levels(tree)
-- A list of lists, grouping the root
-- values of each level of the tree.
script go
on |λ|(node, a)
if {} ≠ a then
tell a to set {h, t} to {item 1, rest}
else
set {h, t} to {{}, {}}
end if
{{root of node} & h} & foldr(go, t, nest of node)
end |λ|
end script
|λ|(tree, {}) of go
end levels
-- mReturn :: First-class m => (a -> b) -> m (a -> b) on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper.
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- map :: (a -> b) -> [a] -> [b]
on map(f)
-- The list obtained by applying f
-- to each element of xs.
script
on |λ|(xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end |λ|
end script
end map
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min
-- nest :: Tree a -> [a]
on nest(oTree)
nest of oTree
end nest
-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> a -> [a]
on replicate(n, a)
set out to {}
if 1 > n then return out
set dbl to {a}
repeat while (1 < n)
if 0 < (n mod 2) then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate
-- root :: Tree a -> a on root(oTree)
root of oTree
end root
-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set c to class of xs
if list is c then
if 0 < n then
items 1 thru min(n, length of xs) of xs
else
{}
end if
else if string is c then
if 0 < n then
text 1 thru min(n, length of xs) of xs
else
""
end if
else if script is c then
set ys to {}
repeat with i from 1 to n
set v to |λ|() of xs
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
else
missing value
end if
end take
-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation
-- of a list of strings with the newline character.
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines
-- unwords :: [String] -> String
on unwords(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, space}
set s to xs as text
set my text item delimiters to dlm
return s
end unwords
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f, xs, ys)
set lng to min(|length|(xs), |length|(ys))
if 1 > lng then return {}
set xs_ to take(lng, xs) -- Allow for non-finite
set ys_ to take(lng, ys) -- generators like cycle etc
set lst to {}
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs_, item i of ys_)
end repeat
return lst
end tell
end zipWith</lang>
- Output:
┌ 4 ─ 7
┌ 2 ┤
│ └ 5
1 ┤
│ ┌ 8
└ 3 ─ 6 ┤
└ 9
preorder: 1 2 4 7 5 3 6 8 9
inorder: 7 4 2 5 1 8 6 9 3
postorder: 7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9
ARM Assembly
<lang ARM Assembly>
/* ARM assembly Raspberry PI */ /* program deftree2.s */
/* Constantes */ .equ STDOUT, 1 @ Linux output console .equ EXIT, 1 @ Linux syscall .equ READ, 3 .equ WRITE, 4
.equ NBVAL, 9
/*******************************************/ /* Structures */ /********************************************/ /* structure tree */
.struct 0
tree_root: @ root pointer
.struct tree_root + 4
tree_size: @ number of element of tree
.struct tree_size + 4
tree_fin: /* structure node tree */
.struct 0
node_left: @ left pointer
.struct node_left + 4
node_right: @ right pointer
.struct node_right + 4
node_value: @ element value
.struct node_value + 4
node_fin: /* structure queue*/
.struct 0
queue_begin: @ next pointer
.struct queue_begin + 4
queue_end: @ element value
.struct queue_end + 4
queue_fin: /* structure node queue */
.struct 0
queue_node_next: @ next pointer
.struct queue_node_next + 4
queue_node_value: @ element value
.struct queue_node_value + 4
queue_node_fin: /* Initialized data */ .data szMessInOrder: .asciz "inOrder :\n" szMessPreOrder: .asciz "PreOrder :\n" szMessPostOrder: .asciz "PostOrder :\n" szMessLevelOrder: .asciz "LevelOrder :\n" szCarriageReturn: .asciz "\n" /* datas error display */ szMessErreur: .asciz "Error detected.\n" /* datas message display */ szMessResult: .ascii "Element value :" sValue: .space 12,' '
.asciz "\n"
/* UnInitialized data */ .bss stTree: .skip tree_fin @ place to structure tree stQueue: .skip queue_fin @ place to structure queue /* code section */ .text .global main main:
mov r1,#1 @ node tree value
1:
ldr r0,iAdrstTree @ structure tree address bl insertElement @ add element value r1 cmp r0,#-1 beq 99f add r1,#1 @ increment value cmp r1,#NBVAL @ end ? ble 1b @ no -> loop
ldr r0,iAdrszMessPreOrder bl affichageMess ldr r3,iAdrstTree @ tree root address (begin structure) ldr r0,[r3,#tree_root] ldr r1,iAdrdisplayElement @ function to execute bl preOrder
ldr r0,iAdrszMessInOrder bl affichageMess ldr r3,iAdrstTree ldr r0,[r3,#tree_root] ldr r1,iAdrdisplayElement @ function to execute bl inOrder
ldr r0,iAdrszMessPostOrder bl affichageMess ldr r3,iAdrstTree ldr r0,[r3,#tree_root] ldr r1,iAdrdisplayElement @ function to execute bl postOrder
ldr r0,iAdrszMessLevelOrder bl affichageMess ldr r3,iAdrstTree ldr r0,[r3,#tree_root] ldr r1,iAdrdisplayElement @ function to execute bl levelOrder b 100f
99: @ display error
ldr r0,iAdrszMessErreur bl affichageMess
100: @ standard end of the program
mov r7, #EXIT @ request to exit program svc 0 @ perform system call
iAdrszMessInOrder: .int szMessInOrder iAdrszMessPreOrder: .int szMessPreOrder iAdrszMessPostOrder: .int szMessPostOrder iAdrszMessLevelOrder: .int szMessLevelOrder iAdrszMessErreur: .int szMessErreur iAdrszCarriageReturn: .int szCarriageReturn iAdrstTree: .int stTree iAdrstQueue: .int stQueue iAdrdisplayElement: .int displayElement /******************************************************************/ /* insert element in the tree */ /******************************************************************/ /* r0 contains the address of the tree structure */ /* r1 contains the value of element */ /* r0 returns address of element or - 1 if error */ insertElement:
push {r1-r7,lr} @ save registers
mov r4,r0
mov r0,#node_fin @ reservation place one element
bl allocHeap
cmp r0,#-1 @ allocation error
beq 100f
mov r5,r0
str r1,[r5,#node_value] @ store value in address heap
mov r1,#0
str r1,[r5,#node_left] @ init left pointer with zero
str r1,[r5,#node_right] @ init right pointer with zero
ldr r2,[r4,#tree_size] @ load tree size
cmp r2,#0 @ 0 element ?
bne 1f
str r5,[r4,#tree_root] @ yes -> store in root
b 4f
1: @ else search free address in tree
ldr r3,[r4,#tree_root] @ start with address root add r6,r2,#1 @ increment tree size clz r7,r6 @ compute zeroes left bits add r7,#1 @ for sustract the first left bit lsl r6,r7 @ shift number in left
2:
lsls r6,#1 @ read left bit bcs 3f @ is 1 ? ldr r1,[r3,#node_left] @ no store node address in left pointer cmp r1,#0 @ if equal zero streq r5,[r3,#node_left] beq 4f mov r3,r1 @ else loop with next node b 2b
3: @ yes
ldr r1,[r3,#node_right] @ store node address in right pointer cmp r1,#0 @ if equal zero streq r5,[r3,#node_right] beq 4f mov r3,r1 @ else loop with next node b 2b
4:
add r2,#1 @ increment tree size str r2,[r4,#tree_size]
100:
pop {r1-r7,lr} @ restaur registers
bx lr @ return
/******************************************************************/ /* preOrder */ /******************************************************************/ /* r0 contains the address of the node */ /* r1 function address */ preOrder:
push {r1-r2,lr} @ save registers
cmp r0,#0
beq 100f
mov r2,r0
blx r1 @ call function
ldr r0,[r2,#node_left] bl preOrder ldr r0,[r2,#node_right] bl preOrder
100:
pop {r1-r2,lr} @ restaur registers
bx lr
/******************************************************************/ /* inOrder */ /******************************************************************/ /* r0 contains the address of the node */ /* r1 function address */ inOrder:
push {r1-r3,lr} @ save registers
cmp r0,#0
beq 100f
mov r3,r0
mov r2,r1
ldr r0,[r3,#node_left]
bl inOrder
mov r0,r3
blx r2 @ call function
ldr r0,[r3,#node_right] mov r1,r2 bl inOrder
100:
pop {r1-r3,lr} @ restaur registers
bx lr @ return
/******************************************************************/ /* postOrder */ /******************************************************************/ /* r0 contains the address of the node */ /* r1 function address */ postOrder:
push {r1-r3,lr} @ save registers
cmp r0,#0
beq 100f
mov r3,r0
mov r2,r1
ldr r0,[r3,#node_left]
bl postOrder
ldr r0,[r3,#node_right] mov r1,r2 bl postOrder mov r0,r3 blx r2 @ call function
100:
pop {r1-r3,lr} @ restaur registers
bx lr @ return
/******************************************************************/ /* levelOrder */ /******************************************************************/ /* r0 contains the address of the node */ /* r1 function address */ levelOrder:
push {r1-r4,lr} @ save registers
cmp r0,#0
beq 100f
mov r2,r1
mov r1,r0
ldr r0,iAdrstQueue @ adresse queue
bl enqueueNode @ queue the node
1: @ begin loop
ldr r0,iAdrstQueue bl isEmptyQueue @ is queue empty cmp r0,#0 beq 100f @ yes -> end ldr r0,iAdrstQueue bl dequeueNode mov r3,r0 @ save node blx r2 @ call function ldr r4,[r3,#node_left] @ left node ok ? cmp r4,#0 beq 2f @ no ldr r0,iAdrstQueue @ yes -> enqueue mov r1,r4 bl enqueueNode
2:
ldr r4,[r3,#node_right] @ right node ok ? cmp r4,#0 beq 3f @ no ldr r0,iAdrstQueue @ yes -> enqueue mov r1,r4 bl enqueueNode
3:
b 1b @ and loop
100:
pop {r1-r4,lr} @ restaur registers
bx lr @ return
/******************************************************************/ /* display node */ /******************************************************************/ /* r0 contains node address */ displayElement:
push {r1,lr} @ save registers
ldr r0,[r0,#node_value]
ldr r1,iAdrsValue
bl conversion10S
ldr r0,iAdrszMessResult
bl affichageMess
100:
pop {r1,lr} @ restaur registers
bx lr @ return
iAdrszMessResult: .int szMessResult iAdrsValue: .int sValue /******************************************************************/ /* enqueue node */ /******************************************************************/ /* r0 contains the address of the queue */ /* r1 contains the value of element */ /* r0 returns address of element or - 1 if error */ enqueueNode:
push {r1-r5,lr} @ save registers
mov r4,r0
mov r0,#queue_node_fin @ allocation place heap
bl allocHeap
cmp r0,#-1 @ allocation error
beq 100f
mov r5,r0 @ save heap address
str r1,[r5,#queue_node_value] @ store node value
mov r1,#0
str r1,[r5,#queue_node_next] @ init pointer next
ldr r0,[r4,#queue_end]
cmp r0,#0
strne r5,[r0,#queue_node_next]
streq r5,[r4,#queue_begin]
str r5,[r4,#queue_end]
mov r0,#0
pop {r1-r5,lr}
bx lr @ return
/******************************************************************/ /* dequeue node */ /******************************************************************/ /* r0 contains the address of the queue */ /* r0 returns address of element or - 1 if error */ dequeueNode:
push {r1-r5,lr} @ save registers
ldr r4,[r0,#queue_begin]
ldr r5,[r4,#queue_node_value]
ldr r6,[r4,#queue_node_next]
str r6,[r0,#queue_begin]
cmp r6,#0
streq r6,[r0,#queue_end]
mov r0,r5
100:
pop {r1-r5,lr}
bx lr @ return
/******************************************************************/ /* dequeue node */ /******************************************************************/ /* r0 contains the address of the queue */ /* r0 returns 0 if empty else 1 */ isEmptyQueue:
ldr r0,[r0,#queue_begin] cmp r0,#0 movne r0,#1 bx lr @ return
/******************************************************************/ /* memory allocation on the heap */ /******************************************************************/ /* r0 contains the size to allocate */ /* r0 returns address of memory heap or - 1 if error */ /* CAUTION : The size of the allowance must be a multiple of 4 */ allocHeap:
push {r5-r7,lr} @ save registers
@ allocation
mov r6,r0 @ save size
mov r0,#0 @ read address start heap
mov r7,#0x2D @ call system 'brk'
svc #0
mov r5,r0 @ save address heap for return
add r0,r6 @ reservation place for size
mov r7,#0x2D @ call system 'brk'
svc #0
cmp r0,#-1 @ allocation error
movne r0,r5 @ return address memory heap
pop {r5-r7,lr} @ restaur registers
bx lr @ return
/******************************************************************/ /* display text with size calculation */ /******************************************************************/ /* r0 contains the address of the message */ affichageMess:
push {r0,r1,r2,r7,lr} @ save registers
mov r2,#0 @ counter length */
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index
cmp r1,#0 @ if 0 its over
addne r2,r2,#1 @ else add 1 in the length
bne 1b @ and loop
@ so here r2 contains the length of the message
mov r1,r0 @ address message in r1
mov r0,#STDOUT @ code to write to the standard output Linux
mov r7, #WRITE @ code call system "write"
svc #0 @ call system
pop {r0,r1,r2,r7,lr} @ restaur registers
bx lr @ return
/***************************************************/ /* Converting a register to a signed decimal */ /***************************************************/ /* r0 contains value and r1 area address */ conversion10S:
push {r0-r4,lr} @ save registers
mov r2,r1 @ debut zone stockage
mov r3,#'+' @ par defaut le signe est +
cmp r0,#0 @ negative number ?
movlt r3,#'-' @ yes
mvnlt r0,r0 @ number inversion
addlt r0,#1
mov r4,#10 @ length area
1: @ start loop
bl divisionpar10U add r1,#48 @ digit strb r1,[r2,r4] @ store digit on area sub r4,r4,#1 @ previous position cmp r0,#0 @ stop if quotient = 0 bne 1b
strb r3,[r2,r4] @ store signe subs r4,r4,#1 @ previous position blt 100f @ if r4 < 0 -> end
mov r1,#' ' @ space
2:
strb r1,[r2,r4] @store byte space subs r4,r4,#1 @ previous position bge 2b @ loop if r4 > 0
100:
pop {r0-r4,lr} @ restaur registers
bx lr
/***************************************************/ /* division par 10 unsigned */ /***************************************************/ /* r0 dividende */ /* r0 quotient */ /* r1 remainder */ divisionpar10U:
push {r2,r3,r4, lr}
mov r4,r0 @ save value
//mov r3,#0xCCCD @ r3 <- magic_number lower raspberry 3
//movt r3,#0xCCCC @ r3 <- magic_number higter raspberry 3
ldr r3,iMagicNumber @ r3 <- magic_number raspberry 1 2
umull r1, r2, r3, r0 @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)
mov r0, r2, LSR #3 @ r2 <- r2 >> shift 3
add r2,r0,r0, lsl #2 @ r2 <- r0 * 5
sub r1,r4,r2, lsl #1 @ r1 <- r4 - (r2 * 2) = r4 - (r0 * 10)
pop {r2,r3,r4,lr}
bx lr @ leave function
iMagicNumber: .int 0xCCCCCCCD
</lang>
- Output:
PreOrder : Element value : +1 Element value : +2 Element value : +4 Element value : +8 Element value : +9 Element value : +5 Element value : +3 Element value : +6 Element value : +7 inOrder : Element value : +8 Element value : +4 Element value : +9 Element value : +2 Element value : +5 Element value : +1 Element value : +6 Element value : +3 Element value : +7 PostOrder : Element value : +8 Element value : +9 Element value : +4 Element value : +5 Element value : +2 Element value : +6 Element value : +7 Element value : +3 Element value : +1 LevelOrder : Element value : +1 Element value : +2 Element value : +3 Element value : +4 Element value : +5 Element value : +6 Element value : +7 Element value : +8 Element value : +9
ATS
<lang ATS>#include "share/atspre_staload.hats" // (* ****** ****** *) // datatype tree (a:t@ype) =
| tnil of () | tcons of (tree a, a, tree a)
// (* ****** ****** *)
symintr ++ infixr (+) ++ overload ++ with list_append
(* ****** ****** *)
- define sing list_sing
(* ****** ****** *)
fun{ a:t@ype } preorder
(t0: tree a): List0 a = case t0 of | tnil () => nil () | tcons (tl, x, tr) => sing(x) ++ preorder(tl) ++ preorder(tr)
(* ****** ****** *)
fun{ a:t@ype } inorder
(t0: tree a): List0 a = case t0 of | tnil () => nil () | tcons (tl, x, tr) => inorder(tl) ++ sing(x) ++ inorder(tr)
(* ****** ****** *)
fun{ a:t@ype } postorder
(t0: tree a): List0 a = case t0 of | tnil () => nil () | tcons (tl, x, tr) => postorder(tl) ++ postorder(tr) ++ sing(x)
(* ****** ****** *)
fun{ a:t@ype } levelorder
(t0: tree a): List0 a = let
// fun auxlst
(ts: List (tree(a))): List0 a =
case ts of
| list_nil () => list_nil ()
| list_cons (t, ts) =>
(
case+ t of
| tnil () => auxlst (ts)
| tcons (tl, x, tr) => cons (x, auxlst (ts ++ $list{tree(a)}(tl, tr)))
)
// in
auxlst (sing(t0))
end // end of [levelorder]
(* ****** ****** *)
macdef tsing(x) = tcons (tnil, ,(x), tnil)
(* ****** ****** *)
implement main0 () = let // val t0 = tcons{int} (
tcons (tcons (tsing (7), 4, tnil ()), 2, tsing (5))
, 1 ,
tcons (tcons (tsing (8), 6, tsing (9)), 3, tnil ())
) // in
println! ("preorder:\t", preorder(t0));
println! ("inorder:\t", inorder(t0));
println! ("postorder:\t", postorder(t0));
println! ("level-order:\t", levelorder(t0));
end (* end of [main0] *)</lang>
- Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
AutoHotkey
<lang AutoHotkey>AddNode(Tree,1,2,3,1) ; Build global Tree AddNode(Tree,2,4,5,2) AddNode(Tree,3,6,0,3) AddNode(Tree,4,7,0,4) AddNode(Tree,5,0,0,5) AddNode(Tree,6,8,9,6) AddNode(Tree,7,0,0,7) AddNode(Tree,8,0,0,8) AddNode(Tree,9,0,0,9)
MsgBox % "Preorder: " PreOrder(Tree,1) ; 1 2 4 7 5 3 6 8 9 MsgBox % "Inorder: " InOrder(Tree,1) ; 7 4 2 5 1 8 6 9 3 MsgBox % "postorder: " PostOrder(Tree,1) ; 7 4 5 2 8 9 6 3 1 MsgBox % "levelorder: " LevOrder(Tree,1) ; 1 2 3 4 5 6 7 8 9
AddNode(ByRef Tree,Node,Left,Right,Value) {
if !isobject(Tree)
Tree := object()
Tree[Node, "L"] := Left Tree[Node, "R"] := Right Tree[Node, "V"] := Value
}
PreOrder(Tree,Node) { ptree := Tree[Node, "V"] " "
. ((L:=Tree[Node, "L"]) ? PreOrder(Tree,L) : "")
. ((R:=Tree[Node, "R"]) ? PreOrder(Tree,R) : "")
return ptree } InOrder(Tree,Node) {
Return itree := ((L:=Tree[Node, "L"]) ? InOrder(Tree,L) : "")
. Tree[Node, "V"] " "
. ((R:=Tree[Node, "R"]) ? InOrder(Tree,R) : "")
} PostOrder(Tree,Node) {
Return ptree := ((L:=Tree[Node, "L"]) ? PostOrder(Tree,L) : "")
. ((R:=Tree[Node, "R"]) ? PostOrder(Tree,R) : "")
. Tree[Node, "V"] " "
} LevOrder(Tree,Node,Lev=1) {
Static ; make node lists static
i%Lev% .= Tree[Node, "V"] " " ; build node lists in every level
If (L:=Tree[Node, "L"])
LevOrder(Tree,L,Lev+1)
If (R:=Tree[Node, "R"])
LevOrder(Tree,R,Lev+1)
If (Lev > 1)
Return
While i%Lev% ; concatenate node lists from all levels
t .= i%Lev%, Lev++
Return t
}</lang>
AWK
<lang awk> function preorder(tree, node, res, child) {
if (node == "")
return
res[res["count"]++] = node
split(tree[node], child, ",")
preorder(tree,child[1],res)
preorder(tree,child[2],res)
}
function inorder(tree, node, res, child) {
if (node == "")
return
split(tree[node], child, ",")
inorder(tree,child[1],res)
res[res["count"]++] = node
inorder(tree,child[2],res)
}
function postorder(tree, node, res, child) {
if (node == "")
return
split(tree[node], child, ",")
postorder(tree,child[1], res)
postorder(tree,child[2], res)
res[res["count"]++] = node
}
function levelorder(tree, node, res, nextnode, queue, child) {
if (node == "")
return
queue["tail"] = 0 queue[queue["head"]++] = node
while (queue["head"] - queue["tail"] >= 1) {
nextnode = queue[queue["tail"]]
delete queue[queue["tail"]++]
res[res["count"]++] = nextnode
split(tree[nextnode], child, ",")
if (child[1] != "")
queue[queue["head"]++] = child[1]
if (child[2] != "")
queue[queue["head"]++] = child[2]
}
delete queue
}
BEGIN {
tree["1"] = "2,3"
tree["2"] = "4,5"
tree["3"] = "6,"
tree["4"] = "7,"
tree["5"] = ","
tree["6"] = "8,9"
tree["7"] = ","
tree["8"] = ","
tree["9"] = ","
preorder(tree,"1",result)
printf "preorder:\t"
for (n = 0; n < result["count"]; n += 1)
printf result[n]" "
printf "\n"
delete result
inorder(tree,"1",result)
printf "inorder:\t"
for (n = 0; n < result["count"]; n += 1)
printf result[n]" "
printf "\n"
delete result
postorder(tree,"1",result)
printf "postorder:\t"
for (n = 0; n < result["count"]; n += 1)
printf result[n]" "
printf "\n"
delete result
levelorder(tree,"1",result)
printf "level-order:\t"
for (n = 0; n < result["count"]; n += 1)
printf result[n]" "
printf "\n"
delete result
} </lang>
Bracmat
<lang bracmat>(
( tree
= 1
. (2.(4.7.) (5.))
(3.6.(8.) (9.))
)
& ( preorder
= K sub
. !arg:(?K.?sub) ?arg
& !K preorder$!sub preorder$!arg
|
)
& out$("preorder: " preorder$!tree) & ( inorder
= K lhs rhs
. !arg:(?K.?sub) ?arg
& ( !sub:%?lhs ?rhs
& inorder$!lhs !K inorder$!rhs inorder$!arg
| !K
)
)
& out$("inorder: " inorder$!tree) & ( postorder
= K sub
. !arg:(?K.?sub) ?arg
& postorder$!sub !K postorder$!arg
|
)
& out$("postorder: " postorder$!tree) & ( levelorder
= todo tree sub
. !arg:(.)&
| !arg:(?tree.?todo)
& ( !tree:(?K.?sub) ?tree
& !K levelorder$(!tree.!todo !sub)
| levelorder$(!todo.)
)
)
& out$("level-order:" levelorder$(!tree.)) & )</lang>
C
<lang c>#include <stdlib.h>
- include <stdio.h>
typedef struct node_s {
int value; struct node_s* left; struct node_s* right;
} *node;
node tree(int v, node l, node r) {
node n = malloc(sizeof(struct node_s)); n->value = v; n->left = l; n->right = r; return n;
}
void destroy_tree(node n) {
if (n->left) destroy_tree(n->left); if (n->right) destroy_tree(n->right); free(n);
}
void preorder(node n, void (*f)(int)) {
f(n->value); if (n->left) preorder(n->left, f); if (n->right) preorder(n->right, f);
}
void inorder(node n, void (*f)(int)) {
if (n->left) inorder(n->left, f); f(n->value); if (n->right) inorder(n->right, f);
}
void postorder(node n, void (*f)(int)) {
if (n->left) postorder(n->left, f); if (n->right) postorder(n->right, f); f(n->value);
}
/* helper queue for levelorder */ typedef struct qnode_s {
struct qnode_s* next; node value;
} *qnode;
typedef struct { qnode begin, end; } queue;
void enqueue(queue* q, node n) {
qnode node = malloc(sizeof(struct qnode_s)); node->value = n; node->next = 0; if (q->end) q->end->next = node; else q->begin = node; q->end = node;
}
node dequeue(queue* q) {
node tmp = q->begin->value; qnode second = q->begin->next; free(q->begin); q->begin = second; if (!q->begin) q->end = 0; return tmp;
}
int queue_empty(queue* q) {
return !q->begin;
}
void levelorder(node n, void(*f)(int)) {
queue nodequeue = {};
enqueue(&nodequeue, n);
while (!queue_empty(&nodequeue))
{
node next = dequeue(&nodequeue);
f(next->value);
if (next->left)
enqueue(&nodequeue, next->left);
if (next->right)
enqueue(&nodequeue, next->right);
}
}
void print(int n) {
printf("%d ", n);
}
int main() {
node n = tree(1,
tree(2,
tree(4,
tree(7, 0, 0),
0),
tree(5, 0, 0)),
tree(3,
tree(6,
tree(8, 0, 0),
tree(9, 0, 0)),
0));
printf("preorder: ");
preorder(n, print);
printf("\n");
printf("inorder: ");
inorder(n, print);
printf("\n");
printf("postorder: ");
postorder(n, print);
printf("\n");
printf("level-order: ");
levelorder(n, print);
printf("\n");
destroy_tree(n);
return 0;
}</lang>
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
class Node {
int Value; Node Left; Node Right;
Node(int value = default(int), Node left = default(Node), Node right = default(Node))
{
Value = value;
Left = left;
Right = right;
}
IEnumerable<int> Preorder()
{
yield return Value;
if (Left != null)
foreach (var value in Left.Preorder())
yield return value;
if (Right != null)
foreach (var value in Right.Preorder())
yield return value;
}
IEnumerable<int> Inorder()
{
if (Left != null)
foreach (var value in Left.Inorder())
yield return value;
yield return Value;
if (Right != null)
foreach (var value in Right.Inorder())
yield return value;
}
IEnumerable<int> Postorder()
{
if (Left != null)
foreach (var value in Left.Postorder())
yield return value;
if (Right != null)
foreach (var value in Right.Postorder())
yield return value;
yield return Value;
}
IEnumerable<int> LevelOrder()
{
var queue = new Queue<Node>();
queue.Enqueue(this);
while (queue.Any())
{
var node = queue.Dequeue();
yield return node.Value;
if (node.Left != null)
queue.Enqueue(node.Left);
if (node.Right != null)
queue.Enqueue(node.Right);
}
}
static void Main()
{
var tree = new Node(1, new Node(2, new Node(4, new Node(7)), new Node(5)), new Node(3, new Node(6, new Node(8), new Node(9))));
foreach (var traversal in new Func<IEnumerable<int>>[] { tree.Preorder, tree.Inorder, tree.Postorder, tree.LevelOrder })
Console.WriteLine("{0}:\t{1}", traversal.Method.Name, string.Join(" ", traversal()));
}
}</lang>
C++
Compiler: g++ (version 4.3.2 20081105 (Red Hat 4.3.2-7))
<lang cpp>#include <boost/scoped_ptr.hpp>
- include <iostream>
- include <queue>
template<typename T> class TreeNode { public:
TreeNode(const T& n, TreeNode* left = NULL, TreeNode* right = NULL)
: mValue(n),
mLeft(left),
mRight(right) {}
T getValue() const {
return mValue;
}
TreeNode* left() const {
return mLeft.get();
}
TreeNode* right() const {
return mRight.get();
}
void preorderTraverse() const {
std::cout << " " << getValue();
if(mLeft) { mLeft->preorderTraverse(); }
if(mRight) { mRight->preorderTraverse(); }
}
void inorderTraverse() const {
if(mLeft) { mLeft->inorderTraverse(); }
std::cout << " " << getValue();
if(mRight) { mRight->inorderTraverse(); }
}
void postorderTraverse() const {
if(mLeft) { mLeft->postorderTraverse(); }
if(mRight) { mRight->postorderTraverse(); }
std::cout << " " << getValue();
}
void levelorderTraverse() const {
std::queue<const TreeNode*> q;
q.push(this);
while(!q.empty()) {
const TreeNode* n = q.front();
q.pop();
std::cout << " " << n->getValue();
if(n->left()) { q.push(n->left()); }
if(n->right()) { q.push(n->right()); }
}
}
protected:
T mValue; boost::scoped_ptr<TreeNode> mLeft; boost::scoped_ptr<TreeNode> mRight;
private:
TreeNode();
};
int main() {
TreeNode<int> root(1,
new TreeNode<int>(2,
new TreeNode<int>(4,
new TreeNode<int>(7)),
new TreeNode<int>(5)),
new TreeNode<int>(3,
new TreeNode<int>(6,
new TreeNode<int>(8),
new TreeNode<int>(9))));
std::cout << "preorder: "; root.preorderTraverse(); std::cout << std::endl;
std::cout << "inorder: "; root.inorderTraverse(); std::cout << std::endl;
std::cout << "postorder: "; root.postorderTraverse(); std::cout << std::endl;
std::cout << "level-order:"; root.levelorderTraverse(); std::cout << std::endl;
return 0;
}</lang>
Array version
<lang cpp>#include <iostream>
using namespace std;
const int MAX_DIM = 16;
typedef int* tree;
int left(int index) {
return index*2+1;
}
int right(int index) {
return index*2+2;
}
void preorder(tree t, int index = 0) {
if(index < MAX_DIM && t[index] != 0){
cout << t[index] << ' ';
preorder(t, left(index));
preorder(t, right(index));
}
}
void inorder(tree t, int index = 0) {
if(index < MAX_DIM && t[index] != 0){
inorder(t, left(index));
cout << t[index] << ' ';
inorder(t, right(index));
}
}
void postorder(tree t, int index = 0) {
if(index < MAX_DIM && t[index] != 0){
postorder(t, left(index));
postorder(t, right(index));
cout << t[index] << ' ';
}
}
void level_order(tree t, int index = 0) {
for(int i = 0; i < MAX_DIM; ++i){
if(t[i] != 0)
cout << t[i] << ' ';
}
}
int main() {
int t[MAX_DIM] = {1,2,3,4,5,6,0,7,0,0,0,8,9};
cout << "preorder: ";
preorder(t);
cout << endl;
cout << "inorder: ";
inorder(t);
cout << endl;
cout << "postorder: ";
postorder(t);
cout << endl;
cout << "level_order: ";
level_order(t);
cout << endl;
}</lang>
Modern C++
<lang cpp>#include <iostream>
- include <memory>
- include <queue>
template <typename T> class node { public:
node(T value) : value_(value) {}
node(T value, std::unique_ptr<node>&& left)
: value_(value), left_(std::move(left)) {}
node(T value, std::unique_ptr<node>&& left, std::unique_ptr<node>&& right)
: value_(value), left_(std::move(left)), right_(std::move(right)) {}
template <typename Function>
void pre_order(Function f) {
f(value_);
if (left_)
left_->pre_order(f);
if (right_)
right_->pre_order(f);
}
template <typename Function>
void in_order(Function f) {
if (left_)
left_->in_order(f);
f(value_);
if (right_)
right_->in_order(f);
}
template <typename Function>
void post_order(Function f) {
if (left_)
left_->post_order(f);
if (right_)
right_->post_order(f);
f(value_);
}
template <typename Function>
void level_order(Function f) {
std::queue<node*> queue;
queue.push(this);
while (!queue.empty()) {
node* next = queue.front();
queue.pop();
f(next->value_);
if (next->left_)
queue.push(next->left_.get());
if (next->right_)
queue.push(next->right_.get());
}
}
private:
T value_; std::unique_ptr<node> left_; std::unique_ptr<node> right_;
};
template <typename T, typename... Args> std::unique_ptr<node<T>> tree(T value, Args&&... args) {
return std::make_unique<node<T>>(value, std::forward<Args>(args)...);
}
int main() {
node<int> n(1,
tree(2,
tree(4,
tree(7)),
tree(5)),
tree(3,
tree(6,
tree(8),
tree(9))));
auto print = [](int n) { std::cout << n << ' '; };
std::cout << "pre-order: "; n.pre_order(print); std::cout << '\n';
std::cout << "in-order: "; n.in_order(print); std::cout << '\n';
std::cout << "post-order: "; n.post_order(print); std::cout << '\n';
std::cout << "level-order: "; n.level_order(print); std::cout << '\n';
}</lang>
- Output:
pre-order: 1 2 4 7 5 3 6 8 9 in-order: 7 4 2 5 1 8 6 9 3 post-order: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
Ceylon
<lang ceylon>import ceylon.collection { ArrayList }
shared void run() {
class Node(label, left = null, right = null) { shared Integer label; shared Node? left; shared Node? right; string => label.string; }
void preorder(Node node) { process.write(node.string + " "); if(exists left = node.left) { preorder(left); } if(exists right = node.right) { preorder(right); } }
void inorder(Node node) { if(exists left = node.left) { inorder(left); } process.write(node.string + " "); if(exists right = node.right) { inorder(right); } }
void postorder(Node node) { if(exists left = node.left) { postorder(left); } if(exists right = node.right) { postorder(right); } process.write(node.string + " "); }
void levelOrder(Node node) { value nodes = ArrayList<Node> {node}; while(exists current = nodes.accept()) { process.write(current.string + " "); if(exists left = current.left) { nodes.offer(left); } if(exists right = current.right) { nodes.offer(right); } } }
value tree = Node { label = 1; left = Node { label = 2; left = Node { label = 4; left = Node { label = 7; }; }; right = Node { label = 5; }; }; right = Node { label = 3; left = Node { label = 6; left = Node { label = 8; }; right = Node { label = 9; }; }; }; };
process.write("preorder: "); preorder(tree); print(""); process.write("inorder: "); inorder(tree); print(""); process.write("postorder: "); postorder(tree); print(""); process.write("levelorder: "); levelOrder(tree); print(""); }</lang>
Clojure
<lang clojure>(defn walk [node f order]
(when node
(doseq [o order]
(if (= o :visit)
(f (:val node))
(walk (node o) f order)))))
(defn preorder [node f]
(walk node f [:visit :left :right]))
(defn inorder [node f]
(walk node f [:left :visit :right]))
(defn postorder [node f]
(walk node f [:left :right :visit]))
(defn queue [& xs]
(when (seq xs) (apply conj clojure.lang.PersistentQueue/EMPTY xs)))
(defn level-order [root f]
(loop [q (queue root)]
(when-not (empty? q)
(if-let [node (first q)]
(do
(f (:val node))
(recur (conj (pop q) (:left node) (:right node))))
(recur (pop q))))))
(defn vec-to-tree [t]
(if (vector? t)
(let [[val left right] t]
{:val val
:left (vec-to-tree left)
:right (vec-to-tree right)})
t))
(let [tree (vec-to-tree [1 [2 [4 [7]] [5]] [3 [6 [8] [9]]]])
fs '[preorder inorder postorder level-order]
pr-node #(print (format "%2d" %))]
(doseq [f fs]
(print (format "%-12s" (str f ":")))
((resolve f) tree pr-node)
(println)))</lang>
CoffeeScript
<lang coffeescript>
- In this example, we don't encapsulate binary trees as objects; instead, we have a
- convention on how to store them as arrays, and we namespace the functions that
- operate on those data structures.
binary_tree =
preorder: (tree, visit) -> return unless tree? [node, left, right] = tree visit node binary_tree.preorder left, visit binary_tree.preorder right, visit
inorder: (tree, visit) -> return unless tree? [node, left, right] = tree binary_tree.inorder left, visit visit node binary_tree.inorder right, visit
postorder: (tree, visit) ->
return unless tree?
[node, left, right] = tree
binary_tree.postorder left, visit
binary_tree.postorder right, visit
visit node
levelorder: (tree, visit) ->
q = []
q.push tree
while q.length > 0
t = q.shift()
continue unless t?
[node, left, right] = t
visit node
q.push left
q.push right
do ->
tree = [1, [2, [4, [7]], [5]], [3, [6, [8],[9]]]] test_walk = (walk_function_name) -> output = [] binary_tree[walk_function_name] tree, output.push.bind(output) console.log walk_function_name, output.join ' ' test_walk "preorder" test_walk "inorder" test_walk "postorder" test_walk "levelorder"
</lang> output <lang> > coffee tree_traversal.coffee preorder 1 2 4 7 5 3 6 8 9 inorder 7 4 2 5 1 8 6 9 3 postorder 7 4 5 2 8 9 6 3 1 levelorder 1 2 3 4 5 6 7 8 9 </lang>
Common Lisp
<lang lisp>(defun preorder (node f)
(when node (funcall f (first node)) (preorder (second node) f) (preorder (third node) f)))
(defun inorder (node f)
(when node (inorder (second node) f) (funcall f (first node)) (inorder (third node) f)))
(defun postorder (node f)
(when node (postorder (second node) f) (postorder (third node) f) (funcall f (first node))))
(defun level-order (node f)
(loop with level = (list node)
while level
do
(setf level (loop for node in level
when node
do (funcall f (first node))
and collect (second node)
and collect (third node)))))
(defparameter *tree* '(1 (2 (4 (7))
(5))
(3 (6 (8)
(9)))))
(defun show (traversal-function)
(format t "~&~(~A~):~12,0T" traversal-function) (funcall traversal-function *tree* (lambda (value) (format t " ~A" value))))
(map nil #'show '(preorder inorder postorder level-order))</lang>
Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 2 5 1 8 6 9 3 level-order: 1 2 3 4 5 6 7 8 9
Coq
<lang coq>Require Import Utf8. Require Import List.
Unset Elimination Schemes.
(* Rose tree, with numbers on nodes *) Inductive tree := Tree { value : nat ; children : list tree }.
Fixpoint height (t: tree) : nat :=
1 + fold_left (λ n t, max n (height t)) (children t) 0.
Example leaf n : tree := {| value := n ; children := nil |}.
Example t2 : tree := {| value := 2 ; children := {| value := 4 ; children := leaf 7 :: nil |} :: leaf 5 :: nil |}.
Example t3 : tree := {| value := 3 ; children := {| value := 6 ; children := leaf 8 :: leaf 9 :: nil |} :: nil |}.
Example t9 : tree := {| value := 1 ; children := t2 :: t3 :: nil |}.
Fixpoint preorder (t: tree) : list nat :=
let '{| value := n ; children := c |} := t in
n :: flat_map preorder c.
Fixpoint inorder (t: tree) : list nat :=
let '{| value := n ; children := c |} := t in
match c with
| nil => n :: nil
| ℓ :: r => inorder ℓ ++ n :: flat_map inorder r
end.
Fixpoint postorder (t: tree) : list nat :=
let '{| value := n ; children := c |} := t in
flat_map postorder c ++ n :: nil.
(* Auxiliary function for levelorder, which operates on forests *) (* Since the recursion is tricky, it relies on a fuel parameter which obviously decreases. *) Fixpoint levelorder_forest (fuel: nat) (f: list tree) : list nat:=
match fuel with | O => nil | S fuel' => let '(p, f) := fold_right (λ t r, let '(x, f) := r in (value t :: x, children t ++ f) ) (nil, nil) f in p ++ levelorder_forest fuel' f end.
Definition levelorder (t: tree) : list nat :=
levelorder_forest (height t) (t :: nil).
Compute preorder t9. Compute inorder t9. Compute postorder t9. Compute levelorder t9. </lang>
Crystal
<lang crystal> class Node(T)
property left : Nil | Node(T) property right : Nil | Node(T) property data : T
def initialize(@data, @left = nil, @right = nil) end
def preorder_traverse
print " #{data}"
if left = @left
left.preorder_traverse
end
if right = @right
right.preorder_traverse
end
end
def inorder_traverse
if left = @left
left.inorder_traverse
end
print " #{data}"
if right = @right
right.inorder_traverse
end
end
def postorder_traverse
if left = @left
left.postorder_traverse
end
if right = @right
right.postorder_traverse
end
print " #{data}"
end
def levelorder_traverse queue = Array(Node(T)).new queue << self
until queue.size <= 0
node = queue.shift
unless node
next
end
print " #{node.data}"
if left = node.left
queue << left
end
if right = node.right
queue << right
end
end
end
end
tree = Node(Int32).new(1,
Node(Int32).new(2,
Node(Int32).new(4,
Node(Int32).new(7)),
Node(Int32).new(5)),
Node(Int32).new(3,
Node(Int32).new(6,
Node(Int32).new(8),
Node(Int32).new(9))))
print "preorder: " tree.preorder_traverse print "\ninorder: " tree.inorder_traverse print "\npostorder: " tree.postorder_traverse print "\nlevelorder: " tree.levelorder_traverse puts
</lang> Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
D
This code is long because it's very generic. <lang d>import std.stdio, std.traits;
const final class Node(T) {
T data; Node left, right;
this(in T data, in Node left=null, in Node right=null)
const pure nothrow {
this.data = data;
this.left = left;
this.right = right;
}
}
// 'static' templated opCall can't be used in Node auto node(T)(in T data, in Node!T left=null, in Node!T right=null) pure nothrow {
return new const(Node!T)(data, left, right);
}
void show(T)(in T x) {
write(x, " ");
}
enum Visit { pre, inv, post }
// 'visitor' can be any kind of callable or it uses a default visitor. // TNode can be any kind of Node, with data, left and right fields, // so this is more generic than a member function of Node. void backtrackingOrder(Visit v, TNode, TyF=void*)
(in TNode node, TyF visitor=null) {
alias trueVisitor = Select!(is(TyF == void*), show, visitor);
if (node !is null) {
static if (v == Visit.pre)
trueVisitor(node.data);
backtrackingOrder!v(node.left, visitor);
static if (v == Visit.inv)
trueVisitor(node.data);
backtrackingOrder!v(node.right, visitor);
static if (v == Visit.post)
trueVisitor(node.data);
}
}
void levelOrder(TNode, TyF=void*)
(in TNode node, TyF visitor=null, const(TNode)[] more=[]) {
alias trueVisitor = Select!(is(TyF == void*), show, visitor);
if (node !is null) {
more ~= [node.left, node.right];
trueVisitor(node.data);
}
if (more.length)
levelOrder(more[0], visitor, more[1 .. $]);
}
void main() {
alias N = node;
const tree = N(1,
N(2,
N(4,
N(7)),
N(5)),
N(3,
N(6,
N(8),
N(9))));
write(" preOrder: ");
tree.backtrackingOrder!(Visit.pre);
write("\n inorder: ");
tree.backtrackingOrder!(Visit.inv);
write("\n postOrder: ");
tree.backtrackingOrder!(Visit.post);
write("\nlevelorder: ");
tree.levelOrder;
writeln;
}</lang>
- Output:
preOrder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postOrder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
Alternative Version
Generic as the first version, but not lazy as the Haskell version. <lang d>const struct Node(T) {
T v; Node* l, r;
}
T[] preOrder(T)(in Node!T* t) pure nothrow {
return t ? t.v ~ preOrder(t.l) ~ preOrder(t.r) : [];
}
T[] inOrder(T)(in Node!T* t) pure nothrow {
return t ? inOrder(t.l) ~ t.v ~ inOrder(t.r) : [];
}
T[] postOrder(T)(in Node!T* t) pure nothrow {
return t ? postOrder(t.l) ~ postOrder(t.r) ~ t.v : [];
}
T[] levelOrder(T)(in Node!T* t) pure nothrow {
static T[] loop(in Node!T*[] a) pure nothrow {
if (!a.length) return [];
if (!a[0]) return loop(a[1 .. $]);
return a[0].v ~ loop(a[1 .. $] ~ [a[0].l, a[0].r]);
}
return loop([t]);
}
void main() {
alias N = Node!int;
auto tree = new N(1,
new N(2,
new N(4,
new N(7)),
new N(5)),
new N(3,
new N(6,
new N(8),
new N(9))));
import std.stdio; writeln(preOrder(tree)); writeln(inOrder(tree)); writeln(postOrder(tree)); writeln(levelOrder(tree));
}</lang>
- Output:
[1, 2, 4, 7, 5, 3, 6, 8, 9] [7, 4, 2, 5, 1, 8, 6, 9, 3] [7, 4, 5, 2, 8, 9, 6, 3, 1] [1, 2, 3, 4, 5, 6, 7, 8, 9]
Alternative Lazy Version
This version is not complete, it lacks the level order visit. <lang d>import std.stdio, std.algorithm, std.range, std.string;
const struct Tree(T) {
T value; Tree* left, right;
}
alias VisitRange(T) = InputRange!(const Tree!T);
VisitRange!T preOrder(T)(in Tree!T* t) /*pure nothrow*/ {
enum self = mixin("&" ~ __FUNCTION__.split(".").back);
if (t == null)
return typeof(return).init.takeNone.inputRangeObject;
return [*t]
.chain([t.left, t.right]
.filter!(t => t != null)
.map!(a => self(a))
.joiner)
.inputRangeObject;
}
VisitRange!T inOrder(T)(in Tree!T* t) /*pure nothrow*/ {
enum self = mixin("&" ~ __FUNCTION__.split(".").back);
if (t == null)
return typeof(return).init.takeNone.inputRangeObject;
return [t.left]
.filter!(t => t != null)
.map!(a => self(a))
.joiner
.chain([*t])
.chain([t.right]
.filter!(t => t != null)
.map!(a => self(a))
.joiner)
.inputRangeObject;
}
VisitRange!T postOrder(T)(in Tree!T* t) /*pure nothrow*/ {
enum self = mixin("&" ~ __FUNCTION__.split(".").back);
if (t == null)
return typeof(return).init.takeNone.inputRangeObject;
return [t.left, t.right]
.filter!(t => t != null)
.map!(a => self(a))
.joiner
.chain([*t])
.inputRangeObject;
}
void main() {
alias N = Tree!int;
const tree = new N(1,
new N(2,
new N(4,
new N(7)),
new N(5)),
new N(3,
new N(6,
new N(8),
new N(9))));
tree.preOrder.map!(t => t.value).writeln; tree.inOrder.map!(t => t.value).writeln; tree.postOrder.map!(t => t.value).writeln;
}</lang>
- Output:
[1, 2, 4, 7, 5, 3, 6, 8, 9] [7, 4, 2, 5, 1, 8, 6, 9, 3] [7, 4, 5, 2, 8, 9, 6, 3, 1]
E
<lang e>def btree := [1, [2, [4, [7, null, null],
null],
[5, null, null]],
[3, [6, [8, null, null],
[9, null, null]],
null]]
def backtrackingOrder(node, pre, mid, post) {
switch (node) {
match ==null {}
match [value, left, right] {
pre(value)
backtrackingOrder(left, pre, mid, post)
mid(value)
backtrackingOrder(right, pre, mid, post)
post(value)
}
}
}
def levelOrder(root, func) {
var level := [root].diverge()
while (level.size() > 0) {
for node in level.removeRun(0) {
switch (node) {
match ==null {}
match [value, left, right] {
func(value)
level.push(left)
level.push(right)
} } } } }
print("preorder: ") backtrackingOrder(btree, fn v { print(" ", v) }, fn _ {}, fn _ {}) println()
print("inorder: ") backtrackingOrder(btree, fn _ {}, fn v { print(" ", v) }, fn _ {}) println()
print("postorder: ") backtrackingOrder(btree, fn _ {}, fn _ {}, fn v { print(" ", v) }) println()
print("level-order:") levelOrder(btree, fn v { print(" ", v) }) println()</lang>
Eiffel
Void-Safety has been disabled for simplicity of the code. <lang eiffel >note description : "Application for tree traversal demonstration"
output : "[ Prints preorder, inorder, postorder and levelorder traversal of an example binary tree. ]"
author : "Jascha Grübel" date : "$2014-01-07$" revision : "$1.0$"
class APPLICATION
create make
feature {NONE} -- Initialization
make -- Run Tree traversal example. local tree:NODE do create tree.make (1) tree.set_left_child (create {NODE}.make (2)) tree.set_right_child (create {NODE}.make (3)) tree.left_child.set_left_child (create {NODE}.make (4)) tree.left_child.set_right_child (create {NODE}.make (5)) tree.left_child.left_child.set_left_child (create {NODE}.make (7)) tree.right_child.set_left_child (create {NODE}.make (6)) tree.right_child.left_child.set_left_child (create {NODE}.make (8)) tree.right_child.left_child.set_right_child (create {NODE}.make (9))
Io.put_string ("preorder: ") tree.print_preorder Io.put_new_line
Io.put_string ("inorder: ") tree.print_inorder Io.put_new_line
Io.put_string ("postorder: ") tree.print_postorder Io.put_new_line
Io.put_string ("level-order:") tree.print_levelorder Io.put_new_line
end
end -- class APPLICATION</lang> <lang eiffel >note description : "A simple node for a binary tree"
libraries : "Relies on LINKED_LIST from EiffelBase"
author : "Jascha Grübel" date : "$2014-01-07$" revision : "$1.0$"
implementation : "[
All traversals but the levelorder traversal have been implemented recursively.
The levelorder traversal is solved iteratively.
]"
class NODE create make
feature {NONE} -- Initialization
make (a_value:INTEGER) -- Creates a node with no children. do value := a_value set_right_child(Void) set_left_child(Void) end
feature -- Modification
set_right_child (a_node:NODE) -- Sets `right_child' to `a_node'. do right_child:=a_node end
set_left_child (a_node:NODE) -- Sets `left_child' to `a_node'. do left_child:=a_node end
feature -- Representation
print_preorder -- Recursively prints the value of the node and all its children in preorder do Io.put_string (" " + value.out) if has_left_child then left_child.print_preorder end if has_right_child then right_child.print_preorder end end
print_inorder -- Recursively prints the value of the node and all its children in inorder do if has_left_child then left_child.print_inorder end Io.put_string (" " + value.out) if has_right_child then right_child.print_inorder end end
print_postorder -- Recursively prints the value of the node and all its children in postorder do if has_left_child then left_child.print_postorder end if has_right_child then right_child.print_postorder end Io.put_string (" " + value.out) end
print_levelorder -- Iteratively prints the value of the node and all its children in levelorder local l_linked_list:LINKED_LIST[NODE] l_node:NODE do from create l_linked_list.make l_linked_list.extend (Current) until l_linked_list.is_empty loop l_node := l_linked_list.first if l_node.has_left_child then l_linked_list.extend (l_node.left_child) end if l_node.has_right_child then l_linked_list.extend (l_node.right_child) end Io.put_string (" " + l_node.value.out) l_linked_list.prune (l_node) end end
feature -- Access
value:INTEGER -- Value stored in the node.
right_child:NODE -- Reference to right child, possibly void.
left_child:NODE -- Reference to left child, possibly void.
has_right_child:BOOLEAN -- Test right child for existence. do Result := right_child /= Void end
has_left_child:BOOLEAN -- Test left child for existence. do Result := left_child /= Void end
end
-- class NODE</lang>
Elena
ELENA 5.0 : <lang elena>import extensions; import extensions'routines; import system'collections;
singleton DummyNode {
get generic()
= EmptyEnumerable;
}
class Node {
rprop int Value;
rprop Node Left;
rprop Node Right;
constructor new(int value)
{
Value := value
}
constructor new(int value, Node left)
{
Value := value;
Left := left;
}
constructor new(int value, Node left, Node right)
{
Value := value;
Left := left;
Right := right
}
Preorder = new Enumerable
{
Enumerator enumerator() = CompoundEnumerator.new(
SingleEnumerable.new(Value),
(Left ?? DummyNode).Preorder,
(Right ?? DummyNode).Preorder);
};
Inorder = new Enumerable
{
Enumerator enumerator()
{
if (nil != Left)
{
^ CompoundEnumerator.new(Left.Inorder, SingleEnumerable.new(Value), (Right ?? DummyNode).Inorder)
}
else
{
^ SingleEnumerable.new(Value).enumerator()
}
}
};
Postorder = new Enumerable
{
Enumerator enumerator()
{
if (nil == Left)
{
^ SingleEnumerable.new(Value).enumerator()
}
else if (nil == Right)
{
^ CompoundEnumerator.new(Left.Postorder, SingleEnumerable.new(Value))
}
else
{
^ CompoundEnumerator.new(Left.Postorder, Right.Postorder, SingleEnumerable.new(Value))
}
}
};
LevelOrder = new Enumerable
{
Queue<Node> queue := class Queue<Node>.allocate(4).push:self;
Enumerator enumerator() = new Enumerator
{
bool next() = queue.isNotEmpty();
get()
{
Node item := queue.pop();
Node left := item.Left;
Node right := item.Right;
if (nil != left)
{
queue.push(left)
};
if (nil != right)
{
queue.push(right)
};
^ item.Value
}
reset()
{
NotSupportedException.raise()
}
enumerable() = queue;
};
};
}
public program() {
var tree := Node.new(1, Node.new(2, Node.new(4, Node.new(7)), Node.new(5)), Node.new(3, Node.new(6, Node.new(8), Node.new(9))));
console.printLine("Preorder :", tree.Preorder);
console.printLine("Inorder :", tree.Inorder);
console.printLine("Postorder :", tree.Postorder);
console.printLine("LevelOrder:", tree.LevelOrder)
}</lang>
- Output:
Preorder :1,2,4,7,5,3,6,8,9 Inorder :7,4,2,5,1,8,6,9,3 Postorder :7,4,5,2,8,9,6,3,1 LevelOrder:1,2,3,4,5,6,7,8,9
Elisa
This is a generic component for binary tree traversals. More information about binary trees in Elisa are given in trees. <lang Elisa> component BinaryTreeTraversals (Tree, Element); type Tree; type Node = Tree;
Tree (LeftTree = Tree, Element, RightTree = Tree) -> Tree;
Leaf (Element) -> Node;
Node (Tree) -> Node;
Item (Node) -> Element;
Preorder (Tree) -> multi (Node);
Inorder (Tree) -> multi (Node);
Postorder (Tree) -> multi (Node);
Level_order(Tree) -> multi (Node);
begin
Tree (Lefttree, Item, Righttree) = Tree: [ Lefttree; Item; Righttree ];
Leaf (anItem) = Tree (null(Tree), anItem, null(Tree) );
Node (aTree) = aTree;
Item (aNode) = aNode.Item;
Preorder (=null(Tree)) = no(Tree);
Preorder (T) = ( T, Preorder (T.Lefttree), Preorder (T.Righttree));
Inorder (=null(Tree)) = no(Tree);
Inorder (T) = ( Inorder (T.Lefttree), T, Inorder (T.Righttree));
Postorder (=null(Tree)) = no(Tree);
Postorder (T) = ( Postorder (T.Lefttree), Postorder (T.Righttree), T);
Level_order(T) = [ Queue = {T};
node = Tree:items(Queue); [ result(node); add(Queue, node.Lefttree) when valid(node.Lefttree);
add(Queue, node.Righttree) when valid(node.Righttree);
]; no(Tree); ]; end component BinaryTreeTraversals; </lang> Tests <lang Elisa> use BinaryTreeTraversals (Tree, integer);
BT = Tree( Tree(
Tree(Leaf(7), 4, null(Tree)), 2 , Leaf(5)), 1,
Tree(
Tree(Leaf(8), 6, Leaf(9)), 3 ,null(Tree)));
{Item(Preorder(BT))}? { 1, 2, 4, 7, 5, 3, 6, 8, 9}
{Item(Inorder(BT))}? { 7, 4, 2, 5, 1, 8, 6, 9, 3}
{Item(Postorder(BT))}? { 7, 4, 5, 2, 8, 9, 6, 3, 1}
{Item(Level_order(BT))}? { 1, 2, 3, 4, 5, 6, 7, 8, 9} </lang>
Elixir
<lang elixir>defmodule Tree_Traversal do
defp tnode, do: {}
defp tnode(v), do: {:node, v, {}, {}}
defp tnode(v,l,r), do: {:node, v, l, r}
defp preorder(_,{}), do: :ok
defp preorder(f,{:node,v,l,r}) do
f.(v)
preorder(f,l)
preorder(f,r)
end
defp inorder(_,{}), do: :ok
defp inorder(f,{:node,v,l,r}) do
inorder(f,l)
f.(v)
inorder(f,r)
end
defp postorder(_,{}), do: :ok
defp postorder(f,{:node,v,l,r}) do
postorder(f,l)
postorder(f,r)
f.(v)
end
defp levelorder(_, []), do: []
defp levelorder(f, [{}|t]), do: levelorder(f, t)
defp levelorder(f, [{:node,v,l,r}|t]) do
f.(v)
levelorder(f, t++[l,r])
end
defp levelorder(f, x), do: levelorder(f, [x])
def main do
tree = tnode(1,
tnode(2,
tnode(4, tnode(7), tnode()),
tnode(5, tnode(), tnode())),
tnode(3,
tnode(6, tnode(8), tnode(9)),
tnode()))
f = fn x -> IO.write "#{x} " end
IO.write "preorder: "
preorder(f, tree)
IO.write "\ninorder: "
inorder(f, tree)
IO.write "\npostorder: "
postorder(f, tree)
IO.write "\nlevelorder: "
levelorder(f, tree)
IO.puts ""
end
end
Tree_Traversal.main</lang>
- Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
Erlang
<lang erlang>-module(tree_traversal). -export([main/0]). -export([preorder/2, inorder/2, postorder/2, levelorder/2]). -export([tnode/0, tnode/1, tnode/3]).
-define(NEWLINE, io:format("~n")).
tnode() -> {}. tnode(V) -> {node, V, {}, {}}. tnode(V,L,R) -> {node, V, L, R}.
preorder(_,{}) -> ok; preorder(F,{node,V,L,R}) ->
F(V), preorder(F,L), preorder(F,R).
inorder(_,{}) -> ok; inorder(F,{node,V,L,R}) ->
inorder(F,L), F(V), inorder(F,R).
postorder(_,{}) -> ok; postorder(F,{node,V,L,R}) ->
postorder(F,L), postorder(F,R), F(V).
levelorder(_, []) -> []; levelorder(F, [{}|T]) -> levelorder(F, T); levelorder(F, [{node,V,L,R}|T]) ->
F(V), levelorder(F, T++[L,R]);
levelorder(F, X) -> levelorder(F, [X]).
main() ->
Tree = tnode(1,
tnode(2,
tnode(4, tnode(7), tnode()),
tnode(5, tnode(), tnode())),
tnode(3,
tnode(6, tnode(8), tnode(9)),
tnode())),
F = fun(X) -> io:format("~p ",[X]) end,
preorder(F, Tree), ?NEWLINE,
inorder(F, Tree), ?NEWLINE,
postorder(F, Tree), ?NEWLINE,
levelorder(F, Tree), ?NEWLINE.</lang>
Output:
1 2 4 7 5 3 6 8 9 7 4 2 5 1 8 6 9 3 7 4 5 2 8 9 6 3 1 1 2 3 4 5 6 7 8 9
Euphoria
<lang euphoria>constant VALUE = 1, LEFT = 2, RIGHT = 3
constant tree = {1,
{2,
{4,
{7, 0, 0},
0},
{5, 0, 0}},
{3,
{6,
{8, 0, 0},
{9, 0, 0}},
0}}
procedure preorder(object tree)
if sequence(tree) then
printf(1,"%d ",{tree[VALUE]})
preorder(tree[LEFT])
preorder(tree[RIGHT])
end if
end procedure
procedure inorder(object tree)
if sequence(tree) then
inorder(tree[LEFT])
printf(1,"%d ",{tree[VALUE]})
inorder(tree[RIGHT])
end if
end procedure
procedure postorder(object tree)
if sequence(tree) then
postorder(tree[LEFT])
postorder(tree[RIGHT])
printf(1,"%d ",{tree[VALUE]})
end if
end procedure
procedure lo(object tree, sequence more)
if sequence(tree) then
more &= {tree[LEFT],tree[RIGHT]}
printf(1,"%d ",{tree[VALUE]})
end if
if length(more) > 0 then
lo(more[1],more[2..$])
end if
end procedure
procedure level_order(object tree)
lo(tree,{})
end procedure
puts(1,"preorder: ") preorder(tree) puts(1,'\n')
puts(1,"inorder: ") inorder(tree) puts(1,'\n')
puts(1,"postorder: ") postorder(tree) puts(1,'\n')
puts(1,"level-order: ") level_order(tree) puts(1,'\n')</lang>
Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
F#
<lang fsharp>open System open System.IO
type Tree<'a> =
| Tree of 'a * Tree<'a> * Tree<'a> | Empty
let rec inorder tree =
seq {
match tree with
| Tree(x, left, right) ->
yield! inorder left
yield x
yield! inorder right
| Empty -> ()
}
let rec preorder tree =
seq {
match tree with
| Tree(x, left, right) ->
yield x
yield! preorder left
yield! preorder right
| Empty -> ()
}
let rec postorder tree =
seq {
match tree with
| Tree(x, left, right) ->
yield! postorder left
yield! postorder right
yield x
| Empty -> ()
}
let levelorder tree =
let rec loop queue =
seq {
match queue with
| [] -> ()
| (Empty::tail) -> yield! loop tail
| (Tree(x, l, r)::tail) ->
yield x
yield! loop (tail @ [l; r])
}
loop [tree]
[<EntryPoint>] let main _ =
let tree =
Tree (1,
Tree (2,
Tree (4,
Tree (7, Empty, Empty),
Empty),
Tree (5, Empty, Empty)),
Tree (3,
Tree (6,
Tree (8, Empty, Empty),
Tree (9, Empty, Empty)),
Empty))
let show x = printf "%d " x
printf "preorder: " preorder tree |> Seq.iter show printf "\ninorder: " inorder tree |> Seq.iter show printf "\npostorder: " postorder tree |> Seq.iter show printf "\nlevel-order: " levelorder tree |> Seq.iter show 0</lang>
Factor
<lang factor>USING: accessors combinators deques dlists fry io kernel math.parser ; IN: rosetta.tree-traversal
TUPLE: node data left right ;
CONSTANT: example-tree
T{ node f 1
T{ node f 2
T{ node f 4
T{ node f 7 f f }
f
}
T{ node f 5 f f }
}
T{ node f 3
T{ node f 6
T{ node f 8 f f }
T{ node f 9 f f }
}
f
}
}
- preorder ( node quot: ( data -- ) -- )
[ [ data>> ] dip call ] [ [ left>> ] dip over [ preorder ] [ 2drop ] if ] [ [ right>> ] dip over [ preorder ] [ 2drop ] if ] 2tri ; inline recursive
- inorder ( node quot: ( data -- ) -- )
[ [ left>> ] dip over [ inorder ] [ 2drop ] if ] [ [ data>> ] dip call ] [ [ right>> ] dip over [ inorder ] [ 2drop ] if ] 2tri ; inline recursive
- postorder ( node quot: ( data -- ) -- )
[ [ left>> ] dip over [ postorder ] [ 2drop ] if ] [ [ right>> ] dip over [ postorder ] [ 2drop ] if ] [ [ data>> ] dip call ] 2tri ; inline recursive
- (levelorder) ( dlist quot: ( data -- ) -- )
over deque-empty? [ 2drop ] [
[ dup pop-front ] dip {
[ [ data>> ] dip call drop ]
[ drop left>> [ swap push-back ] [ drop ] if* ]
[ drop right>> [ swap push-back ] [ drop ] if* ]
[ nip (levelorder) ]
} 3cleave
] if ; inline recursive
- levelorder ( node quot: ( data -- ) -- )
[ 1dlist ] dip (levelorder) ; inline
- levelorder2 ( node quot: ( data -- ) -- )
[ 1dlist ] dip
[ dup deque-empty? not ] swap '[
dup pop-front
[ data>> @ ]
[ left>> [ over push-back ] when* ]
[ right>> [ over push-back ] when* ] tri
] while drop ; inline
- main ( -- )
example-tree [ number>string write " " write ] {
[ "preorder: " write preorder nl ]
[ "inorder: " write inorder nl ]
[ "postorder: " write postorder nl ]
[ "levelorder: " write levelorder nl ]
[ "levelorder2: " write levelorder2 nl ]
} 2cleave ;</lang>
Fantom
<lang fantom> class Tree {
readonly Int label readonly Tree? left readonly Tree? right
new make (Int label, Tree? left := null, Tree? right := null)
{
this.label = label
this.left = left
this.right = right
}
Void preorder(|Int->Void| func)
{
func(label)
left?.preorder(func) // ?. will not call method if 'left' is null
right?.preorder(func)
}
Void postorder(|Int->Void| func)
{
left?.postorder(func)
right?.postorder(func)
func(label)
}
Void inorder(|Int->Void| func)
{
left?.inorder(func)
func(label)
right?.inorder(func)
}
Void levelorder(|Int->Void| func)
{
Tree[] nodes := [this]
while (nodes.size > 0)
{
Tree cur := nodes.removeAt(0)
func(cur.label)
if (cur.left != null) nodes.add (cur.left)
if (cur.right != null) nodes.add (cur.right)
}
}
}
class Main {
public static Void main ()
{
tree := Tree(1,
Tree(2, Tree(4, Tree(7)), Tree(5)),
Tree(3, Tree(6, Tree(8), Tree(9))))
List result := [,]
collect := |Int a -> Void| { result.add(a) }
tree.preorder(collect)
echo ("preorder: " + result.join(" "))
result = [,]
tree.inorder(collect)
echo ("inorder: " + result.join(" "))
result = [,]
tree.postorder(collect)
echo ("postorder: " + result.join(" "))
result = [,]
tree.levelorder(collect)
echo ("levelorder: " + result.join(" "))
}
} </lang>
Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
Forth
<lang forth>\ binary tree (dictionary)
- node ( l r data -- node ) here >r , , , r> ;
- leaf ( data -- node ) 0 0 rot node ;
- >data ( node -- ) @ ;
- >right ( node -- ) cell+ @ ;
- >left ( node -- ) cell+ cell+ @ ;
- preorder ( xt tree -- )
dup 0= if 2drop exit then
2dup >data swap execute
2dup >left recurse
>right recurse ;
- inorder ( xt tree -- )
dup 0= if 2drop exit then
2dup >left recurse
2dup >data swap execute
>right recurse ;
- postorder ( xt tree -- )
dup 0= if 2drop exit then
2dup >left recurse
2dup >right recurse
>data swap execute ;
- max-depth ( tree -- n )
dup 0= if exit then dup >left recurse swap >right recurse max 1+ ;
defer depthaction
- depthorder ( depth tree -- )
dup 0= if 2drop exit then
over 0=
if >data depthaction drop
else over 1- over >left recurse
swap 1- swap >right recurse
then ;
- levelorder ( xt tree -- )
swap is depthaction dup max-depth 0 ?do i over depthorder loop drop ;
7 leaf 0 4 node
5 leaf 2 node
8 leaf 9 leaf 6 node
0 3 node 1 node value tree
cr ' . tree preorder \ 1 2 4 7 5 3 6 8 9 cr ' . tree inorder \ 7 4 2 5 1 8 6 9 3 cr ' . tree postorder \ 7 4 5 2 8 9 6 3 1 cr tree max-depth . \ 4 cr ' . tree levelorder \ 1 2 3 4 5 6 7 8 9</lang>
Fortran
Recursion? Oh dear.
For many years it has been routine to hear murmured exchanges that "Fortran is not a recursive language", which is rather odd because any computer language that allows arithmetic expressions in the usual infix notation as learnt at primary school is fundamentally recursive. Moreover, nothing in Fortran's syntax prevents recursion: routines can invoke each other or themselves without difficulty. It is the implementation that is at fault. Typically, a Fortran compiler produces code for a computer lacking an in-built stack mechanism and this became a habit. For instance, on the IBM1130, entry to a routine was via a BSI instruction, "Branch and Save IAR", which placed the return address (the value of the Instruction Address Register, IAR) at the routine's entry point and commenced execution at the following address. For the IBM360 et al, the instruction was BALR, "Branch and Load Register" (I always edited listings to read BALROG, ahem) whereby the return address was loaded into a specified register. Should such a routine then invoke itself in the same manner, then the first return address will be overwritten by the new address. Only if the routine included special code to save multiple return addresses could such recursion work.
In other words, there has never been any problem with recursive invocations in Fortran, merely in organising the correct return from them. Unless you used the Burroughs Fortran compiler, which being for a computer whose hardware employed a stack mechanism, meant that it all just worked and there was no reason to prevent recursion from working. Except for a large system for the formal manipulation of mathematical expressions, whose major components repeatedly invoked each other without ever bothering to return: large jobs failed via stack overflow!
Otherwise, one can always write detailed code that gives effect to recursive usage, typically involving a variable called SP and an array called STACK. Oddly, such proceedings for the QuickSort algorithm are often declared to be "iterative", presumably because the absence of formally-declared recursive phrases blocks recognition of recursive action.
In the example source, the mainline, GORILLA, does its recursion via array twiddling and in that spirit, uses multiple lists for the "level" style traversal so that one tree clamber only need be made, whereas the recursive equivalent cheats by commanding one clamber for each level. The recursive routines store their state in part via the position within their code - that is, before, between, or after the recursive invocations, and are much easier to compare. Rather than litter the source with separate routines and their declarations for each of the four styles required, routine TARZAN has the four versions together for easy comparison, distinguished by a CASE statement. Actually, the code could be even more compact as in <lang Fortran>
IF (STYLE.EQ."PRE") CALL OUT(HAS)
IF (LINKL(HAS).GT.0) CALL TARZAN(LINKL(HAS),STYLE)
IF (STYLE.EQ."IN") CALL OUT(HAS)
IF (LINKR(HAS).GT.0) CALL TARZAN(LINKR(HAS),STYLE)
IF (STYLE.EQ."POST") CALL OUT(HAS)</lang>
But that would cloud the simplicity of each separate version, and would be extra messy with the fourth option included. On the other hand, the requirements for formal recursion carry the cost of the entry/exit protocol and moreover must do so for every invocation (though there is sometimes opportunity for end-recursion to be converted into a secret "go to") - avoiding this is why every invocation of TARZAN first checks that it has a live link, rather than coding this once only within TARZAN to return immediately when invoked with a dead link - whereas the array twiddling via SP deals only with what is required and notably, avoids raising the stack if it can. Further, the GORILLA version can if necessary maintain additional information, as is needed for the postorder traversal where, not having state information stored via position in the code (as with the recursive version) it needs to know whether it is returning to a node from which it departed via the rightwards link and so is in the post-traversal state and thus due a postorder action. This could involve an auxiliary array, but here is handled by taking advantage of the sign of the STACK element. This sort of trick might still be possible even if the link values were memory addresses rather than array indices, as many computers do not use their full word size for addressing.
The tree is represented via arrays NODE, LINKL and LINKR, initialised to the set example via some DATA statements rather than being built via a sequence of calls to something like ADDNODE. Old-style Fortran would require separate arrays, though one could mess about with two-dimensional arrays if the type of NODE was compatible. F90 and later enable the definition of compound data types, so that one might speak of NODE(i).CONTENT, NODE(i).LINKLEFT, and NODE(i).LINKRIGHT, or similar. While this offers clear benefits in organisation and documentation there can be surprises, as when a binary search routine was invoked on something like NODE(1:n).KEY and the programme ran a lot slower than the multi-array version! This was because rather than present the routine with an array having a "stride" other than one, the KEY values were copied from the data aggregate to a work area so that they were contiguous for the binary search routine, thereby vitiating its speed advantage over a linear search.
Except for the usage of array MIST having an element zero and the use of an array assignment MIST(:,0) = 0, the GORILLA code is old-style Fortran. One could play tricks with EQUIVALENCE statements to arrange that an array's first element was at index zero, but that would rely on the absence of array bound checking and is more difficult with multi-dimensional arrays. Instead, one would make do either by having a separate list length variable, or else remembering the offsets... The MODULE usage requires F90 or later and provides a convenient protocol for global data, otherwise one must mess about with COMMON or parameter hordes. If that were done, the B6700 compiler would have handled it. But for the benefit of trembling modern compilers it also contains the fearsome new attribute, RECURSIVE, to flog the compilers into what was formalised for Algol in 1960 and was available for free via Burroughs in the 1970s.
On the other hand, the early-style Fortran DO-loop would always execute once, because the test was made only at the end of an iteration, and here, routine JANE does not know the value of MAXLEVEL until after the first iteration. Code such as <lang Fortran>
DO GASP = 1,MAXLEVEL
CALL TARZAN(1,HOW)
END DO</lang>
Would not work with modern Fortran, because the usual approach is to calculate the iteration count from the DO-loop parameters at the start of the DO-loop, and possibly not execute it at all if that count is not positive. This also means that with each iteration, the count must be decremented and the index variable adjusted; extra effort. There is no equivalent of Pascal's Repeat ... until condition;, so, in place of a nice "structured" statement with clear interpretation, there is some messy code with a label and a GO TO, oh dear.
Source
<lang Fortran>
MODULE ARAUCARIA !Cunning crosswords, also.
INTEGER ENUFF !To suit the set example.
PARAMETER (ENUFF = 9) !This will do.
INTEGER NODE(ENUFF),LINKL(ENUFF),LINKR(ENUFF) !The nodes, and their links.
DATA NODE/ 1,2,3,4,5,6,7,8,9/ !Value = index. A rather boring payload.
DATA LINKL/2,4,6,7,0,8,0,0,0/ !"Left" and "Right" are as looking at the page.
DATA LINKR/3,5,0,0,0,9,0,0,0/ !If one thinks within the tree, they're the other way around!
C 1 !Thus, looking from the "1", to the right is "2" and to the left is "3". C / \ !But, looking at the scheme, to the left is "2" and to the right is "3". C / \ !This latter seems to be the popular view from the outside, not within the data. C / \ !Similarily, although called a "tree", the depiction is upside down! C 2 3 !How can computers be expected to keep up with this contrariness? C / \ / !Humm, no example of a rightwards link with no leftwards link. C 4 5 6 !Topologically equivalent, but not so in usage. C / / \ C 7 8 9
INTEGER N,LIST(ENUFF) !This is to be developed.
INTEGER LEVEL,MAXLEVEL !While these vary in various ways.
INTEGER GASP !Communication from JANE.
CONTAINS !No checks for invalid links, etc.
SUBROUTINE OUT(IS) !Append a value to a list.
INTEGER IS !The value.
N = N + 1 !The list's count so far.
LIST(N) = IS !Place.
END SUBROUTINE OUT !Eventually, the list can be written in one go.
RECURSIVE SUBROUTINE TARZAN(HAS,STYLE) !Skilled at tree traversal, is he.
INTEGER HAS !The current position.
CHARACTER*(*) STYLE !Traversal type.
LEVEL = LEVEL + 1 !A leap is made.
IF (LEVEL.GT.MAXLEVEL) MAXLEVEL = LEVEL !Staring at the moon.
SELECT CASE(STYLE) !And, in what manner?
CASE ("PRE") !Declare the position first.
CALL OUT(HAS) !Thus.
IF (LINKL(HAS).GT.0) CALL TARZAN(LINKL(HAS),STYLE)
IF (LINKR(HAS).GT.0) CALL TARZAN(LINKR(HAS),STYLE)
CASE ("IN") !Or in the middle.
IF (LINKL(HAS).GT.0) CALL TARZAN(LINKL(HAS),STYLE)
CALL OUT(HAS) !Thus.
IF (LINKR(HAS).GT.0) CALL TARZAN(LINKR(HAS),STYLE)
CASE ("POST") !Or at the end.
IF (LINKL(HAS).GT.0) CALL TARZAN(LINKL(HAS),STYLE)
IF (LINKR(HAS).GT.0) CALL TARZAN(LINKR(HAS),STYLE)
CALL OUT(HAS) !Thus.
CASE ("LEVEL") !Or at specified levels.
IF (LEVEL.EQ.GASP) CALL OUT(HAS) !Such as this?
IF (LINKL(HAS).GT.0) CALL TARZAN(LINKL(HAS),STYLE)
IF (LINKR(HAS).GT.0) CALL TARZAN(LINKR(HAS),STYLE)
CASE DEFAULT !This shouldn't happen.
WRITE (6,*) "Unknown style ",STYLE !But, paranoia.
STOP "No can do!" !Rather than flounder about.
END SELECT !That was simple.
LEVEL = LEVEL - 1 !Sag back.
END SUBROUTINE TARZAN !Not like George of the Jungle.
SUBROUTINE JANE(HOW) !Tells Tarzan what to do.
CHARACTER*(*) HOW !A single word suffices.
N = 0 !No positions trampled.
LEVEL = 0 !Starting on the ground.
MAXLEVEL = 0 !The ascent follows.
IF (HOW.NE."LEVEL") THEN !Ordinary styles?
CALL TARZAN(1,HOW) !Yes. From the root, go...
ELSE !But this is not tree-structured.
GASP = 0 !Instead, we ascend through the canopy in stages.
1 GASP = GASP + 1 !Up one stage.
CALL TARZAN(1,HOW) !And do it all again.
IF (GASP.LT.MAXLEVEL) GO TO 1 !Are we there yet?
END IF !Don't know MAXLEVEL until after the first clamber.
Cast forth the list.
WRITE (6,10) HOW,NODE(LIST(1:N)) !Show spoor.
10 FORMAT (A6,"-order:",66(1X,I0)) !Large enough.
WRITE (6,*) !Sigh.
END SUBROUTINE JANE !That was simple.
END MODULE ARAUCARIA !The monkeys are puzzled.
PROGRAM GORILLA !No fancy stuff. Just brute force.
USE ARAUCARIA !This is for lightweight but cunning monkeys.
INTEGER IT !A finger.
INTEGER SP,STACK(ENUFF) !The tree may be slim.
INTEGER SLEVL(ENUFF) !So prepare for maximum usage.
INTEGER MIST(ENUFF,0:ENUFF) !Multiple lists.
Chase the links preorder style: name the node, delve its left link, delve its right link.
N = 0 !No nodes have been visited.
SP = 0 !My stack is empty.
IT = 1 !I start at the root.
10 N = N + 1 !Another node arrived at.
LIST(N) = IT !Finger it.
IF (LINKL(IT).GT.0) THEN !A left link?
IF (LINKR(IT).GT.0) THEN !Yes. A right link also?
SP = SP + 1 !Yes. Stack it up.
STACK(SP) = LINKR(IT) !For later investigation.
END IF !So much for the right link.
IT = LINKL(IT) !Fingered by the left link.
GO TO 10 !See what happens.
END IF !But if there is no left link,
IF (LINKR(IT).GT.0) THEN !There still might be a right link.
IT = LINKR(IT) !There is.
GO TO 10 !See what happens.
END IF !And if there are no links,
IF (SP.GT.0) THEN !Perhaps the stack has bottomed out too?
IT = STACK(SP) !No, this was deferred.
SP = SP - 1 !So, pick up where we left off.
GO TO 10 !And carry on.
END IF !So much for unstacking.
WRITE (6,12) "Preorder",NODE(LIST(1:N)) !I've got a little list!
12 FORMAT (A12,":",66(1X,I0))
CALL JANE("PRE") !Try it fancy style.
Chase the links inorder style: delve left fully, name the node and try its right, then unstack.
N = 0 !No nodes have been visited.
SP = 0 !My stack is empty.
IT = 1 !I start at the root.
20 SP = SP + 1 !I'm on the way down.
STACK(SP) = IT !So, save this position to later retreat to.
IF (LINKL(IT).GT.0) THEN !Can I delve further left?
IT = LINKL(IT) !Yes.
GO TO 20 !And see what happens.
END IF !So much for diving.
21 IF (SP.GT.0) THEN !Can I retreat?
IT = STACK(SP) !Yes.
SP = SP - 1 !Go back to whence I had delved left.
N = N + 1 !This now counts as a place in order.
LIST(N) = IT !So list it.
IF (LINKR(IT).GT.0) THEN!Have I a rightwards path?
IT = LINKR(IT) !Yes. Take it.
GO TO 20 !And delve therefrom.
END IF !This node is now finished with.
GO TO 21 !So, try for another retreat.
END IF !So much for unstacking.
WRITE (6,12) "Inorder",NODE(LIST(1:N)) !I've got a little list!
CALL JANE("IN") !Try with more style.
Chase the links postorder style: delve left fully, delve right, name the node, then unstack.
N = 0 !No nodes have been visited.
SP = 0 !My stack is empty.
IT = 1 !I start at the root.
30 SP = SP + 1 !Action follows delving,
STACK(SP) = IT !So this node will be returned to.
IF (LINKL(IT).GT.0) THEN !Take any leftwards link straightaway.
IT = LINKL(IT) !Thus.
GO TO 30 !Thanks to the stack, we'll return to IT (as was).
END IF !But if there is no leftwards link to follow,
IF (LINKR(IT).GT.0) THEN !Perhaps there is a rightwards one?
STACK(SP) = -STACK(SP) !=-IT Mark the stacked finger as a rightwards lurch!
IT = LINKR(IT) !The rightwards link is now to be taken.
GO TO 30 !Thus start on a sub-tree.
END IF !But if there is no rightwards link either,
31 IF (SP.GT.0) THEN !See if there is anywhere to retreat to.
IT = STACK(SP) !The same IT placed at 30 if we dropped into 31.
SP = SP - 1 !But now we're in a different mood.
IF (IT.LT.0) THEN !Returning to what had been a rightwards departure?
N = N + 1 !Yes! Then this node is post-interest.
LIST(N) = -IT !So, time to roll it forth at last.
GO TO 31 !And retreat some more.
END IF !But if we hadn't gone right from IT,
IF (LINKR(IT).LE.0) THEN!We had gone left.
N = N + 1 !And now there is nowhere rightwards.
LIST(N) = IT !So this node is post-interest.
GO TO 31 !And retreat some more.
END IF !But if there is a rightwards leap,
SP = SP + 1 !Prepare to return to it,
STACK(SP) = -IT !Marked as having gone rightwards.
IT = LINKR(IT) !The rightwards move.
GO TO 30 !Peruse a fresh sub-tree.
END IF !And if the stack is reduced,
WRITE (6,12) "Postorder",NODE(LIST(1:N)) !Results!
CALL JANE("POST") !The same again?
Chase the nodes level style.
SP = 0 !My stack is empty.
IT = 1 !I start at the root.
LEVEL = 0 !On the ground.
MAXLEVEL = 0 !No ascent as yet.
MIST(:,0) = 0 !At all levels, nothing.
40 LEVEL = LEVEL + 1 !Every arrival is one level up.
IF (LEVEL.GT.MAXLEVEL) MAXLEVEL = LEVEL !Note the most high.
MIST(LEVEL,0) = MIST(LEVEL,0) + 1 !The count at that level.
MIST(LEVEL,MIST(LEVEL,0)) = IT !Add to the level's list.
IF (LINKL(IT).GT.0) THEN !Righto, can we go left?
IF (LINKR(IT).GT.0) THEN !Yes. Rightwards as well?
SP = SP + 1 !Yes! This will have to wait.
STACK(SP) = LINKR(IT) !So remember it,
SLEVL(SP) = LEVEL !And what level we're at now.
END IF !I can only go one way at a time.
IT = LINKL(IT) !Accept the fingered leftwards lurch.
GO TO 40 !Go to IT.
END IF !But if there is no leftwards link,
IF (LINKR(IT).GT.0) THEN !Perhaps there is a rightwards one?
IT = LINKR(IT) !There is.
GO TO 40 !Go to IT.
END IF !And if there are no further links,
IF (SP.GT.0) THEN !Perhaps we can retreat to what was deferred.
IT = STACK(SP) !The finger.
LEVEL = SLEVL(SP) !The level.
SP = SP - 1 !Wind back the stack.
GO TO 40 !Go to IT.
END IF !So much for the stack.
WRITE (6,12) "Levelorder", !Roll the lists in ascending LEVEL order.
1 (NODE(MIST(LEVEL,1:MIST(LEVEL,0))), LEVEL = 1,MAXLEVEL)
CALL JANE("LEVEL") !Alternatively...
END !So much for that.
</lang>
Output
Alternately GORILLA-style, and JANE-style:
Preorder: 1 2 4 7 5 3 6 8 9
PRE-order: 1 2 4 7 5 3 6 8 9
Inorder: 7 4 2 5 1 8 6 9 3
IN-order: 7 4 2 5 1 8 6 9 3
Postorder: 7 4 5 2 8 9 6 3 1
POST-order: 7 4 5 2 8 9 6 3 1
Levelorder: 1 2 3 4 5 6 7 8 9
LEVEL-order: 1 2 3 4 5 6 7 8 9
FreeBASIC
<lang freebasic>
- define NULL 0
Dim Shared As Byte maxnodos = 100 Dim Shared As Byte raiz = 0 Dim Shared As Byte izda = 1 Dim Shared As Byte dcha = 2 Dim Shared As Byte arbol(maxnodos, 3)
Sub crear_arbol()
arbol(1, raiz) = 1 arbol(1, izda) = 2 : arbol(1, dcha) = 3 arbol(2, raiz) = 2 arbol(2, izda) = 4 : arbol(2, dcha) = 5 arbol(3, raiz) = 3 arbol(3, izda) = 6 : arbol(3, dcha) = NULL arbol(4, raiz) = 4 arbol(4, izda) = 7 : arbol(4, dcha) = NULL arbol(5, raiz) = 5 arbol(5, izda) = NULL : arbol(5, dcha) = NULL arbol(6, raiz) = 6 arbol(6, izda) = 8 : arbol(6, dcha) = 9 arbol(7, raiz) = 7 arbol(7, izda) = NULL : arbol(7, dcha) = NULL arbol(8, raiz) = 8 arbol(8, izda) = NULL : arbol(8, dcha) = NULL arbol(9, raiz) = 9 arbol(9, izda) = NULL : arbol(9, dcha) = NULL
End Sub
Sub recorrido_preorder(nodo As Byte)
If nodo <> NULL Then
Print arbol(nodo, raiz);
recorrido_preorder(arbol(nodo, izda))
recorrido_preorder(arbol(nodo, dcha))
End If
End Sub
Sub recorrido_postorder(nodo As Byte)
If nodo <> NULL Then
recorrido_postorder(arbol(nodo, izda))
recorrido_postorder(arbol(nodo, dcha))
Print arbol(nodo, raiz);
End If
End Sub
Sub recorrido_inorden(nodo As Byte)
If nodo <> NULL Then
recorrido_inorden(arbol(nodo, izda))
Print arbol(nodo, raiz);
recorrido_inorden(arbol(nodo, dcha))
End If
End Sub
Sub recorrido_ordenXnivel(nodo As Byte)
Dim As Byte actual = 1
Dim As Byte primero_libre = actual + 1
Dim As Byte cola(maxnodos)
cola(actual) = nodo
While cola(actual) <> NULL
If arbol(cola(actual), izda) <> NULL Then
cola(primero_libre) = arbol(cola(actual), izda)
primero_libre += 1
End If
If arbol(cola(actual), dcha) <> NULL Then
cola(primero_libre) = arbol(cola(actual), dcha)
primero_libre += 1
End If
Print arbol(cola(actual), raiz);
actual += 1
Wend
End Sub </lang>
- Output:
Preorder: 1 2 4 7 5 3 6 8 9 Inorder: 7 4 2 5 1 8 6 9 3 Postorder: 7 4 5 2 8 9 6 3 1 Levelorder: 1 2 3 4 5 6 7 8 9
FunL
<lang funl>data Tree = Empty | Node( value, left, right )
def
preorder( Empty ) = [] preorder( Node(v, l, r) ) = [v] + preorder( l ) + preorder( r )
inorder( Empty ) = [] inorder( Node(v, l, r) ) = inorder( l ) + [v] + inorder( r )
postorder( Empty ) = [] postorder( Node(v, l, r) ) = postorder( l ) + postorder( r ) + [v]
levelorder( x ) =
def
order( [] ) = []
order( Empty : xs ) = order( xs )
order( Node(v, l, r) : xs ) = v : order( xs + [l, r] )
order( [x] )
tree = Node( 1,
Node( 2,
Node( 4,
Node( 7, Empty, Empty ),
Empty ),
Node( 5, Empty, Empty ) ),
Node( 3,
Node( 6,
Node( 8, Empty, Empty ),
Node( 9, Empty, Empty ) ),
Empty ) )
println( preorder(tree) ) println( inorder(tree) ) println( postorder(tree) ) println( levelorder(tree) )</lang>
- Output:
[1, 2, 4, 7, 5, 3, 6, 8, 9] [7, 4, 2, 5, 1, 8, 6, 9, 3] [7, 4, 5, 2, 8, 9, 6, 3, 1] [1, 2, 3, 4, 5, 6, 7, 8, 9]
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
GFA Basic
<lang> maxnodes%=100 ! set a limit to size of tree content%=0 ! index of content field left%=1 ! index of left tree right%=2 ! index of right tree DIM tree%(maxnodes%,3) ! create space for tree ' OPENW 1 CLEARW 1 ' @create_tree PRINT "Preorder: "; @preorder_traversal(1) PRINT "" PRINT "Inorder: "; @inorder_traversal(1) PRINT "" PRINT "Postorder: "; @postorder_traversal(1) PRINT "" PRINT "Levelorder: "; @levelorder_traversal(1) PRINT "" ' ~INP(2) CLOSEW 1 ' ' Define the example tree ' PROCEDURE create_tree
tree%(1,content%)=1 tree%(1,left%)=2 tree%(1,right%)=3 tree%(2,content%)=2 tree%(2,left%)=4 tree%(2,right%)=5 tree%(3,content%)=3 tree%(3,left%)=6 tree%(3,right%)=0 ! 0 is used for no subtree tree%(4,content%)=4 tree%(4,left%)=7 tree%(4,right%)=0 tree%(5,content%)=5 tree%(5,left%)=0 tree%(5,right%)=0 tree%(6,content%)=6 tree%(6,left%)=8 tree%(6,right%)=9 tree%(7,content%)=7 tree%(7,left%)=0 tree%(7,right%)=0 tree%(8,content%)=8 tree%(8,left%)=0 tree%(8,right%)=0 tree%(9,content%)=9 tree%(9,left%)=0 tree%(9,right%)=0
RETURN ' ' Preorder traversal from given node ' PROCEDURE preorder_traversal(node%)
IF node%<>0 ! 0 means there is no node PRINT tree%(node%,content%); preorder_traversal(tree%(node%,left%)) preorder_traversal(tree%(node%,right%)) ENDIF
RETURN ' ' Postorder traversal from given node ' PROCEDURE postorder_traversal(node%)
IF node%<>0 ! 0 means there is no node postorder_traversal(tree%(node%,left%)) postorder_traversal(tree%(node%,right%)) PRINT tree%(node%,content%); ENDIF
RETURN ' ' Inorder traversal from given node ' PROCEDURE inorder_traversal(node%)
IF node%<>0 ! 0 means there is no node inorder_traversal(tree%(node%,left%)) PRINT tree%(node%,content%); inorder_traversal(tree%(node%,right%)) ENDIF
RETURN ' ' Level order traversal from given node ' PROCEDURE levelorder_traversal(node%)
LOCAL nodes%,first_free%,current%
'
' Set up initial queue of nodes
'
DIM nodes%(maxnodes%) ! some working space to store queue of nodes
current%=1
nodes%(current%)=node%
first_free%=current%+1
'
WHILE nodes%(current%)<>0
' add the children of current node onto queue
IF tree%(nodes%(current%),left%)<>0
nodes%(first_free%)=tree%(nodes%(current%),left%)
first_free%=first_free%+1
ENDIF
IF tree%(nodes%(current%),right%)<>0
nodes%(first_free%)=tree%(nodes%(current%),right%)
first_free%=first_free%+1
ENDIF
' print the current node content
PRINT tree%(nodes%(current%),content%);
' advance to next node
current%=current%+1
WEND
RETURN </lang>
Go
Individually allocated nodes
This is like many examples on this page. <lang go>package main
import "fmt"
type node struct {
value int left, right *node
}
func (n *node) iterPreorder(visit func(int)) {
if n == nil {
return
}
visit(n.value)
n.left.iterPreorder(visit)
n.right.iterPreorder(visit)
}
func (n *node) iterInorder(visit func(int)) {
if n == nil {
return
}
n.left.iterInorder(visit)
visit(n.value)
n.right.iterInorder(visit)
}
func (n *node) iterPostorder(visit func(int)) {
if n == nil {
return
}
n.left.iterPostorder(visit)
n.right.iterPostorder(visit)
visit(n.value)
}
func (n *node) iterLevelorder(visit func(int)) {
if n == nil {
return
}
for queue := []*node{n}; ; {
n = queue[0]
visit(n.value)
copy(queue, queue[1:])
queue = queue[:len(queue)-1]
if n.left != nil {
queue = append(queue, n.left)
}
if n.right != nil {
queue = append(queue, n.right)
}
if len(queue) == 0 {
return
}
}
}
func main() {
tree := &node{1,
&node{2,
&node{4,
&node{7, nil, nil},
nil},
&node{5, nil, nil}},
&node{3,
&node{6,
&node{8, nil, nil},
&node{9, nil, nil}},
nil}}
fmt.Print("preorder: ")
tree.iterPreorder(visitor)
fmt.Println()
fmt.Print("inorder: ")
tree.iterInorder(visitor)
fmt.Println()
fmt.Print("postorder: ")
tree.iterPostorder(visitor)
fmt.Println()
fmt.Print("level-order: ")
tree.iterLevelorder(visitor)
fmt.Println()
}
func visitor(value int) {
fmt.Print(value, " ")
}</lang>
- Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
Flat slice
Alternative representation. Like Wikipedia Binary tree#Arrays <lang go>package main
import "fmt"
// flat, level-order representation. // for node at index k, left child has index 2k, right child has index 2k+1. // a value of -1 means the node does not exist. type tree []int
func main() {
t := tree{1, 2, 3, 4, 5, 6, -1, 7, -1, -1, -1, 8, 9}
visitor := func(n int) {
fmt.Print(n, " ")
}
fmt.Print("preorder: ")
t.iterPreorder(visitor)
fmt.Print("\ninorder: ")
t.iterInorder(visitor)
fmt.Print("\npostorder: ")
t.iterPostorder(visitor)
fmt.Print("\nlevel-order: ")
t.iterLevelorder(visitor)
fmt.Println()
}
func (t tree) iterPreorder(visit func(int)) {
var traverse func(int)
traverse = func(k int) {
if k >= len(t) || t[k] == -1 {
return
}
visit(t[k])
traverse(2*k + 1)
traverse(2*k + 2)
}
traverse(0)
}
func (t tree) iterInorder(visit func(int)) {
var traverse func(int)
traverse = func(k int) {
if k >= len(t) || t[k] == -1 {
return
}
traverse(2*k + 1)
visit(t[k])
traverse(2*k + 2)
}
traverse(0)
}
func (t tree) iterPostorder(visit func(int)) {
var traverse func(int)
traverse = func(k int) {
if k >= len(t) || t[k] == -1 {
return
}
traverse(2*k + 1)
traverse(2*k + 2)
visit(t[k])
}
traverse(0)
}
func (t tree) iterLevelorder(visit func(int)) {
for _, n := range t {
if n != -1 {
visit(n)
}
}
}</lang>
Groovy
Uses Groovy Node and NodeBuilder classes <lang groovy>def preorder; preorder = { Node node ->
([node] + node.children().collect { preorder(it) }).flatten()
}
def postorder; postorder = { Node node ->
(node.children().collect { postorder(it) } + [node]).flatten()
}
def inorder; inorder = { Node node ->
def kids = node.children() if (kids.empty) [node] else if (kids.size() == 1 && kids[0].'@right') [node] + inorder(kids[0]) else inorder(kids[0]) + [node] + (kids.size()>1 ? inorder(kids[1]) : [])
}
def levelorder = { Node node ->
def nodeList = []
def level = [node]
while (!level.empty) {
nodeList += level
def nextLevel = level.collect { it.children() }.flatten()
level = nextLevel
}
nodeList
}
class BinaryNodeBuilder extends NodeBuilder {
protected Object postNodeCompletion(Object parent, Object node) {
assert node.children().size() < 3
node
}
}</lang>
Verify that BinaryNodeBuilder will not allow a node to have more than 2 children <lang groovy>try {
new BinaryNodeBuilder().'1' {
a {}
b {}
c {}
}
println 'not limited to binary tree\r\n'
} catch (org.codehaus.groovy.transform.powerassert.PowerAssertionError e) {
println 'limited to binary tree\r\n'
}</lang>
Test case #1 (from the task definition) <lang groovy>// 1 // / \ // 2 3 // / \ / // 4 5 6 // / / \ // 7 8 9 def tree1 = new BinaryNodeBuilder(). '1' {
'2' {
'4' { '7' {} }
'5' {}
}
'3' {
'6' { '8' {}; '9' {} }
}
}</lang>
Test case #2 (tests single right child) <lang groovy>// 1 // / \ // 2 3 // / \ / // 4 5 6 // \ / \ // 7 8 9 def tree2 = new BinaryNodeBuilder(). '1' {
'2' {
'4' { '7'(right:true) {} }
'5' {}
}
'3' {
'6' { '8' {}; '9' {} }
}
}</lang>
Run tests: <lang groovy>def test = { tree ->
println "preorder: ${preorder(tree).collect{it.name()}}"
println "preorder: ${tree.depthFirst().collect{it.name()}}"
println "postorder: ${postorder(tree).collect{it.name()}}"
println "inorder: ${inorder(tree).collect{it.name()}}"
println "level-order: ${levelorder(tree).collect{it.name()}}"
println "level-order: ${tree.breadthFirst().collect{it.name()}}"
println()
} test(tree1) test(tree2)</lang>
Output:
limited to binary tree preorder: [1, 2, 4, 7, 5, 3, 6, 8, 9] preorder: [1, 2, 4, 7, 5, 3, 6, 8, 9] postorder: [7, 4, 5, 2, 8, 9, 6, 3, 1] inorder: [7, 4, 2, 5, 1, 8, 6, 9, 3] level-order: [1, 2, 3, 4, 5, 6, 7, 8, 9] level-order: [1, 2, 3, 4, 5, 6, 7, 8, 9] preorder: [1, 2, 4, 7, 5, 3, 6, 8, 9] preorder: [1, 2, 4, 7, 5, 3, 6, 8, 9] postorder: [7, 4, 5, 2, 8, 9, 6, 3, 1] inorder: [4, 7, 2, 5, 1, 8, 6, 9, 3] level-order: [1, 2, 3, 4, 5, 6, 7, 8, 9] level-order: [1, 2, 3, 4, 5, 6, 7, 8, 9]
Haskell
Binary Tree
<lang haskell>---------------------- TREE TRAVERSAL --------------------
data Tree a
= Empty
| Node
{ value :: a,
left :: Tree a,
right :: Tree a
}
preorder, inorder, postorder, levelorder :: Tree a -> [a] preorder Empty = [] preorder (Node v l r) = v : preorder l <> preorder r
inorder Empty = [] inorder (Node v l r) = inorder l <> (v : inorder r)
postorder Empty = [] postorder (Node v l r) = postorder l <> postorder r <> [v]
levelorder x = loop [x]
where loop [] = [] loop (Empty : xs) = loop xs loop (Node v l r : xs) = v : loop (xs <> [l, r])
TEST -------------------------
tree :: Tree Int tree =
Node
1
( Node
2
(Node 4 (Node 7 Empty Empty) Empty)
(Node 5 Empty Empty)
)
( Node
3
(Node 6 (Node 8 Empty Empty) (Node 9 Empty Empty))
Empty
)
asciiTree :: String asciiTree =
unlines
[ " 1",
" / \\",
" / \\",
" / \\",
" 2 3",
" / \\ /",
" 4 5 6",
" / / \\",
" 7 8 9"
]
OUTPUT ------------------------
main :: IO () main = do
putStrLn asciiTree
mapM_ putStrLn $
zipWith
( \s xs ->
justifyLeft 14 ' ' (s <> ":")
<> unwords (show <$> xs)
)
["preorder", "inorder", "postorder", "level-order"]
([preorder, inorder, postorder, levelorder] <*> [tree])
where
justifyLeft n c s = take n (s <> replicate n c)</lang>
- Output:
1
/ \
/ \
/ \
2 3
/ \ /
4 5 6
/ / \
7 8 9
preorder: 1 2 4 7 5 3 6 8 9
inorder: 7 4 2 5 1 8 6 9 3
postorder: 7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9
Rose Tree
Writing the first three traversals in terms of foldTree, and the last as concat . levels:
<lang haskell>import Data.Tree (Tree (..), drawForest, drawTree, foldTree)
TREE TRAVERSAL --------------------
inorder, postorder, preorder :: a -> a -> [a] inorder x [] = [x] inorder x (y : xs) = y <> [x] <> concat xs postorder x xs = concat xs <> [x] preorder x xs = x : concat xs
levelOrder :: Tree a -> [a] levelOrder = concat . levels
levels :: Tree a -> a levels tree = go tree []
where
go (Node x xs) a =
let (h, t) = case a of
[] -> ([], [])
(y : ys) -> (y, ys)
in [x] <> h : foldr go t xs
nodeCount,
treeDepth, treeMax, treeMin, treeProduct, treeSum, treeWidth :: Int -> [Int] -> Int
nodeCount = const (succ . sum)
treeDepth = const (succ . foldr max 1)
treeMax x xs = maximum (x : xs)
treeMin x xs = minimum (x : xs)
treeProduct x xs = x * product xs
treeSum x xs = x + sum xs
treeWidth = const (foldr (+) 1)
TEST -------------------------
tree :: Tree Int tree =
Node
1
[ Node 2 [Node 4 [Node 7 []], Node 5 []],
Node 3 [Node 6 [Node 8 [], Node 9 []]]
]
main :: IO () main = do
putStrLn $ drawTree $ fmap show tree
mapM_
print
( [foldTree]
<*> [preorder, inorder, postorder]
<*> [tree]
)
print $ levelOrder tree
putStrLn ""
(putStrLn . unlines)
( ( \(k, f) ->
justifyRight 7 ' ' k
<> " -> "
<> justifyLeft 6 ' ' (show $ foldTree f tree)
)
<$> [ ("Count", nodeCount),
("Layers", treeDepth),
("Max", treeMax),
("Min", treeMin),
("Product", treeProduct),
("Sum", treeSum),
("Leaves", treeWidth)
]
)
justifyLeft, justifyRight :: Int -> Char -> String -> String justifyLeft n c s = take n (s <> replicate n c) justifyRight n c = (drop . length) <*> (replicate n c <>)</lang>
1
|
+- 2
| |
| +- 4
| | |
| | `- 7
| |
| `- 5
|
`- 3
|
`- 6
|
+- 8
|
`- 9
[1,2,4,7,5,3,6,8,9]
[7,4,2,5,1,8,6,9,3]
[7,4,5,2,8,9,6,3,1]
[1,2,3,4,5,6,7,8,9]
Count -> 9
Layers -> 5
Max -> 9
Min -> 1
Product -> 362880
Sum -> 45
Leaves -> 4
Icon and Unicon
<lang Icon>procedure main()
bTree := [1, [2, [4, [7]], [5]], [3, [6, [8], [9]]]] showTree(bTree, preorder|inorder|postorder|levelorder)
end
procedure showTree(tree, f)
writes(image(f),":\t")
every writes(" ",f(tree)[1])
write()
end
procedure preorder(L)
if \L then suspend L | preorder(L[2|3])
end
procedure inorder(L)
if \L then suspend inorder(L[2]) | L | inorder(L[3])
end
procedure postorder(L)
if \L then suspend postorder(L[2|3]) | L
end
procedure levelorder(L)
if \L then {
queue := [L]
while nextnode := get(queue) do {
every put(queue, \nextnode[2|3])
suspend nextnode
}
}
end</lang>
Output:
->bintree procedure preorder: 1 2 4 7 5 3 6 8 9 procedure inorder: 7 4 2 5 1 8 6 9 3 procedure postorder: 7 4 5 2 8 9 6 3 1 procedure levelorder: 1 2 3 4 5 6 7 8 9 ->
Isabelle
<lang Isabelle>theory Tree imports Main begin
datatype 'a tree = Leaf | Node "'a tree" 'a "'a tree"
definition example :: "int tree" where
"example ≡
Node
(Node
(Node
(Node Leaf 7 Leaf)
4
Leaf
)
2
(Node Leaf 5 Leaf)
)
1
(Node
(Node
(Node Leaf 8 Leaf)
6
(Node Leaf 9 Leaf)
)
3
Leaf
)"
fun preorder :: "'a tree ⇒ 'a list" where
"preorder Leaf = []"
| "preorder (Node l a r) = a # preorder l @ preorder r"
lemma "preorder example = [1, 2, 4, 7, 5, 3, 6, 8, 9]" by code_simp
fun inorder :: "'a tree ⇒ 'a list" where
"inorder Leaf = []"
| "inorder (Node l a r) = inorder l @ [a] @ inorder r"
lemma "inorder example = [7, 4, 2, 5, 1, 8, 6, 9, 3]" by code_simp
fun postorder :: "'a tree ⇒ 'a list" where
"postorder Leaf = []"
| "postorder (Node l a r) = postorder l @ postorder r @ [a]"
lemma "postorder example = [7, 4, 5, 2, 8, 9, 6, 3, 1]" by code_simp
lemma
"set (inorder t) = set (preorder t)" "set (preorder t) = set (postorder t)" "set (inorder t) = set (postorder t)" by(induction t, simp, simp)+
text‹ For a breadth first search, we will have a queue of the nodes we still want to visit. The type of the queue is \<^typ>‹'a tree list›. With each step, summing the sizes of the subtrees in the queue, the queue gets smaller. Thus, the breadth first search terminates. Isabelle cannot figure out this termination argument automatically, so we provide some help by defining what the size of a tree is. › fun tree_size :: "'a tree ⇒ nat" where
"tree_size Leaf = 1"
| "tree_size (Node l _ r) = 1 + tree_size l + tree_size r"
function (sequential) bfs :: "'a tree list ⇒ 'a list" where
"bfs [] = []"
| "bfs (Leaf#q) = bfs q" | "bfs ((Node l a r)#q) = a # bfs (q @ [l,r])"
by pat_completeness auto
termination bfs
by(relation "measure (λqs. sum_list (map tree_size qs))") simp+
fun levelorder :: "'a tree ⇒ 'a list" where
"levelorder t = bfs [t]"
lemma "levelorder example = [1, 2, 3, 4, 5, 6, 7, 8, 9]" by code_simp
end</lang>
J
<lang J>preorder=: ]S:0 postorder=: ([:; postorder&.>@}.) , >@{. levelorder=: ;@({::L:1 _~ [: (/: #@>) <S:1@{::) inorder=: ([:; inorder&.>@("_`(1&{)@.(1<#))) , >@{. , [:; inorder&.>@}.@}.</lang>
Required example:
<lang J>N2=: conjunction def '(<m),(<n),<y' N1=: adverb def '(<m),<y' L=: adverb def '<m'
tree=: 1 N2 (2 N2 (4 N1 (7 L)) 5 L) 3 N1 6 N2 (8 L) 9 L</lang>
This tree is organized in a pre-order fashion
<lang J> preorder tree 1 2 4 7 5 3 6 8 9</lang>
post-order is not that much different from pre-order, except that the children must extracted before the parent.
<lang J> postorder tree 7 4 5 2 8 9 6 3 1</lang>
Implementing in-order is more complex because we must sometimes test whether we have any leaves, instead of relying on J's implicit looping over lists
<lang J> inorder tree 7 4 2 5 1 8 6 9 3</lang>
level-order can be accomplished by constructing a map of the locations of the leaves, sorting these map locations by their non-leaf indices and using the result to extract all leaves from the tree. Elements at the same level with the same parent will have the same sort keys and thus be extracted in preorder fashion, which works just fine.
<lang J> levelorder tree 1 2 3 4 5 6 7 8 9</lang>
For J novices, here's the tree instance with a few redundant parenthesis:
<lang J> tree=: 1 N2 (2 N2 (4 N1 (7 L)) (5 L)) (3 N1 (6 N2 (8 L) (9 L)))</lang>
Syntactically, N2 is a binary node expressed as m N2 n y. N1 is a node with a single child, expressed as m N2 y. L is a leaf node, expressed as m L. In all three cases, the parent value (m) for the node appears on the left, and the child tree(s) appear on the right. (And n must be parenthesized if it is not a single word.)
J: Alternate implementation
Of course, there are other ways of representing tree structures in J. One fairly natural approach pairs a list of data with a matching list of parent indices. For example:
<lang J>example=:1 8 3 4 7 5 9 6 2,: 0 7 0 8 3 8 7 2 0</lang>
Here, we have two possible ways of identifying the root node. It can be in a known place in the list (index 0, for this example). But it is also the only node which is its own parent. For this task we'll use the more general (and thus slower) approach which allows us to place the root node anywhere in the sequence.
Next, let's define a few utilities:
<lang J>depth=: +/@((~: , (~: i.@#@{.)~) {:@,)@({~^:a:)
reorder=:4 :0
'data parent'=. y
data1=. x{data
parent1=. x{data1 i. parent{data
if. 0=L.y do. data1,:parent1 else. data1;parent1 end.
)
data=:3 :'data[data parent=. y' parent=:3 :'parent[data parent=. y'
childinds=: [: <:@(2&{.@-.&> #\) (</. #\)`(]~.)`(a:"0)}~</lang>
Here, data extracts the list of data items from the tree and parent extracts the structure from the tree.
depth examines the parent structure and returns the distance of each node from the root.
reorder is like indexing, except that it returns an equivalent tree (with the structural elements updated to maintain the original tree structure). The left argument for reorder should select the entire tree. Selecting partial trees is a more complex problem which needs specifications about how to deal with issues such as dangling roots and multiple roots. (Our abstraction here has no problem representing trees with multiple roots, but they are not relevant to this task.)
childinds extracts the child pointers which some of these results assume. This implementation assumes we are working with a binary tree (which is an explicit requirement of this task -- the parent node representation is far more general and can represent trees with any number of children at each node, but what would an "inorder" traversal look like with a trinary tree?).
Next, we define our "traversal" routines (actually, we are going a bit overboard here - we really only need to extract the data for this tasks's concept of traversal):
<lang J>dataorder=: /:@data reorder ] levelorder=: /:@depth@parent reorder ]
inorder=: inperm@parent reorder ] inperm=:3 :0
chil=. childinds y
node=. {.I.(= i.@#) y
todo=. i.0 2
r=. i.0
whilst. (#todo)+.0<:node do.
if. 0 <: node do.
if. 0 <: {.ch=. node{chil do.
todo=. todo, node,{:ch
node=. {.ch
else.
r=. r, node
node=. _1 end.
else.
r=. r, {.ch=. {: todo
todo=. }: todo
node=. {:ch end. end.
r
)
postorder=: postperm@parent reorder ] postperm=:3 :0
chil=. 0,1+childinds y
todo=. 1+I.(= i.@#) y
r=. i.0
whilst. (#todo) do.
node=. {: todo
todo=. }: todo
if. 0 < node do.
if. #ch=. (node{chil)-.0 do.
todo=. todo,(-node),|.ch
else.
r=. r, <:node end.
else.
r=. r, <:|node end. end.
)
preorder=: preperm@parent reorder ] preperm=:3 :0
chil=. childinds y
todo=. I.(= i.@#) y
r=. i.0
whilst. (#todo) do.
r=. r,node=. {: todo
todo=. }: todo
if. #ch=. (node{chil)-._1 do.
todo=. todo,|.ch end. end.
r
)</lang>
These routines assume that children of a node are arranged so that the lower index appears to the left of the higher index. If instead we wanted to rely on the ordering of their values, we could first use dataorder to enforce the assumption that child indexes are ordered properly.
Example use:
<lang J> levelorder dataorder example 1 2 3 4 5 6 7 8 9 0 0 0 1 1 2 3 5 5
inorder dataorder example
7 4 2 5 1 8 6 9 3 1 2 4 2 4 6 8 6 4
preorder dataorder example
1 2 4 7 5 3 6 8 9 0 0 1 2 1 0 5 6 6
postorder dataorder example
7 4 5 2 8 9 6 3 1 1 3 3 8 6 6 7 8 8</lang>
(Once again, all we really need for this task is the first row of those results - the part that represents data.)
Java
Java: Procedural
This solution relies on a binary tree that allows null as left or right child nodes. Consequently, the traversal code has to check for null on each decent. The traversal variants are implemented within a monolithic switch statement.
<lang java5>import java.util.*;
public class TreeTraversal {
static class Node<T> {
T value; Node<T> left; Node<T> right;
Node(T value) { this.value = value; }
void visit() { System.out.print(this.value + " "); } }
static enum ORDER { PREORDER, INORDER, POSTORDER, LEVEL }
static <T> void traverse(Node<T> node, ORDER order) {
if (node == null) { return; } switch (order) { case PREORDER: node.visit(); traverse(node.left, order); traverse(node.right, order); break; case INORDER: traverse(node.left, order); node.visit(); traverse(node.right, order); break; case POSTORDER: traverse(node.left, order); traverse(node.right, order); node.visit(); break; case LEVEL: Queue<Node<T>> queue = new LinkedList<>(); queue.add(node); while(!queue.isEmpty()){ Node<T> next = queue.remove(); next.visit(); if(next.left!=null) queue.add(next.left); if(next.right!=null) queue.add(next.right); } } }
public static void main(String[] args) {
Node<Integer> one = new Node<Integer>(1); Node<Integer> two = new Node<Integer>(2); Node<Integer> three = new Node<Integer>(3); Node<Integer> four = new Node<Integer>(4); Node<Integer> five = new Node<Integer>(5); Node<Integer> six = new Node<Integer>(6); Node<Integer> seven = new Node<Integer>(7); Node<Integer> eight = new Node<Integer>(8); Node<Integer> nine = new Node<Integer>(9);
one.left = two; one.right = three; two.left = four; two.right = five; three.left = six; four.left = seven; six.left = eight; six.right = nine;
traverse(one, ORDER.PREORDER); System.out.println(); traverse(one, ORDER.INORDER); System.out.println(); traverse(one, ORDER.POSTORDER); System.out.println(); traverse(one, ORDER.LEVEL);
} }</lang> Output:
1 2 4 7 5 3 6 8 9 7 4 2 5 1 8 6 9 3 7 4 5 2 8 9 6 3 1 1 2 3 4 5 6 7 8 9
Java: Object Oriented
This solution relies on a binary tree that distinguishes between ordinary and empty nodes. Therefore, the tree can be traversed using a visitor pattern that uses a polymorphic access method instead of null checks. The traversal variants are implemented as subclasses of a generic visitor. The action to be performed with each (non-empty) node is provided as function to the traversal algorithm.
<lang java5>import java.util.function.Consumer; import java.util.Queue; import java.util.LinkedList;
class TreeTraversal {
static class EmptyNode {
void accept(Visitor aVisitor) {}
void accept(LevelOrder aVisitor, Queue<EmptyNode> data) {}
}
static class Node<T> extends EmptyNode {
T data;
EmptyNode left = new EmptyNode();
EmptyNode right = new EmptyNode();
Node(T data) {
this.data = data;
}
Node<T> left(Node<?> aNode) {
this.left = aNode;
return this;
}
Node<T> right(Node<?> aNode) {
this.right = aNode;
return this;
}
void accept(Visitor aVisitor) {
aVisitor.visit(this);
}
void accept(LevelOrder aVisitor, Queue<EmptyNode> data) {
aVisitor.visit(this, data);
}
}
static abstract class Visitor {
Consumer<Node<?>> action;
Visitor(Consumer<Node<?>> action) {
this.action = action;
}
abstract <T> void visit(Node<T> aNode); }
static class PreOrder extends Visitor {
PreOrder(Consumer<Node<?>> action) {
super(action);
}
<T> void visit(Node<T> aNode) {
action.accept(aNode);
aNode.left.accept(this);
aNode.right.accept(this);
}
}
static class InOrder extends Visitor {
InOrder(Consumer<Node<?>> action) {
super(action);
}
<T> void visit(Node<T> aNode) {
aNode.left.accept(this);
action.accept(aNode);
aNode.right.accept(this);
}
}
static class PostOrder extends Visitor {
PostOrder(Consumer<Node<?>> action) {
super(action);
}
<T> void visit(Node<T> aNode) {
aNode.left.accept(this);
aNode.right.accept(this);
action.accept(aNode);
}
}
static class LevelOrder extends Visitor {
LevelOrder(Consumer<Node<?>> action) {
super(action);
}
<T> void visit(Node<T> aNode) {
Queue<EmptyNode> queue = new LinkedList<>();
queue.add(aNode);
do {
queue.remove().accept(this, queue);
} while (!queue.isEmpty());
}
<T> void visit(Node<T> aNode, Queue<EmptyNode> queue) {
action.accept(aNode);
queue.add(aNode.left);
queue.add(aNode.right);
}
}
public static void main(String[] args) {
Node<Integer> tree = new Node<Integer>(1)
.left(new Node<Integer>(2)
.left(new Node<Integer>(4)
.left(new Node<Integer>(7)))
.right(new Node<Integer>(5)))
.right(new Node<Integer>(3)
.left(new Node<Integer>(6)
.left(new Node<Integer>(8))
.right(new Node<Integer>(9))));
Consumer<Node<?>> print = aNode -> System.out.print(aNode.data + " ");
tree.accept(new PreOrder(print));
System.out.println();
tree.accept(new InOrder(print));
System.out.println();
tree.accept(new PostOrder(print));
System.out.println();
tree.accept(new LevelOrder(print));
System.out.println();
}
}</lang>
Output:
1 2 4 7 5 3 6 8 9 7 4 2 5 1 8 6 9 3 7 4 5 2 8 9 6 3 1 1 2 3 4 5 6 7 8 9
JavaScript
ES5
Iteration
inspired by Ruby <lang javascript>function BinaryTree(value, left, right) {
this.value = value; this.left = left; this.right = right;
} BinaryTree.prototype.preorder = function(f) {this.walk(f,['this','left','right'])} BinaryTree.prototype.inorder = function(f) {this.walk(f,['left','this','right'])} BinaryTree.prototype.postorder = function(f) {this.walk(f,['left','right','this'])} BinaryTree.prototype.walk = function(func, order) {
for (var i in order)
switch (order[i]) {
case "this": func(this.value); break;
case "left": if (this.left) this.left.walk(func, order); break;
case "right": if (this.right) this.right.walk(func, order); break;
}
} BinaryTree.prototype.levelorder = function(func) {
var queue = [this];
while (queue.length != 0) {
var node = queue.shift();
func(node.value);
if (node.left) queue.push(node.left);
if (node.right) queue.push(node.right);
}
}
// convenience function for creating a binary tree function createBinaryTreeFromArray(ary) {
var left = null, right = null; if (ary[1]) left = createBinaryTreeFromArray(ary[1]); if (ary[2]) right = createBinaryTreeFromArray(ary[2]); return new BinaryTree(ary[0], left, right);
}
var tree = createBinaryTreeFromArray([1, [2, [4, [7]], [5]], [3, [6, [8],[9]]]]);
print("*** preorder ***"); tree.preorder(print); print("*** inorder ***"); tree.inorder(print); print("*** postorder ***"); tree.postorder(print); print("*** levelorder ***"); tree.levelorder(print);</lang>
Functional composition
(for binary trees consisting of nested lists)
<lang javascript>(function () {
function preorder(n) {
return [n[v]].concat(
n[l] ? preorder(n[l]) : []
).concat(
n[r] ? preorder(n[r]) : []
);
}
function inorder(n) {
return (
n[l] ? inorder(n[l]) : []
).concat(
n[v]
).concat(
n[r] ? inorder(n[r]) : []
);
}
function postorder(n) {
return (
n[l] ? postorder(n[l]) : []
).concat(
n[r] ? postorder(n[r]) : []
).concat(
n[v]
);
}
function levelorder(n) {
return (function loop(x) {
return x.length ? (
x[0] ? (
[x[0][v]].concat(
loop(
x.slice(1).concat(
[x[0][l], x[0][r]]
)
)
)
) : loop(x.slice(1))
) : [];
})([n]);
}
var v = 0,
l = 1,
r = 2,
tree = [1,
[2,
[4,
[7]
],
[5]
],
[3,
[6,
[8],
[9]
]
]
],
lstTest = "Traversal", "Nodes visited".concat( [preorder, inorder, postorder, levelorder].map( function (f) { return [f.name, f(tree)]; } ) );
// a -> bool -> s -> s function wikiTable(lstRows, blnHeaderRow, strStyle) { return '{| class="wikitable" ' + ( strStyle ? 'style="' + strStyle + '"' : ) + lstRows.map(function (lstRow, iRow) { var strDelim = ((blnHeaderRow && !iRow) ? '!' : '|');
return '\n|-\n' + strDelim + ' ' + lstRow.map(function (v) {
return typeof v === 'undefined' ? ' ' : v;
}).join(' ' + strDelim + strDelim + ' ');
}).join() + '\n|}';
}
return wikiTable(lstTest, true) + '\n\n' + JSON.stringify(lstTest);
})();</lang>
Output:
| Traversal | Nodes visited |
|---|---|
| preorder | 1,2,4,7,5,3,6,8,9 |
| inorder | 7,4,2,5,1,8,6,9,3 |
| postorder | 7,4,5,2,8,9,6,3,1 |
| levelorder | 1,2,3,4,5,6,7,8,9 |
<lang JavaScript>[["Traversal","Nodes visited"], ["preorder",[1,2,4,7,5,3,6,8,9]],["inorder",[7,4,2,5,1,8,6,9,3]], ["postorder",[7,4,5,2,8,9,6,3,1]],["levelorder",[1,2,3,4,5,6,7,8,9]]]</lang>
or, again functionally, but:
- for a tree of nested dictionaries (rather than a simple nested list),
- defining a single traverse() function
- checking that the tree is indeed binary, and returning undefined for the in-order traversal if any node in the tree has more than two children. (The other 3 traversals are still defined for rose trees).
<lang JavaScript>(function () {
'use strict';
// 'preorder' | 'inorder' | 'postorder' | 'level-order'
// traverse :: String -> Tree {value: a, nest: [Tree]} -> [a]
function traverse(strOrderName, dctTree) {
var strName = strOrderName.toLowerCase();
if (strName.startsWith('level')) {
// LEVEL-ORDER
return levelOrder([dctTree]);
} else if (strName.startsWith('in')) {
var lstNest = dctTree.nest;
if ((lstNest ? lstNest.length : 0) < 3) {
var left = lstNest[0] || [],
right = lstNest[1] || [],
lstLeft = left.nest ? (
traverse(strName, left)
) : (left.value || []),
lstRight = right.nest ? (
traverse(strName, right)
) : (right.value || []);
return (lstLeft !== undefined && lstRight !== undefined) ?
// IN-ORDER
(lstLeft instanceof Array ? lstLeft : [lstLeft])
.concat(dctTree.value)
.concat(lstRight) : undefined;
} else { // in-order only defined here for binary trees
return undefined;
}
} else {
var lstTraversed = concatMap(function (x) {
return traverse(strName, x);
}, (dctTree.nest || []));
return (
strName.startsWith('pre') ? (
// PRE-ORDER
[dctTree.value].concat(lstTraversed)
) : strName.startsWith('post') ? (
// POST-ORDER
lstTraversed.concat(dctTree.value)
) : []
);
}
}
// levelOrder :: [Tree {value: a, nest: [Tree]}] -> [a]
function levelOrder(lstTree) {
var lngTree = lstTree.length,
head = lngTree ? lstTree[0] : undefined,
tail = lstTree.slice(1);
// Recursively take any value found in the head node
// of the remaining tail, deferring any child nodes
// of that head to the end of the tail
return lngTree ? (
head ? (
[head.value].concat(
levelOrder(
tail
.concat(head.nest || [])
)
)
) : levelOrder(tail)
) : [];
}
// concatMap :: (a -> [b]) -> [a] -> [b]
function concatMap(f, xs) {
return [].concat.apply([], xs.map(f));
}
var dctTree = {
value: 1,
nest: [{
value: 2,
nest: [{
value: 4,
nest: [{
value: 7
}]
}, {
value: 5
}]
}, {
value: 3,
nest: [{
value: 6,
nest: [{
value: 8
}, {
value: 9
}]
}]
}]
};
return ['preorder', 'inorder', 'postorder', 'level-order']
.reduce(function (a, k) {
return (
a[k] = traverse(k, dctTree),
a
);
}, {});
})();</lang>
- Output:
<lang JavaScript>{"preorder":[1, 2, 4, 7, 5, 3, 6, 8, 9], "inorder":[7, 4, 2, 5, 1, 8, 6, 9, 3], "postorder":[7, 4, 5, 2, 8, 9, 6, 3, 1], "level-order":[1, 2, 3, 4, 5, 6, 7, 8, 9]}</lang>
ES6
In terms of a general foldTree function:
<lang JavaScript>(() => {
'use strict';
// foldTree :: (a -> [b] -> b) -> Tree a -> b
const foldTree = f =>
// The catamorphism on trees. A summary
// value obtained by a depth-first fold.
tree => {
const go = x => f(x.root)(
x.nest.map(go)
);
return go(tree);
};
// preorder :: a -> a -> [a] const preorder = x => xs => [x, ...concat(xs)];
// inorder :: a -> a -> [a] const inorder = x => xs => length(xs) ? ( [...xs[0], x, ...concat(xs.slice(1))] ) : [x];
// postorder :: a -> a -> [a] const postorder = x => xs => [...concat(xs), x];
// levelOrder :: Tree a -> [a]
const levelOrder = tree =>
concatMap(map(root))(
takeWhile(length)(
iterate(concatMap(nest))(
[tree]
)
)
);
// ------------------------TEST------------------------
const main = () => {
const tree = Node(1)([
Node(2)([
Node(4)([
Node(7)([])
]),
Node(5)([])
]),
Node(3)([
Node(6)([
Node(8)([]),
Node(9)([])
])
])
]);
// Generated by code in Rosetta Code
// task: 'Visualize a tree'
console.log([
' ┌ 4 ─ 7',
' ┌ 2 ┤',
' │ └ 5',
' 1 ┤',
' │ ┌ 8',
' └ 3 ─ 6 ┤',
' └ 9'
].join('\n'));
[preorder, inorder, postorder]
.forEach(
f => console.log(
justifyRight(11)(' ')(f.name + ':'),
foldTree(f)(
tree
)
)
);
console.log(
'levelOrder:', levelOrder(tree)
)
};
// -----------------GENERIC FUNCTIONS------------------
// Node :: a -> [Tree a] -> Tree a
const Node = v =>
// Constructor for a Tree node which connects a
// value of some kind to a list of zero or
// more child trees.
xs => ({
type: 'Node',
root: v,
nest: xs || []
});
// concat :: a -> [a] // concat :: [String] -> String const concat = xs => 0 < xs.length ? ( xs.every(x => 'string' === typeof x) ? ( ) : [] ).concat(...xs) : xs;
// concatMap :: (a -> [b]) -> [a] -> [b]
const concatMap = f =>
xs => xs.flatMap(f);
// iterate :: (a -> a) -> a -> Gen [a]
const iterate = f =>
function*(x) {
let v = x;
while (true) {
yield(v);
v = f(v);
}
};
// justifyRight :: Int -> Char -> String -> String
const justifyRight = n =>
// The string s, preceded by enough padding (with
// the character c) to reach the string length n.
c => s => n > s.length ? (
s.padStart(n, c)
) : s;
// length :: [a] -> Int
const length = xs =>
// Returns Infinity over objects without finite
// length. This enables zip and zipWith to choose
// the shorter argument when one is non-finite,
// like cycle, repeat etc
(Array.isArray(xs) || 'string' === typeof xs) ? (
xs.length
) : Infinity;
// map :: (a -> b) -> [a] -> [b]
const map = f =>
// The list obtained by applying f to each element of xs.
// (The image of xs under f).
xs => (Array.isArray(xs) ? (
xs
) : xs.split()).map(f);
// nest :: Tree a -> [a] const nest = tree => tree.nest;
// root :: Tree a -> a const root = tree => tree.root;
// takeWhile :: (a -> Bool) -> Gen [a] -> [a]
const takeWhile = p => xs => {
const ys = [];
let
nxt = xs.next(),
v = nxt.value;
while (!nxt.done && p(v)) {
ys.push(v);
nxt = xs.next();
v = nxt.value
}
return ys;
};
// MAIN --- return main();
})();</lang>
- Output:
┌ 4 ─ 7
┌ 2 ┤
│ └ 5
1 ┤
│ ┌ 8
└ 3 ─ 6 ┤
└ 9
preorder: 1,2,4,7,5,3,6,8,9
inorder: 7,4,2,5,1,8,6,9,3
postorder: 7,4,5,2,8,9,6,3,1
levelOrder: 1,2,3,4,5,6,7,8,9
jq
All the ordering filters defined here produce streams. For the final output, each stream is condensed into an array.
The implementation assumes an array structured recursively as [ node, left, right ], where "left" and "right" may be [] or null equivalently. <lang jq>def preorder:
if length == 0 then empty else .[0], (.[1]|preorder), (.[2]|preorder) end;
def inorder:
if length == 0 then empty else (.[1]|inorder), .[0] , (.[2]|inorder) end;
def postorder:
if length == 0 then empty else (.[1] | postorder), (.[2]|postorder), .[0] end;
- Helper functions for levelorder:
# Produce a stream of the first elements def heads: map( .[0] | select(. != null)) | .[];
- Produce a stream of the left/right branches:
def tails: if length == 0 then empty else [map ( .[1], .[2] ) | .[] | select( . != null)] end;
def levelorder: [.] | recurse( tails ) | heads; </lang> The task: <lang jq>def task:
# [node, left, right]
def atree: [1, [2, [4, [7,[],[]],
[]],
[5, [],[]]],
[3, [6, [8,[],[]],
[9,[],[]]],
[]]] ;
"preorder: \( [atree|preorder ])", "inorder: \( [atree|inorder ])", "postorder: \( [atree|postorder ])", "levelorder: \( [atree|levelorder])"
task</lang>
- Output:
$ jq -n -c -r -f Tree_traversal.jq preorder: [1,2,4,7,5,3,6,8,9] inorder: [7,4,2,5,1,8,6,9,3] postorder: [7,4,5,2,8,9,6,3,1] levelorder: [1,2,3,4,5,6,7,8,9]
Julia
<lang Julia>tree = Any[1, Any[2, Any[4, Any[7, Any[],
Any[]],
Any[]],
Any[5, Any[],
Any[]]],
Any[3, Any[6, Any[8, Any[],
Any[]],
Any[9, Any[],
Any[]]],
Any[]]]
preorder(t, f) = if !isempty(t)
f(t[1]); preorder(t[2], f); preorder(t[3], f)
end
inorder(t, f) = if !isempty(t)
inorder(t[2], f); f(t[1]); inorder(t[3], f)
end
postorder(t, f) = if !isempty(t)
postorder(t[2], f); postorder(t[3], f); f(t[1])
end
levelorder(t, f) = while !isempty(t)
t = mapreduce(x -> isa(x, Number) ? (f(x); []) : x, vcat, t)
end
</lang>
- Output:
julia> for f in [preorder, inorder, postorder, levelorder]
print((lpad("$f: ", 12))); f(tree, x -> print(x, " ")); println()
end
preorder: 1 2 4 7 5 3 6 8 9
inorder: 7 4 2 5 1 8 6 9 3
postorder: 7 4 5 2 8 9 6 3 1
levelorder: 1 2 3 4 5 6 7 8 9
Kotlin
procedural style
<lang scala>data class Node(val v: Int, var left: Node? = null, var right: Node? = null) {
override fun toString() = "$v"
}
fun preOrder(n: Node?) {
n?.let {
print("$n ")
preOrder(n.left)
preOrder(n.right)
}
}
fun inorder(n: Node?) {
n?.let {
inorder(n.left)
print("$n ")
inorder(n.right)
}
}
fun postOrder(n: Node?) {
n?.let {
postOrder(n.left)
postOrder(n.right)
print("$n ")
}
}
fun levelOrder(n: Node?) {
n?.let {
val queue = mutableListOf(n)
while (queue.isNotEmpty()) {
val node = queue.removeAt(0)
print("$node ")
node.left?.let { queue.add(it) }
node.right?.let { queue.add(it) }
}
}
}
inline fun exec(name: String, n: Node?, f: (Node?) -> Unit) {
print(name) f(n) println()
}
fun main(args: Array<String>) {
val nodes = Array(10) { Node(it) }
nodes[1].left = nodes[2] nodes[1].right = nodes[3]
nodes[2].left = nodes[4] nodes[2].right = nodes[5]
nodes[4].left = nodes[7]
nodes[3].left = nodes[6]
nodes[6].left = nodes[8] nodes[6].right = nodes[9]
exec(" preOrder: ", nodes[1], ::preOrder)
exec(" inorder: ", nodes[1], ::inorder)
exec(" postOrder: ", nodes[1], ::postOrder)
exec("level-order: ", nodes[1], ::levelOrder)
}</lang>
- Output:
preOrder: 1 2 4 7 5 3 6 8 9
inorder: 7 4 2 5 1 8 6 9 3
postOrder: 7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9
object-oriented style
<lang scala>fun main(args: Array<String>) {
data class Node(val v: Int, var left: Node? = null, var right: Node? = null) {
override fun toString() = " $v"
fun preOrder() { print(this); left?.preOrder(); right?.preOrder() }
fun inorder() { left?.inorder(); print(this); right?.inorder() }
fun postOrder() { left?.postOrder(); right?.postOrder(); print(this) }
fun levelOrder() = with(mutableListOf(this)) {
do {
val node = removeAt(0)
print(node)
node.left?.let { add(it) }
node.right?.let { add(it) }
} while (any())
}
inline fun exec(name: String, f: (Node) -> Unit) {
print(name)
f(this)
println()
}
}
val nodes = Array(10) { Node(it) }
nodes[1].left = nodes[2] nodes[1].right = nodes[3] nodes[2].left = nodes[4] nodes[2].right = nodes[5] nodes[4].left = nodes[7] nodes[3].left = nodes[6] nodes[6].left = nodes[8] nodes[6].right = nodes[9]
with(nodes[1]) {
exec(" preOrder:", Node::preOrder)
exec(" inorder:", Node::inorder)
exec(" postOrder:", Node::postOrder)
exec("level-order:", Node::levelOrder)
}
}</lang>
Lambdatalk
Lambdatalk has primitives working on a word, sentences (sequences of words) and arrays:
- {W.equal? word1 word2} returns true or false
- {S.replace rex by exp1 in exp2}
replaces a regular expression by some expression in another one
- {S.sort comp words} sorts the sequence of words according to comp
- {A.new words} creates a new array from the sequence of words
- {A.get index array} gets the value of array at index
<lang scheme> {def walk
{def walk.r
{lambda {:o :t}
{if {W.equal? :t nil}
then
else {if {W.equal? :o preorder} then {A.get 0 :t} else}
{walk.r :order {A.get 1 :t}}
{if {W.equal? :o inorder} then {A.get 0 :t} else}
{walk.r :order {A.get 2 :t}}
{if {W.equal? :o postorder} then {A.get 0 :t} else} }}}
{lambda {:o :t}
{S.replace \s by space in {walk.r :o :t}}}}
{def sort
{lambda {:o :t} {S.sort :o {walk preorder :t}}}}
{def T
{A.new 1
{A.new 2
{A.new 4
{A.new 7 nil nil} nil}
{A.new 5 nil nil}}
{A.new 3
{A.new 6
{A.new 8 nil nil}
{A.new 9 nil nil}} nil}}}
{walk preorder {T}} -> 1 2 4 7 5 3 6 8 9 {walk inorder {T}} -> 7 4 2 5 1 8 6 9 3 {walk postorder {T}} -> 7 4 5 2 8 9 6 3 1 {sort < {T}} -> 1 2 3 4 5 6 7 8 9 {sort > {T}} -> 9 8 7 6 5 4 3 2 1 </lang>
Lingo
<lang lingo>-- parent script "BinaryTreeNode"
property _val, _left, _right
on new (me, val)
me._val = val return me
end
on getValue (me)
return me._val
end
on setLeft (me, node)
me._left = node
end
on setRight (me, node)
me._right = node
end
on getLeft (me)
return me._left
end
on getRight (me)
return me._right
end</lang>
<lang lingo>-- parent script "BinaryTreeTraversal"
on inOrder (me, node, l)
if voidP(l) then l = [] if voidP(node) then return l if not voidP(node.getLeft()) then l = me.inOrder(node.getLeft(), l) l.add(node) if not voidP(node.getRight()) then l = me.inOrder(node.getRight(), l) return l
end
on preOrder (me, node, l)
if voidP(l) then l = [] if voidP(node) then return l l.add(node) if not voidP(node.getLeft()) then l = me.preOrder(node.getLeft(), l) if not voidP(node.getRight()) then l = me.preOrder(node.getRight(), l) return l
end
on postOrder (me, node, l)
if voidP(l) then l = [] if voidP(node) then return l if not voidP(node.getLeft()) then l = me.postOrder(node.getLeft(), l) if not voidP(node.getRight()) then l = me.postOrder(node.getRight(), l) l.add(node) return l
end
on levelOrder (me, node)
l = [] queue = [node] repeat while queue.count node = queue[1] queue.deleteAt(1) l.add(node) if not voidP(node.getLeft()) then queue.add(node.getLeft()) if not voidP(node.getRight()) then queue.add(node.getRight()) end repeat return l
end
-- print utility function on serialize (me, l)
str = "" repeat with node in l put node.getValue()&" " after str end repeat delete the last char of str return str
end</lang>
Usage: <lang lingo>-- create the tree l = [] repeat with i = 1 to 10
l[i] = script("BinaryTreeNode").new(i)
end repeat l[6].setLeft (l[8]) l[6].setRight(l[9]) l[3].setLeft (l[6]) l[4].setLeft (l[7]) l[2].setLeft (l[4]) l[2].setRight(l[5]) l[1].setLeft (l[2]) l[1].setRight(l[3])
-- print traversal results trav = script("BinaryTreeTraversal") put "preorder: " & trav.serialize(trav.preOrder(l[1])) put "inorder: " & trav.serialize(trav.inOrder(l[1])) put "postorder: " & trav.serialize(trav.postOrder(l[1])) put "level-order: " & trav.serialize(trav.levelOrder(l[1]))</lang>
- Output:
-- "preorder: 1 2 4 7 5 3 6 8 9" -- "inorder: 7 4 2 5 1 8 6 9 3" -- "postorder: 7 4 5 2 8 9 6 3 1" -- "level-order: 1 2 3 4 5 6 7 8 9"
Logo
<lang logo>; nodes are [data left right], use "first" to get data
to node.left :node
if empty? butfirst :node [output []] output first butfirst :node
end to node.right :node
if empty? butfirst :node [output []] if empty? butfirst butfirst :node [output []] output first butfirst butfirst :node
end to max :a :b
output ifelse :a > :b [:a] [:b]
end to tree.depth :tree
if empty? :tree [output 0] output 1 + max tree.depth node.left :tree tree.depth node.right :tree
end
to pre.order :tree :action
if empty? :tree [stop] invoke :action first :tree pre.order node.left :tree :action pre.order node.right :tree :action
end to in.order :tree :action
if empty? :tree [stop] in.order node.left :tree :action invoke :action first :tree in.order node.right :tree :action
end to post.order :tree :action
if empty? :tree [stop] post.order node.left :tree :action post.order node.right :tree :action invoke :action first :tree
end to at.depth :n :tree :action
if empty? :tree [stop] ifelse :n = 1 [invoke :action first :tree] [ at.depth :n-1 node.left :tree :action at.depth :n-1 node.right :tree :action ]
end to level.order :tree :action
for [i 1 [tree.depth :tree]] [at.depth :i :tree :action]
end
make "tree [1 [2 [4 [7]]
[5]]
[3 [6 [8]
[9]]]]
pre.order :tree [(type ? "| |)] (print) in.order :tree [(type ? "| |)] (print) post.order :tree [(type ? "| |)] (print)
level.order :tree [(type ? "| |)] (print)</lang>
Logtalk
<lang logtalk>
- - object(tree_traversal).
:- public(orders/1).
orders(Tree) :-
write('Pre-order: '), pre_order(Tree), nl,
write('In-order: '), in_order(Tree), nl,
write('Post-order: '), post_order(Tree), nl,
write('Level-order: '), level_order(Tree).
:- public(orders/0).
orders :-
tree(Tree),
orders(Tree).
tree(
t(1,
t(2,
t(4,
t(7, t, t),
t
),
t(5, t, t)
),
t(3,
t(6,
t(8, t, t),
t(9, t, t)
),
t
)
)
).
pre_order(t).
pre_order(t(Value, Left, Right)) :-
write(Value), write(' '),
pre_order(Left),
pre_order(Right).
in_order(t).
in_order(t(Value, Left, Right)) :-
in_order(Left),
write(Value), write(' '),
in_order(Right).
post_order(t).
post_order(t(Value, Left, Right)) :-
post_order(Left),
post_order(Right),
write(Value), write(' ').
level_order(t).
level_order(t(Value, Left, Right)) :-
% write tree root value
write(Value), write(' '),
% write rest of the tree
level_order([Left, Right], Tail-Tail).
level_order([], Trees-[]) :-
( Trees \= [] ->
% print next level
level_order(Trees, Tail-Tail)
; % no more levels
true
).
level_order([Tree| Trees], Rest0) :-
( Tree = t(Value, Left, Right) ->
write(Value), write(' '),
% collect the subtrees to print the next level
append(Rest0, [Left, Right| Tail]-Tail, Rest1),
% continue printing the current level
level_order(Trees, Rest1)
; % continue printing the current level
level_order(Trees, Rest0)
).
% use difference-lists for constant time append append(List1-Tail1, Tail1-Tail2, List1-Tail2).
- - end_object.
</lang> Sample output: <lang text> | ?- ?- tree_traversal::orders. Pre-order: 1 2 4 7 5 3 6 8 9 In-order: 7 4 2 5 1 8 6 9 3 Post-order: 7 4 5 2 8 9 6 3 1 Level-order: 1 2 3 4 5 6 7 8 9 yes </lang>
Lua
<lang Lua>-- Utility local function append(t1, t2)
for _, v in ipairs(t2) do
table.insert(t1, v)
end
end
-- Node class local Node = {} Node.__index = Node
function Node:order(order)
local r = {}
append(r, type(self[order[1]]) == "table" and self[order[1]]:order(order) or {self[order[1]]})
append(r, type(self[order[2]]) == "table" and self[order[2]]:order(order) or {self[order[2]]})
append(r, type(self[order[3]]) == "table" and self[order[3]]:order(order) or {self[order[3]]})
return r
end
function Node:levelorder()
local levelorder = {}
local queue = {self}
while next(queue) do
local node = table.remove(queue, 1)
table.insert(levelorder, node[1])
table.insert(queue, node[2])
table.insert(queue, node[3])
end
return levelorder
end
-- Node creator local function new(value, left, right)
return value and setmetatable({
value,
(type(left) == "table") and new(unpack(left)) or new(left),
(type(right) == "table") and new(unpack(right)) or new(right),
}, Node) or nil
end
-- Example local tree = new(1, {2, {4, 7}, 5}, {3, {6, 8, 9}}) print("preorder: " .. table.concat(tree:order({1, 2, 3}), " ")) print("inorder: " .. table.concat(tree:order({2, 1, 3}), " ")) print("postorder: " .. table.concat(tree:order({2, 3, 1}), " ")) print("level-order: " .. table.concat(tree:levelorder(), " "))</lang>
M2000 Interpreter
Using Tuple as Tree
A tuple is an "auto array" in M2000 Interpreter. (,) is the zero length array.
<lang M2000 Interpreter> Module CheckIt {
Null=(,)
Tree=((((Null,7,Null),4,Null),2,(Null,5,Null)),1,(((Null,8,Null),6,(Null,9,Null)),3,Null))
Module preorder (T) {
Print "preorder: ";
printtree(T)
Print
sub printtree(T)
Print T#val(1);" ";
If len(T#val(0))>0 then printtree(T#val(0))
If len(T#val(2))>0 then printtree(T#val(2))
end sub
}
preorder Tree
Module inorder (T) {
Print "inorder: ";
printtree(T)
Print
sub printtree(T)
If len(T#val(0))>0 then printtree(T#val(0))
Print T#val(1);" ";
If len(T#val(2))>0 then printtree(T#val(2))
end sub
}
inorder Tree
Module postorder (T) {
Print "postorder: ";
printtree(T)
Print
sub printtree(T)
If len(T#val(0))>0 then printtree(T#val(0))
If len(T#val(2))>0 then printtree(T#val(2))
Print T#val(1);" ";
end sub
}
postorder Tree
Module level_order (T) {
Print "level-order: ";
Stack New {
printtree(T)
if empty then exit
Read T
Loop
}
Print
sub printtree(T)
If Len(T)>0 then
Print T#val(1);" ";
Data T#val(0), T#val(2)
end if
end sub
}
level_order Tree
} CheckIt </lang>
Using OOP
Now tree is nodes with pointers to nodes (a node ifs a Group, the user object) The "as pointer" is optional, but we can use type check if we want.
<lang M2000 Interpreter> Module OOP {
\\ Class is a global function (until this module end)
Class Null {
}
\\ Null is a pointer to an object returned from class Null()
Global Null->Null()
Class Node {
Public:
x, Group LeftNode, Group RightNode
Class:
\\ after class: anything exist one time,
\\ not included in final object
Module Node {
.LeftNode<=Null
.RightNode<=Null
Read .x
\\ read ? for optional values
Read ? .LeftNode, .RightNode
}
}
\\ NodeTree return a pointer to a new Node
Function NodeTree {
\\ ![] pass currrent stack to Node()
->Node(![])
}
Tree=NodeTree(1, NodeTree(2,NodeTree(4, NodeTree(7)), NodeTree(5)), NodeTree(3, NodeTree(6, NodeTree(8), NodeTree(9))))
Module preorder (T) {
Print "preorder: ";
printtree(T)
Print
sub printtree(T as pointer)
If T is Null then Exit sub
Print T=>x;" ";
printtree(T=>LeftNode)
printtree(T=>RightNode)
end sub
}
preorder Tree
Module inorder (T) {
Print "inorder: ";
printtree(T)
Print
sub printtree(T as pointer)
If T is Null then Exit sub
printtree(T=>LeftNode)
Print T=>x;" ";
printtree(T=>RightNode)
end sub
}
inorder Tree
Module postorder (T) {
Print "postorder: ";
printtree(T)
Print
sub printtree(T as pointer)
If T is Null then Exit sub
printtree(T=>LeftNode)
printtree(T=>RightNode)
Print T=>x;" ";
end sub
}
postorder Tree
Module level_order (T) {
Print "level-order: ";
Stack New {
printtree(T)
if empty then exit
Read T
Loop
}
Print
sub printtree(T as pointer)
If T is Null else
Print T=>x;" ";
Data T=>LeftNode, T=>RightNode
end if
end sub
}
level_order Tree
} OOP </lang>
or we can put modules inside Node Class as methods also i put a visitor as a call back (a lambda function called as module)
<lang M2000 Interpreter> Module OOP {
\\ Class is a global function (until this module end)
Class Null {
}
\\ Null is a pointer to an object returned from class Null()
Global Null->Null()
Class Node {
Public:
x, Group LeftNode, Group RightNode
Module preorder (visitor){
T->This
printtree(T)
sub printtree(T as pointer)
If T is Null then Exit sub
call visitor(T=>x)
printtree(T=>LeftNode)
printtree(T=>RightNode)
end sub
}
Module inorder (visitor){
T->This
printtree(T)
sub printtree(T as pointer)
If T is Null then Exit sub
printtree(T=>LeftNode)
call visitor(T=>x)
printtree(T=>RightNode)
end sub
}
Module postorder (visitor) {
T->This
printtree(T)
sub printtree(T as pointer)
If T is Null then Exit sub
printtree(T=>LeftNode)
printtree(T=>RightNode)
call visitor(T=>x)
end sub
}
Module level_order (visitor){
T->This
Stack New {
printtree(T)
if empty then exit
Read T
Loop
}
sub printtree(T as pointer)
If T is Null else
call visitor(T=>x)
Data T=>LeftNode, T=>RightNode
end if
end sub
}
Class:
\\ after class: anything exist one time,
\\ not included in final object
Module Node {
.LeftNode<=Null
.RightNode<=Null
Read .x
\\ read ? for optional values
Read ? .LeftNode, .RightNode
}
}
\\ NodeTree return a pointer to a new Node
Function NodeTree {
\\ ![] pass currrent stack to Node()
->Node(![])
}
Tree=NodeTree(1, NodeTree(2,NodeTree(4, NodeTree(7)), NodeTree(5)), NodeTree(3, NodeTree(6, NodeTree(8), NodeTree(9))))
printnum=lambda (title$) -> {
Print
Print title$;
=lambda (x)-> {
Print x;" ";
}
}
Tree=>preorder printnum("preorder: ")
Tree=>inorder printnum("inorder: ")
Tree=>postorder printnum("postorder: ")
Tree=>level_order printnum("level-order: ")
} OOP </lang>
Using Event object as visitor
<lang M2000 Interpreter> Module OOP {
\\ Class is a global function (until this module end)
Class Null {
}
\\ Null is a pointer to an object returned from class Null()
Global Null->Null()
Class Node {
Public:
x, Group LeftNode, Group RightNode
Module preorder (visitor){
T->This
printtree(T)
sub printtree(T as pointer)
If T is Null then Exit sub
call event visitor, T=>x
printtree(T=>LeftNode)
printtree(T=>RightNode)
end sub
}
Module inorder (visitor){
T->This
printtree(T)
sub printtree(T as pointer)
If T is Null then Exit sub
printtree(T=>LeftNode)
call event visitor, T=>x
printtree(T=>RightNode)
end sub
}
Module postorder (visitor) {
T->This
printtree(T)
sub printtree(T as pointer)
If T is Null then Exit sub
printtree(T=>LeftNode)
printtree(T=>RightNode)
call event visitor, T=>x
end sub
}
Module level_order (visitor){
T->This
Stack New {
printtree(T)
if empty then exit
Read T
Loop
}
sub printtree(T as pointer)
If T is Null else
call event visitor, T=>x
Data T=>LeftNode, T=>RightNode
end if
end sub
}
Class:
\\ after class: anything exist one time,
\\ not included in final object
Module Node {
.LeftNode<=Null
.RightNode<=Null
Read .x
\\ read ? for optional values
Read ? .LeftNode, .RightNode
}
}
\\ NodeTree return a pointer to a new Node
Function NodeTree {
\\ ![] pass currrent stack to Node()
->Node(![])
}
Tree=NodeTree(1, NodeTree(2,NodeTree(4, NodeTree(7)), NodeTree(5)), NodeTree(3, NodeTree(6, NodeTree(8), NodeTree(9))))
Event PrintAnum {
read x
}
Function PrintThis(x) {
Print x;" ";
}
Event PrintAnum New PrintThis()
printnum=lambda PrintAnum (title$) -> {
Print
Print title$;
=PrintAnum
}
Tree=>preorder printnum("preorder: ")
Tree=>inorder printnum("inorder: ")
Tree=>postorder printnum("postorder: ")
Tree=>level_order printnum("level-order: ")
} OOP </lang>
- Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
Mathematica/Wolfram Language
<lang mathematica>preorder[a_Integer] := a; preorder[a_[b__]] := Flatten@{a, preorder /@ {b}}; inorder[a_Integer] := a; inorder[a_[b_, c_]] := Flatten@{inorder@b, a, inorder@c}; inorder[a_[b_]] := Flatten@{inorder@b, a}; postorder[a_Integer] := a; postorder[a_[b__]] := Flatten@{postorder /@ {b}, a}; levelorder[a_] :=
Flatten[Table[Level[a, {n}], {n, 0, Depth@a}]] /. {b_Integer[__] :>
b};</lang>
Example: <lang mathematica>preorder[1[2[4[7], 5], 3[6[8, 9]]]] inorder[1[2[4[7], 5], 3[6[8, 9]]]] postorder[1[2[4[7], 5], 3[6[8, 9]]]] levelorder[1[2[4[7], 5], 3[6[8, 9]]]]</lang>
- Output:
{1, 2, 4, 7, 5, 3, 6, 8, 9}
{7, 4, 2, 5, 1, 8, 6, 9, 3}
{7, 4, 5, 2, 8, 9, 6, 3, 1}
{1, 2, 3, 4, 5, 6, 7, 8, 9}
Mercury
<lang mercury>:- module tree_traversal.
- - interface.
- - import_module io.
- - pred main(io::di, io::uo) is det.
- - implementation.
- - import_module list.
- - type tree(V)
---> empty ; node(V, tree(V), tree(V)).
- - pred preorder(pred(V, A, A), tree(V), A, A).
- - mode preorder(pred(in, di, uo) is det, in, di, uo) is det.
preorder(_, empty, !Acc). preorder(P, node(Value, Left, Right), !Acc) :-
P(Value, !Acc), preorder(P, Left, !Acc), preorder(P, Right, !Acc).
- - pred inorder(pred(V, A, A), tree(V), A, A).
- - mode inorder(pred(in, di, uo) is det, in, di, uo) is det.
inorder(_, empty, !Acc). inorder(P, node(Value, Left, Right), !Acc) :-
inorder(P, Left, !Acc), P(Value, !Acc), inorder(P, Right, !Acc).
- - pred postorder(pred(V, A, A), tree(V), A, A).
- - mode postorder(pred(in, di, uo) is det, in, di, uo) is det.
postorder(_, empty, !Acc). postorder(P, node(Value, Left, Right), !Acc) :-
postorder(P, Left, !Acc), postorder(P, Right, !Acc), P(Value, !Acc).
- - pred levelorder(pred(V, A, A), tree(V), A, A).
- - mode levelorder(pred(in, di, uo) is det, in, di, uo) is det.
levelorder(P, Tree, !Acc) :-
do_levelorder(P, [Tree], !Acc).
- - pred do_levelorder(pred(V, A, A), list(tree(V)), A, A).
- - mode do_levelorder(pred(in, di, uo) is det, in, di, uo) is det.
do_levelorder(_, [], !Acc). do_levelorder(P, [empty | Xs], !Acc) :-
do_levelorder(P, Xs, !Acc).
do_levelorder(P, [node(Value, Left, Right) | Xs], !Acc) :-
P(Value, !Acc), do_levelorder(P, Xs ++ [Left, Right], !Acc).
- - func tree = tree(int).
tree =
node(1,
node(2,
node(4,
node(7, empty, empty),
empty
),
node(5, empty, empty)
),
node(3,
node(6,
node(8, empty, empty),
node(9, empty, empty)
),
empty
)
).
main(!IO) :-
io.write_string("preorder: " ,!IO),
preorder(print_value, tree, !IO), io.nl(!IO),
io.write_string("inorder: " ,!IO),
inorder(print_value, tree, !IO), io.nl(!IO),
io.write_string("postorder: " ,!IO),
postorder(print_value, tree, !IO), io.nl(!IO),
io.write_string("levelorder: " ,!IO),
levelorder(print_value, tree, !IO), io.nl(!IO).
- - pred print_value(V::in, io::di, io::uo) is det.
print_value(V, !IO) :-
io.print(V, !IO),
io.write_string(" ", !IO).</lang>
Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
Nim
<lang nim>import deques
type
Node[T] = ref object data: T left, right: Node[T]
proc newNode[T](data: T; left, right: Node[T] = nil): Node[T] =
Node[T](data: data, left: left, right: right)
proc preorder[T](n: Node[T]): seq[T] =
if n.isNil: @[] else: @[n.data] & preorder(n.left) & preorder(n.right)
proc inorder[T](n: Node[T]): seq[T] =
if n.isNil: @[] else: inorder(n.left) & @[n.data] & inorder(n.right)
proc postorder[T](n: Node[T]): seq[T] =
if n.isNil: @[] else: postorder(n.left) & postorder(n.right) & @[n.data]
proc levelorder[T](n: Node[T]): seq[T] =
var queue: Deque[Node[T]] queue.addLast(n) while queue.len > 0: let next = queue.popFirst() result.add next.data if not next.left.isNil: queue.addLast(next.left) if not next.right.isNil: queue.addLast(next.right)
let tree = 1.newNode(
2.newNode(
4.newNode(
7.newNode),
5.newNode),
3.newNode(
6.newNode(
8.newNode,
9.newNode)))
echo preorder tree echo inorder tree echo postorder tree echo levelorder tree</lang>
- Output:
@[1, 2, 4, 7, 5, 3, 6, 8, 9] @[7, 4, 2, 5, 1, 8, 6, 9, 3] @[7, 4, 5, 2, 8, 9, 6, 3, 1] @[1, 2, 3, 4, 5, 6, 7, 8, 9]
Objeck
<lang objeck> use Collection;
class Test {
function : Main(args : String[]) ~ Nil {
one := Node->New(1);
two := Node->New(2);
three := Node->New(3);
four := Node->New(4);
five := Node->New(5);
six := Node->New(6);
seven := Node->New(7);
eight := Node->New(8);
nine := Node->New(9);
one->SetLeft(two); one->SetRight(three); two->SetLeft(four); two->SetRight(five); three->SetLeft(six); four->SetLeft(seven); six->SetLeft(eight); six->SetRight(nine); "Preorder: "->Print(); Preorder(one); "\nInorder: "->Print(); Inorder(one); "\nPostorder: "->Print(); Postorder(one); "\nLevelorder: "->Print(); Levelorder(one); "\n"->Print(); }
function : Preorder(node : Node) ~ Nil {
if(node <> Nil) {
System.IO.Console->Print(node->GetData())->Print(", ");
Preorder(node->GetLeft());
Preorder(node->GetRight());
};
}
function : Inorder(node : Node) ~ Nil {
if(node <> Nil) {
Inorder(node->GetLeft());
System.IO.Console->Print(node->GetData())->Print(", ");
Inorder(node->GetRight());
};
}
function : Postorder(node : Node) ~ Nil {
if(node <> Nil) {
Postorder(node->GetLeft());
Postorder(node->GetRight());
System.IO.Console->Print(node->GetData())->Print(", ");
};
}
function : Levelorder(node : Node) ~ Nil {
nodequeue := Collection.Queue->New();
if(node <> Nil) {
nodequeue->Add(node);
};
while(nodequeue->IsEmpty() = false) {
next := nodequeue->Remove()->As(Node);
System.IO.Console->Print(next->GetData())->Print(", ");
if(next->GetLeft() <> Nil) {
nodequeue->Add(next->GetLeft());
};
if(next->GetRight() <> Nil) {
nodequeue->Add(next->GetRight());
};
};
}
}
class Node from BasicCompare {
@left : Node; @right : Node; @data : Int;
New(data : Int) {
Parent();
@data := data;
}
method : public : GetData() ~ Int {
return @data;
}
method : public : SetLeft(left : Node) ~ Nil {
@left := left;
}
method : public : GetLeft() ~ Node {
return @left;
}
method : public : SetRight(right : Node) ~ Nil {
@right := right;
}
method : public : GetRight() ~ Node {
return @right;
}
method : public : Compare(rhs : Compare) ~ Int {
right : Node := rhs->As(Node);
if(@data = right->GetData()) {
return 0;
}
else if(@data < right->GetData()) {
return -1;
};
return 1;
}
} </lang>
Output:
Preorder: 1, 2, 4, 7, 5, 3, 6, 8, 9, Inorder: 7, 4, 2, 5, 1, 8, 6, 9, 3, Postorder: 7, 4, 5, 2, 8, 9, 6, 3, 1, Levelorder: 1, 2, 3, 4, 5, 6, 7, 8, 9,
OCaml
<lang ocaml>type 'a tree = Empty
| Node of 'a * 'a tree * 'a tree
let rec preorder f = function
Empty -> ()
| Node (v,l,r) -> f v;
preorder f l;
preorder f r
let rec inorder f = function
Empty -> ()
| Node (v,l,r) -> inorder f l;
f v;
inorder f r
let rec postorder f = function
Empty -> ()
| Node (v,l,r) -> postorder f l;
postorder f r;
f v
let levelorder f x =
let queue = Queue.create () in
Queue.add x queue;
while not (Queue.is_empty queue) do
match Queue.take queue with
Empty -> ()
| Node (v,l,r) -> f v;
Queue.add l queue;
Queue.add r queue
done
let tree =
Node (1,
Node (2,
Node (4,
Node (7, Empty, Empty),
Empty),
Node (5, Empty, Empty)),
Node (3,
Node (6,
Node (8, Empty, Empty),
Node (9, Empty, Empty)),
Empty))
let () =
preorder (Printf.printf "%d ") tree; print_newline (); inorder (Printf.printf "%d ") tree; print_newline (); postorder (Printf.printf "%d ") tree; print_newline (); levelorder (Printf.printf "%d ") tree; print_newline ()</lang>
Output:
1 2 4 7 5 3 6 8 9 7 4 2 5 1 8 6 9 3 2 4 7 5 3 6 8 9 1 1 2 3 4 5 6 7 8 9
Oforth
<lang Oforth>Object Class new: Tree(v, l, r)
Tree method: initialize(v, l, r) v := v l := l r := r ; Tree method: v @v ; Tree method: l @l ; Tree method: r @r ;
Tree method: preOrder(f)
@v f perform @l ifNotNull: [ @l preOrder(f) ] @r ifNotNull: [ @r preOrder(f) ] ;
Tree method: inOrder(f)
@l ifNotNull: [ @l inOrder(f) ] @v f perform @r ifNotNull: [ @r inOrder(f) ] ;
Tree method: postOrder(f)
@l ifNotNull: [ @l postOrder(f) ] @r ifNotNull: [ @r postOrder(f) ] @v f perform ;
Tree method: levelOrder(f) | c n |
Channel new self over send drop ->c
while(c notEmpty) [
c receive ->n
n v f perform
n l dup ifNotNull: [ c send ] drop
n r dup ifNotNull: [ c send ] drop
] ;</lang>
- Output:
>Tree new(3, Tree new(6, Tree new(8, null, null), Tree new(9, null, null)), null) ok >Tree new(2, Tree new(4, Tree new(7, null, null), null), Tree new(5, null, null)) ok >1 Tree new ok > ok >dup preOrder(#.) 1 2 4 7 5 3 6 8 9 ok >dup inOrder(#.) 7 4 2 5 1 8 6 9 3 ok >dup postOrder(#.) 7 4 5 2 8 9 6 3 1 ok >dup levelOrder(#.) 1 2 3 4 5 6 7 8 9 ok
ooRexx
<lang ooRexx>
one = .Node~new(1); two = .Node~new(2); three = .Node~new(3); four = .Node~new(4); five = .Node~new(5); six = .Node~new(6); seven = .Node~new(7); eight = .Node~new(8); nine = .Node~new(9);
one~left = two one~right = three two~left = four two~right = five three~left = six four~left = seven six~left = eight six~right = nine
out = .array~new
.treetraverser~preorder(one, out);
say "Preorder: " out~toString("l", ", ")
out~empty
.treetraverser~inorder(one, out);
say "Inorder: " out~toString("l", ", ")
out~empty
.treetraverser~postorder(one, out);
say "Postorder: " out~toString("l", ", ")
out~empty
.treetraverser~levelorder(one, out);
say "Levelorder:" out~toString("l", ", ")
- class node
- method init
expose left right data use strict arg data left = .nil right = .nil
- attribute left
- attribute right
- attribute data
- class treeTraverser
- method preorder class
use arg node, out
if node \== .nil then do
out~append(node~data)
self~preorder(node~left, out)
self~preorder(node~right, out)
end
- method inorder class
use arg node, out
if node \== .nil then do
self~inorder(node~left, out)
out~append(node~data)
self~inorder(node~right, out)
end
- method postorder class
use arg node, out
if node \== .nil then do
self~postorder(node~left, out)
self~postorder(node~right, out)
out~append(node~data)
end
- method levelorder class
use arg node, out
if node == .nil then return
nodequeue = .queue~new
nodequeue~queue(node)
loop while \nodequeue~isEmpty
next = nodequeue~pull
out~append(next~data)
if next~left \= .nil then
nodequeue~queue(next~left)
if next~right \= .nil then
nodequeue~queue(next~right)
end
</lang> Output:
Preorder: 1, 2, 4, 7, 5, 3, 6, 8, 9 Inorder: 7, 4, 2, 5, 1, 8, 6, 9, 3 Postorder: 7, 4, 5, 2, 8, 9, 6, 3, 1 Levelorder: 1, 2, 3, 4, 5, 6, 7, 8, 9
Oz
<lang oz>declare
Tree = n(1
n(2
n(4 n(7 e e) e)
n(5 e e))
n(3
n(6 n(8 e e) n(9 e e))
e))
fun {Concat Xs}
{FoldR Xs Append nil}
end
fun {Preorder T}
case T of e then nil
[] n(V L R) then
{Concat [[V]
{Preorder L}
{Preorder R}]}
end
end
fun {Inorder T}
case T of e then nil
[] n(V L R) then
{Concat [{Inorder L}
[V]
{Inorder R}]}
end
end
fun {Postorder T}
case T of e then nil
[] n(V L R) then
{Concat [{Postorder L}
{Postorder R}
[V]]}
end
end
local
fun {Collect Queue}
case Queue of nil then nil
[] e|Xr then {Collect Xr}
[] n(V L R)|Xr then
V|{Collect {Append Xr [L R]}}
end
end
in
fun {Levelorder T}
{Collect [T]}
end
end
in
{Show {Preorder Tree}}
{Show {Inorder Tree}}
{Show {Postorder Tree}}
{Show {Levelorder Tree}}</lang>
Perl
Tree nodes are represented by 3-element arrays: [0] - the value; [1] - left child; [2] - right child. <lang perl>sub preorder { my $t = shift or return (); return ($t->[0], preorder($t->[1]), preorder($t->[2])); }
sub inorder { my $t = shift or return (); return (inorder($t->[1]), $t->[0], inorder($t->[2])); }
sub postorder { my $t = shift or return (); return (postorder($t->[1]), postorder($t->[2]), $t->[0]); }
sub depth { my @ret; my @a = ($_[0]); while (@a) { my $v = shift @a or next; push @ret, $v->[0]; push @a, @{$v}[1,2]; } return @ret; }
my $x = [1,[2,[4,[7]],[5]],[3,[6,[8],[9]]]];
print "pre: @{[preorder($x)]}\n"; print "in: @{[inorder($x)]}\n"; print "post: @{[postorder($x)]}\n"; print "depth: @{[depth($x)]}\n";</lang> Output:
pre: 1 2 4 7 5 3 6 8 9 in: 7 4 2 5 1 8 6 9 3 post: 7 4 5 2 8 9 6 3 1 depth: 1 2 3 4 5 6 7 8 9
Phix
Copy of Euphoria. This is included in the distribution as demo\rosetta\Tree_traversal.exw, which also contains a way to build such a nested structure, and thirdly a "flat list of nodes" tree, that allows more interesting options such as a tag sort.
constant VALUE = 1, LEFT = 2, RIGHT = 3 constant tree = {1, {2, {4, {7, 0, 0}, 0}, {5, 0, 0}}, {3, {6, {8, 0, 0}, {9, 0, 0}}, 0}} procedure preorder(object tree) if sequence(tree) then printf(1,"%d ",{tree[VALUE]}) preorder(tree[LEFT]) preorder(tree[RIGHT]) end if end procedure procedure inorder(object tree) if sequence(tree) then inorder(tree[LEFT]) printf(1,"%d ",{tree[VALUE]}) inorder(tree[RIGHT]) end if end procedure procedure postorder(object tree) if sequence(tree) then postorder(tree[LEFT]) postorder(tree[RIGHT]) printf(1,"%d ",{tree[VALUE]}) end if end procedure procedure level_order(object tree, sequence more = {}) if sequence(tree) then more &= {tree[LEFT],tree[RIGHT]} printf(1,"%d ",{tree[VALUE]}) end if if length(more) > 0 then level_order(more[1],more[2..$]) end if end procedure puts(1,"\n preorder: ") preorder(tree) puts(1,"\n inorder: ") inorder(tree) puts(1,"\n postorder: ") postorder(tree) puts(1,"\n level-order: ") level_order(tree)
- Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
PHP
<lang PHP>class Node {
private $left; private $right; private $value;
function __construct($value) {
$this->value = $value;
}
public function getLeft() {
return $this->left;
}
public function getRight() {
return $this->right;
}
public function getValue() {
return $this->value;
}
public function setLeft($value) {
$this->left = $value;
}
public function setRight($value) {
$this->right = $value;
}
public function setValue($value) {
$this->value = $value;
}
}
class TreeTraversal {
public function preOrder(Node $n) {
echo $n->getValue() . " ";
if($n->getLeft() != null) {
$this->preOrder($n->getLeft());
}
if($n->getRight() != null){
$this->preOrder($n->getRight());
}
}
public function inOrder(Node $n) {
if($n->getLeft() != null) {
$this->inOrder($n->getLeft());
}
echo $n->getValue() . " ";
if($n->getRight() != null){
$this->inOrder($n->getRight());
}
}
public function postOrder(Node $n) {
if($n->getLeft() != null) {
$this->postOrder($n->getLeft());
}
if($n->getRight() != null){
$this->postOrder($n->getRight());
}
echo $n->getValue() . " ";
}
public function levelOrder($arg) {
$q[] = $arg;
while (!empty($q)) {
$n = array_shift($q);
echo $n->getValue() . " ";
if($n->getLeft() != null) {
$q[] = $n->getLeft();
}
if($n->getRight() != null){
$q[] = $n->getRight();
}
}
}
}
$arr = []; for ($i=1; $i < 10; $i++) {
$arr[$i] = new Node($i);
}
$arr[6]->setLeft($arr[8]); $arr[6]->setRight($arr[9]); $arr[3]->setLeft($arr[6]); $arr[4]->setLeft($arr[7]); $arr[2]->setLeft($arr[4]); $arr[2]->setRight($arr[5]); $arr[1]->setLeft($arr[2]); $arr[1]->setRight($arr[3]);
$tree = new TreeTraversal($arr);
echo "preorder:\t"; $tree->preOrder($arr[1]); echo "\ninorder:\t"; $tree->inOrder($arr[1]); echo "\npostorder:\t"; $tree->postOrder($arr[1]); echo "\nlevel-order:\t"; $tree->levelOrder($arr[1]);</lang> Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
PicoLisp
<lang PicoLisp>(de preorder (Node Fun)
(when Node
(Fun (car Node))
(preorder (cadr Node) Fun)
(preorder (caddr Node) Fun) ) )
(de inorder (Node Fun)
(when Node
(inorder (cadr Node) Fun)
(Fun (car Node))
(inorder (caddr Node) Fun) ) )
(de postorder (Node Fun)
(when Node
(postorder (cadr Node) Fun)
(postorder (caddr Node) Fun)
(Fun (car Node)) ) )
(de level-order (Node Fun)
(for (Q (circ Node) Q)
(let N (fifo 'Q)
(Fun (car N))
(and (cadr N) (fifo 'Q @))
(and (caddr N) (fifo 'Q @)) ) ) )
(setq *Tree
(1
(2 (4 (7)) (5))
(3 (6 (8) (9))) ) )
(for Order '(preorder inorder postorder level-order)
(prin (align -13 (pack Order ":"))) (Order *Tree printsp) (prinl) )</lang>
Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
Prolog
Works with SWI-Prolog. <lang Prolog>tree :- Tree= [1, [2, [4, [7, nil, nil], nil], [5, nil, nil]], [3, [6, [8, nil, nil], [9,nil, nil]], nil]],
write('preorder : '), preorder(Tree), nl, write('inorder : '), inorder(Tree), nl, write('postorder : '), postorder(Tree), nl, write('level-order : '), level_order([Tree]).
preorder(nil). preorder([Node, FG, FD]) :- format('~w ', [Node]), preorder(FG), preorder(FD).
inorder(nil).
inorder([Node, FG, FD]) :-
inorder(FG),
format('~w ', [Node]),
inorder(FD).
postorder(nil). postorder([Node, FG, FD]) :- postorder(FG), postorder(FD), format('~w ', [Node]).
level_order([]).
level_order(A) :- level_order_(A, U-U, S), level_order(S).
level_order_([], S-[],S).
level_order_([[Node, FG, FD] | T], CS, FS) :- format('~w ', [Node]), append_dl(CS, [FG, FD|U]-U, CS1), level_order_(T, CS1, FS).
level_order_([nil | T], CS, FS) :- level_order_(T, CS, FS).
append_dl(X-Y, Y-Z, X-Z).
</lang>
Output :
?- tree. preorder : 1 2 4 7 5 3 6 8 9 inorder : 7 4 2 5 1 8 6 9 3 postorder : 7 4 5 2 8 9 6 3 1 level-order : 1 2 3 4 5 6 7 8 9 true .
PureBasic
<lang PureBasic>Structure node
value.i *left.node *right.node
EndStructure
Structure queue
List q.i()
EndStructure
DataSection
tree: Data.s "1(2(4(7),5),3(6(8,9)))"
EndDataSection
- Convenient routine to interpret string data to construct a tree of integers.
Procedure createTree(*n.node, *tPtr.Character)
Protected num.s, *l.node, *ntPtr.Character
Repeat
Select *tPtr\c
Case '0' To '9'
num + Chr(*tPtr\c)
Case '('
*n\value = Val(num): num = ""
*ntPtr = *tPtr + 1
If *ntPtr\c = ','
ProcedureReturn *tPtr
Else
*l = AllocateMemory(SizeOf(node))
*n\left = *l: *tPtr = createTree(*l, *ntPtr)
EndIf
Case ')', ',', #Null
If num: *n\value = Val(num): EndIf
ProcedureReturn *tPtr
EndSelect
If *tPtr\c = ','
*l = AllocateMemory(SizeOf(node)):
*n\right = *l: *tPtr = createTree(*l, *tPtr + 1)
EndIf
*tPtr + 1
ForEver
EndProcedure
Procedure enqueue(List q.i(), element)
LastElement(q()) AddElement(q()) q() = element
EndProcedure
Procedure dequeue(List q.i())
Protected element If FirstElement(q()) element = q() DeleteElement(q()) EndIf ProcedureReturn element
EndProcedure
Procedure onVisit(*n.node)
Print(Str(*n\value) + " ")
EndProcedure
Procedure preorder(*n.node) ;recursive
onVisit(*n) If *n\left preorder(*n\left) EndIf If *n\right preorder(*n\right) EndIf
EndProcedure
Procedure inorder(*n.node) ;recursive
If *n\left inorder(*n\left) EndIf onVisit(*n) If *n\right inorder(*n\right) EndIf
EndProcedure
Procedure postorder(*n.node) ;recursive
If *n\left postorder(*n\left) EndIf If *n\right postorder(*n\right) EndIf onVisit(*n)
EndProcedure
Procedure levelorder(*n.node)
Dim q.queue(1)
Protected readQueue = 1, writeQueue, *currNode.node
enqueue(q(writeQueue)\q(),*n) ;start queue off with root
Repeat
readQueue ! 1: writeQueue ! 1
While ListSize(q(readQueue)\q())
*currNode = dequeue(q(readQueue)\q())
If *currNode\left
enqueue(q(writeQueue)\q(),*currNode\left)
EndIf
If *currNode\right
enqueue(q(writeQueue)\q(),*currNode\right)
EndIf
onVisit(*currNode)
Wend
Until ListSize(q(writeQueue)\q()) = 0
EndProcedure
If OpenConsole()
Define root.node
createTree(root,?tree)
Print("preorder: ")
preorder(root)
PrintN("")
Print("inorder: ")
inorder(root)
PrintN("")
Print("postorder: ")
postorder(root)
PrintN("")
Print("levelorder: ")
levelorder(root)
PrintN("")
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
Input()
CloseConsole()
EndIf</lang> Sample output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
Python
Python: Procedural
<lang python>from collections import namedtuple
Node = namedtuple('Node', 'data, left, right') tree = Node(1,
Node(2,
Node(4,
Node(7, None, None),
None),
Node(5, None, None)),
Node(3,
Node(6,
Node(8, None, None),
Node(9, None, None)),
None))
def printwithspace(i):
print(i, end=' ')
def dfs(order, node, visitor):
if node is not None:
for action in order:
if action == 'N':
visitor(node.data)
elif action == 'L':
dfs(order, node.left, visitor)
elif action == 'R':
dfs(order, node.right, visitor)
def preorder(node, visitor = printwithspace):
dfs('NLR', node, visitor)
def inorder(node, visitor = printwithspace):
dfs('LNR', node, visitor)
def postorder(node, visitor = printwithspace):
dfs('LRN', node, visitor)
def ls(node, more, visitor, order='TB'):
"Level-based Top-to-Bottom or Bottom-to-Top tree search"
if node:
if more is None:
more = []
more += [node.left, node.right]
for action in order:
if action == 'B' and more:
ls(more[0], more[1:], visitor, order)
elif action == 'T' and node:
visitor(node.data)
def levelorder(node, more=None, visitor = printwithspace):
ls(node, more, visitor, 'TB')
- Because we can
def reverse_preorder(node, visitor = printwithspace):
dfs('RLN', node, visitor)
def bottom_up_order(node, more=None, visitor = printwithspace, order='BT'):
ls(node, more, visitor, 'BT')
if __name__ == '__main__':
w = 10
for traversal in [preorder, inorder, postorder, levelorder,
reverse_preorder, bottom_up_order]:
if traversal == reverse_preorder:
w = 20
print('\nThe generalisation of function dfs allows:')
if traversal == bottom_up_order:
print('The generalisation of function ls allows:')
print(f"{traversal.__name__:>{w}}:", end=' ')
traversal(tree)
print()</lang>
Sample output:
preorder: 1 2 4 7 5 3 6 8 9
inorder: 7 4 2 5 1 8 6 9 3
postorder: 7 4 5 2 8 9 6 3 1
levelorder: 1 2 3 4 5 6 7 8 9
The generalisation of function dfs allows:
reverse_preorder: 9 8 6 3 5 7 4 2 1
The generalisation of function ls allows:
bottom_up_order: 9 8 7 6 5 4 3 2 1
Python: Class based
Subclasses a namedtuple adding traversal methods that apply a visitor function to data at nodes of the tree in order <lang python>from collections import namedtuple from sys import stdout
class Node(namedtuple('Node', 'data, left, right')):
__slots__ = ()
def preorder(self, visitor):
if self is not None:
visitor(self.data)
Node.preorder(self.left, visitor)
Node.preorder(self.right, visitor)
def inorder(self, visitor):
if self is not None:
Node.inorder(self.left, visitor)
visitor(self.data)
Node.inorder(self.right, visitor)
def postorder(self, visitor):
if self is not None:
Node.postorder(self.left, visitor)
Node.postorder(self.right, visitor)
visitor(self.data)
def levelorder(self, visitor, more=None):
if self is not None:
if more is None:
more = []
more += [self.left, self.right]
visitor(self.data)
if more:
Node.levelorder(more[0], visitor, more[1:])
def printwithspace(i):
stdout.write("%i " % i)
tree = Node(1,
Node(2,
Node(4,
Node(7, None, None),
None),
Node(5, None, None)),
Node(3,
Node(6,
Node(8, None, None),
Node(9, None, None)),
None))
if __name__ == '__main__':
stdout.write(' preorder: ')
tree.preorder(printwithspace)
stdout.write('\n inorder: ')
tree.inorder(printwithspace)
stdout.write('\n postorder: ')
tree.postorder(printwithspace)
stdout.write('\nlevelorder: ')
tree.levelorder(printwithspace)
stdout.write('\n')</lang>
- Output:
As above.
Python: Composition of pure (curried) functions
Currying by default is probably not particularly 'Pythonic', but it does work well with higher-order functions – giving us more flexibility in compositional structure. It also often protects us from over-proliferation of the slightly noisy lambda keyword. (See for example the use of the curried version of map in the code below).
The approach taken here is to focus on the evaluation of expressions, rather than the sequencing of procedures. To keep evaluation simple and easily rearranged, mutation is stripped back wherever possible, and 'pure' functions, with inputs and outputs but, ideally, with no side-effects (and no sensitivities to global variables) are the basic building-block.
Composing pure functions also works well with library-building and code reuse – the literature on functional programming (particularly in the ML / OCaml / Haskell tradition) is rich in reusable abstractions for our toolkit. Some of them have already been absorbed, with standard or adjusted names, into the Python itertools module. (See the itertools module preface, and the takewhile function below).
Here, for example, for the pre-, in- and post- orders, we can define a very general and reusable foldTree (a catamorphism over trees rather than lists) and just pass 3 different (rather simple) sequencing functions to it.
This level of abstraction and reuse brings real efficiencies – the short and easily-written foldTree, for example, doesn't just traverse and list contents in flexible orders - we can pass any kind of accumulation or tree-transformation to it.
<lang python>Tree traversals
from itertools import chain from functools import reduce from operator import mul
- foldTree :: (a -> [b] -> b) -> Tree a -> b
def foldTree(f):
The catamorphism on trees. A summary
value defined by a depth-first fold.
def go(node):
return f(root(node))([
go(x) for x in nest(node)
])
return go
- levels :: Tree a -> a
def levels(tree):
A list of lists, grouping the root
values of each level of the tree.
def go(a, node):
h, *t = a if a else ([], [])
return [[root(node)] + h] + reduce(
go, reversed(nest(node)), t
)
return go([], tree)
- preorder :: a -> a -> [a]
def preorder(x):
This node followed by the rest. return lambda xs: [x] + concat(xs)
- inorder :: a -> a -> [a]
def inorder(x):
Descendants of any first child,
then this node, then the rest.
return lambda xs: (
xs[0] + [x] + concat(xs[1:]) if xs else [x]
)
- postorder :: a -> a -> [a]
def postorder(x):
Descendants first, then this node. return lambda xs: concat(xs) + [x]
- levelorder :: Tree a -> [a]
def levelorder(tree):
Top-down concatenation of this node
with the rows below.
return concat(levels(tree))
- treeSum :: Int -> [Int] -> Int
def treeSum(x):
This node's value + the sum of its descendants. return lambda xs: x + sum(xs)
- treeProduct :: Int -> [Int] -> Int
def treeProduct(x):
This node's value * the product of its descendants. return lambda xs: x * numericProduct(xs)
- treeMax :: Ord a => a -> [a] -> a
def treeMax(x):
Maximum value of this node and any descendants. return lambda xs: max([x] + xs)
- treeMin :: Ord a => a -> [a] -> a
def treeMin(x):
Minimum value of this node and any descendants. return lambda xs: min([x] + xs)
- nodeCount :: Int -> [Int] -> Int
def nodeCount(_):
One more than the total number of descendants. return lambda xs: 1 + sum(xs)
- treeWidth :: Int -> [Int] -> Int
def treeWidth(_):
Sum of widths of any children, or a minimum of 1. return lambda xs: sum(xs) if xs else 1
- treeDepth :: Int -> [Int] -> Int
def treeDepth(_):
One more than that of the deepest child. return lambda xs: 1 + (max(xs) if xs else 0)
- ------------------------- TEST -------------------------
- main :: IO ()
def main():
Tree traversals - accumulating and folding
# tree :: Tree Int
tree = Node(1)([
Node(2)([
Node(4)([
Node(7)([])
]),
Node(5)([])
]),
Node(3)([
Node(6)([
Node(8)([]),
Node(9)([])
])
])
])
print(
fTable(main.__doc__ + ':\n')(fName)(str)(
lambda f: (
foldTree(f) if 'levelorder' != fName(f) else f
)(tree)
)([
preorder, inorder, postorder, levelorder,
treeSum, treeProduct, treeMin, treeMax,
nodeCount, treeWidth, treeDepth
])
)
- ----------------------- GENERIC ------------------------
- Node :: a -> [Tree a] -> Tree a
def Node(v):
Contructor for a Tree node which connects a
value of some kind to a list of zero or
more child trees.
return lambda xs: {
'type': 'Node', 'root': v, 'nest': xs
}
- nest :: Tree a -> [Tree a]
def nest(tree):
Accessor function for children of tree node return tree['nest'] if 'nest' in tree else None
- root :: Dict -> a
def root(tree):
Accessor function for data of tree node return tree['root'] if 'root' in tree else None
- concat :: a -> [a]
- concat :: [String] -> String
def concat(xxs):
The concatenation of all the elements in a list.
xs = list(chain.from_iterable(xxs))
unit = if isinstance(xs, str) else []
return unit if not xs else (
.join(xs) if isinstance(xs[0], str) else xs
)
- numericProduct :: [Num] -> Num
def numericProduct(xs):
The arithmetic product of all numbers in xs. return reduce(mul, xs, 1)
- ---------------------- FORMATTING ----------------------
- fName :: (a -> b) -> String
def fName(f):
The name bound to the function. return f.__name__
- fTable :: String -> (a -> String) ->
- (b -> String) ->
- (a -> b) -> [a] -> String
def fTable(s):
Heading -> x display function ->
fx display function -> f -> xs -> tabular string.
def go(xShow, fxShow, f, xs):
ys = [xShow(x) for x in xs]
w = max(map(len, ys))
return s + '\n' + '\n'.join(map(
lambda x, y: y.rjust(w, ' ') + (
' -> ' + fxShow(f(x))
),
xs, ys
))
return lambda xShow: lambda fxShow: (
lambda f: lambda xs: go(
xShow, fxShow, f, xs
)
)
if __name__ == '__main__':
main()</lang>
- Output:
Tree traversals - accumulating and folding:
preorder -> [1, 2, 4, 7, 5, 3, 6, 8, 9]
inorder -> [7, 4, 2, 5, 1, 8, 6, 9, 3]
postorder -> [7, 4, 5, 2, 8, 9, 6, 3, 1]
levelorder -> [1, 2, 3, 4, 5, 6, 7, 8, 9]
treeSum -> 45
treeProduct -> 362880
treeMin -> 1
treeMax -> 9
nodeCount -> 9
treeWidth -> 4
treeDepth -> 4
Qi
<lang qi> (set *tree* [1 [2 [4 [7]]
[5]]
[3 [6 [8]
[9]]]])
(define inorder
[] -> []
[V] -> [V]
[V L] -> (append (inorder L)
[V])
[V L R] -> (append (inorder L)
[V]
(inorder R)))
(define postorder
[] -> []
[V] -> [V]
[V L] -> (append (postorder L)
[V])
[V L R] -> (append (postorder L)
(postorder R)
[V]))
(define preorder
[] -> []
[V] -> [V]
[V L] -> (append [V]
(preorder L))
[V L R] -> (append [V]
(preorder L)
(preorder R)))
(define levelorder-0
[] -> [] [[] | Q] -> (levelorder-0 Q) [[V | LR] | Q] -> [V | (levelorder-0 (append Q LR))])
(define levelorder
Node -> (levelorder-0 [Node]))
(preorder (value *tree*)) (postorder (value *tree*)) (inorder (value *tree*)) (levelorder (value *tree*)) </lang>
Output:
[1 2 4 7 5 3 6 8 9] [7 4 2 5 1 8 6 9 3] [7 4 5 2 8 9 6 3 1] [1 2 3 4 5 6 7 8 9]
Racket
<lang racket>
- lang racket
(define the-tree ; Node: (list <left> <right>)
'(1 (2 (4 (7 #f #f) #f) (5 #f #f)) (3 (6 (8 #f #f) (9 #f #f)) #f)))
(define (preorder tree visit)
(let loop ([t tree]) (when t (visit (car t)) (loop (cadr t)) (loop (caddr t)))))
(define (inorder tree visit)
(let loop ([t tree]) (when t (loop (cadr t)) (visit (car t)) (loop (caddr t)))))
(define (postorder tree visit)
(let loop ([t tree]) (when t (loop (cadr t)) (loop (caddr t)) (visit (car t)))))
(define (levelorder tree visit)
(let loop ([trees (list tree)])
(unless (null? trees)
((compose1 loop (curry filter values) append*)
(for/list ([t trees] #:when t) (visit (car t)) (cdr t))))))
(define (run order)
(printf "~a:" (object-name order)) (order the-tree (λ(x) (printf " ~s" x))) (newline))
(for-each run (list preorder inorder postorder levelorder)) </lang>
Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
Raku
(formerly Perl 6) <lang perl6>class TreeNode {
has TreeNode $.parent; has TreeNode $.left; has TreeNode $.right; has $.value;
method pre-order {
flat gather {
take $.value;
take $.left.pre-order if $.left;
take $.right.pre-order if $.right
}
}
method in-order {
flat gather {
take $.left.in-order if $.left;
take $.value;
take $.right.in-order if $.right;
}
}
method post-order {
flat gather {
take $.left.post-order if $.left;
take $.right.post-order if $.right;
take $.value;
}
}
method level-order {
my TreeNode @queue = (self);
flat gather while @queue.elems {
my $n = @queue.shift;
take $n.value;
@queue.push($n.left) if $n.left;
@queue.push($n.right) if $n.right;
}
}
}
my TreeNode $root .= new( value => 1,
left => TreeNode.new( value => 2,
left => TreeNode.new( value => 4, left => TreeNode.new(value => 7)),
right => TreeNode.new( value => 5)
),
right => TreeNode.new( value => 3,
left => TreeNode.new( value => 6,
left => TreeNode.new(value => 8),
right => TreeNode.new(value => 9)
)
)
);
say "preorder: ",$root.pre-order.join(" "); say "inorder: ",$root.in-order.join(" "); say "postorder: ",$root.post-order.join(" "); say "levelorder:",$root.level-order.join(" ");</lang>
- Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder:1 2 3 4 5 6 7 8 9
REXX
<lang rexx> /* REXX ***************************************************************
- Tree traversal
= 1 = / \ = / \ = / \ = 2 3 = / \ / = 4 5 6 = / / \ = 7 8 9 = = The correct output should look like this: = preorder: 1 2 4 7 5 3 6 8 9 = level-order: 1 2 3 4 5 6 7 8 9 = postorder: 7 4 5 2 8 9 6 3 1 = inorder: 7 4 2 5 1 8 6 9 3
- 17.06.2012 Walter Pachl not thoroughly tested
- /
debug=0 wl_soll=1 2 4 7 5 3 6 8 9 il_soll=7 4 2 5 1 8 6 9 3 pl_soll=7 4 5 2 8 9 6 3 1 ll_soll=1 2 3 4 5 6 7 8 9
Call mktree wl.=; wl= /* preorder */ ll.=; ll= /* level-order */
il= /* inorder */
pl= /* postorder */
/**********************************************************************
- First walk the tree and construct preorder and level-order lists
- /
done.=0 lvl=1 z=root Call note z Do Until z=0
z=go_next(z) Call note z End
Call show 'preorder: ',wl,wl_soll Do lvl=1 To 4
ll=ll ll.lvl End
Call show 'level-order:',ll,ll_soll
/**********************************************************************
- Next construct postorder list
- /
done.=0 ridone.=0 z=lbot(root) Call notep z Do Until z=0
br=brother(z)
If br>0 &,
done.br=0 Then Do
ridone.br=1
z=lbot(br)
Call notep z
End
Else
z=father(z)
Call notep z
End
Call show 'postorder: ',pl,pl_soll
/**********************************************************************
- Finally construct inorder list
- /
done.=0 ridone.=0 z=lbot(root) Call notei z Do Until z=0
z=father(z)
Call notei z
ri=node.z.0rite
If ridone.z=0 Then Do
ridone.z=1
If ri>0 Then Do
z=lbot(ri)
Call notei z
End
End
End
/**********************************************************************
- And now show the results and check them for correctness
- /
Call show 'inorder: ',il,il_soll
Exit
show: Parse Arg Which,have,soll /**********************************************************************
- Show our result and show it it's correct
- /
have=space(have) If have=soll Then
tag=
Else
tag='*wrong*'
Say which have tag If tag<> Then
Say '------------>'soll 'is the expected result'
Return
brother: Procedure Expose node. /**********************************************************************
- Return the right node of this node's father or 0
- /
Parse arg no nof=node.no.0father brot1=node.nof.0rite Return brot1
notei: Procedure Expose debug il done. /**********************************************************************
- append the given node to il
- /
Parse Arg nd
If nd<>0 &,
done.nd=0 Then
il=il nd
If debug Then
Say 'notei' nd
done.nd=1
Return
notep: Procedure Expose debug pl done. /**********************************************************************
- append the given node to pl
- /
Parse Arg nd
If nd<>0 &,
done.nd=0 Then Do
pl=pl nd
If debug Then
Say 'notep' nd
End
done.nd=1
Return
father: Procedure Expose node. /**********************************************************************
- Return the father of the argument
- or 0 if the root is given as argument
- /
Parse Arg nd Return node.nd.0father
lbot: Procedure Expose node. /**********************************************************************
- From node z: Walk down on the left side until you reach the bottom
- and return the bottom node
- If z has no left son (at the bottom of the tree) returm itself
- /
Parse Arg z
Do i=1 To 100
If node.z.0left<>0 Then
z=node.z.0left
Else
Leave
End
Return z
note: /**********************************************************************
- add the node to the preorder list unless it's already there
- add the node to the level list
- /
If z<>0 &, /* it's a node */
done.z=0 Then Do /* not yet done */
wl=wl z /* add it to the preorder list*/
ll.lvl=ll.lvl z /* add it to the level list */
done.z=1 /* remember it's done */
End
Return
go_next: Procedure Expose node. lvl /**********************************************************************
- find the next node to visit in the treewalk
- /
next=0
Parse arg z
If node.z.0left<>0 Then Do /* there is a left son */
If node.z.0left.done=0 Then Do /* we have not visited it */
next=node.z.0left /* so we go there */
node.z.0left.done=1 /* note we were here */
lvl=lvl+1 /* increase the level */
End
End
If next=0 Then Do /* not moved yet */
If node.z.0rite<>0 Then Do /* there is a right son */
If node.z.0rite.done=0 Then Do /* we have not visited it */
next=node.z.0rite /* so we go there */
node.z.0rite.done=1 /* note we were here */
lvl=lvl+1 /* increase the level */
End
End
End
If next=0 Then Do /* not moved yet */
next=node.z.0father /* go to the father */
lvl=lvl-1 /* decrease the level */
End
Return next /* that's the next node */
/* or zero if we are done */
mknode: Procedure Expose node. /**********************************************************************
- create a new node
- /
Parse Arg name z=node.0+1 node.z.0name=name node.z.0father=0 node.z.0left =0 node.z.0rite =0 node.0=z Return z /* number of the node just created */
attleft: Procedure Expose node. /**********************************************************************
- make son the left son of father
- /
Parse Arg son,father node.son.0father=father z=node.father.0left If z<>0 Then Do node.z.0father=son node.son.0left=z End node.father.0left=son Return
attrite: Procedure Expose node. /**********************************************************************
- make son the right son of father
- /
Parse Arg son,father node.son.0father=father z=node.father.0rite If z<>0 Then Do node.z.0father=son node.son.0rite=z End node.father.0rite=son le=node.father.0left If le>0 Then node.le.0brother=node.father.0rite Return
mktree: Procedure Expose node. root /**********************************************************************
- build the tree according to the task
- /
node.=0
a=mknode('A'); root=a
b=mknode('B'); Call attleft b,a
c=mknode('C'); Call attrite c,a
d=mknode('D'); Call attleft d,b
e=mknode('E'); Call attrite e,b
f=mknode('F'); Call attleft f,c
g=mknode('G'); Call attleft g,d
h=mknode('H'); Call attleft h,f
i=mknode('I'); Call attrite i,f
Call show_tree 1
Return
show_tree: Procedure Expose node. /**********************************************************************
- Show the tree
- f
- l1 1 r1
- l r l r
- l r l r l r l r
- 12345678901234567890
- /
Parse Arg f
l.=
l.1=overlay(f ,l.1, 9)
l1=node.f.0left ;l.2=overlay(l1 ,l.2, 5)
/*b1=node.f.0brother ;l.2=overlay(b1 ,l.2, 9) */
r1=node.f.0rite ;l.2=overlay(r1 ,l.2,13)
l1g=node.l1.0left ;l.3=overlay(l1g ,l.3, 3)
/*b1g=node.l1.0brother ;l.3=overlay(b1g ,l.3, 5) */
r1g=node.l1.0rite ;l.3=overlay(r1g ,l.3, 7)
l2g=node.r1.0left ;l.3=overlay(l2g ,l.3,11)
/*b2g=node.r1.0brother ;l.3=overlay(b2g ,l.3,13) */
r2g=node.r1.0rite ;l.3=overlay(r2g ,l.3,15)
l1ls=node.l1g.0left ;l.4=overlay(l1ls,l.4, 2)
/*b1ls=node.l1g.0brother ;l.4=overlay(b1ls,l.4, 3) */
r1ls=node.l1g.0rite ;l.4=overlay(r1ls,l.4, 4)
l1rs=node.r1g.0left ;l.4=overlay(l1rs,l.4, 6)
/*b1rs=node.r1g.0brother ;l.4=overlay(b1rs,l.4, 7) */
r1rs=node.r1g.0rite ;l.4=overlay(r1rs,l.4, 8)
l2ls=node.l2g.0left ;l.4=overlay(l2ls,l.4,10)
/*b2ls=node.l2g.0brother ;l.4=overlay(b2ls,l.4,11) */
r2ls=node.l2g.0rite ;l.4=overlay(r2ls,l.4,12)
l2rs=node.r2g.0left ;l.4=overlay(l2rs,l.4,14)
/*b2rs=node.r2g.0brother ;l.4=overlay(b2rs,l.4,15) */
r2rs=node.r2g.0rite ;l.4=overlay(r2rs,l.4,16) Do i=1 To 4 Say translate(l.i,' ','0') Say End Return</lang>
- Output:
1
2 3
4 5 6
7 8 9
preorder: 1 2 4 7 5 3 6 8 9
level-order: 1 2 3 4 5 6 7 8 9
postorder: 7 4 5 2 8 9 6 3 1
inorder: 7 4 2 5 1 8 6 9 3
Ruby
<lang ruby>BinaryTreeNode = Struct.new(:value, :left, :right) do
def self.from_array(nested_list)
value, left, right = nested_list
if value
self.new(value, self.from_array(left), self.from_array(right))
end
end
def walk_nodes(order, &block)
order.each do |node|
case node
when :left then left && left.walk_nodes(order, &block)
when :self then yield self
when :right then right && right.walk_nodes(order, &block)
end
end
end
def each_preorder(&b) walk_nodes([:self, :left, :right], &b) end
def each_inorder(&b) walk_nodes([:left, :self, :right], &b) end
def each_postorder(&b) walk_nodes([:left, :right, :self], &b) end
def each_levelorder
queue = [self]
until queue.empty?
node = queue.shift
yield node
queue << node.left if node.left
queue << node.right if node.right
end
end
end
root = BinaryTreeNode.from_array [1, [2, [4, 7], [5]], [3, [6, [8], [9]]]]
BinaryTreeNode.instance_methods.select{|m| m=~/.+order/}.each do |mthd|
printf "%-11s ", mthd[5..-1] + ':'
root.send(mthd) {|node| print "#{node.value} "}
puts
end</lang>
- Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
Rust
This solution uses iteration (rather than recursion) for all traversal types. <lang Rust>
- ![feature(box_syntax, box_patterns)]
use std::collections::VecDeque;
- [derive(Debug)]
struct TreeNode<T> {
value: T, left: Option<Box<TreeNode<T>>>, right: Option<Box<TreeNode<T>>>,
}
enum TraversalMethod {
PreOrder, InOrder, PostOrder, LevelOrder,
}
impl<T> TreeNode<T> {
pub fn new(arr: &i8; 3) -> TreeNode<i8> {
let l = match arr[0][1] {
-1 => None,
i @ _ => Some(Box::new(TreeNode::<i8>::new(&arr[(i - arr[0][0]) as usize..]))),
};
let r = match arr[0][2] {
-1 => None,
i @ _ => Some(Box::new(TreeNode::<i8>::new(&arr[(i - arr[0][0]) as usize..]))),
};
TreeNode {
value: arr[0][0],
left: l,
right: r,
}
}
pub fn traverse(&self, tr: &TraversalMethod) -> Vec<&TreeNode<T>> {
match tr {
&TraversalMethod::PreOrder => self.iterative_preorder(),
&TraversalMethod::InOrder => self.iterative_inorder(),
&TraversalMethod::PostOrder => self.iterative_postorder(),
&TraversalMethod::LevelOrder => self.iterative_levelorder(),
}
}
fn iterative_preorder(&self) -> Vec<&TreeNode<T>> {
let mut stack: Vec<&TreeNode<T>> = Vec::new();
let mut res: Vec<&TreeNode<T>> = Vec::new();
stack.push(self);
while !stack.is_empty() {
let node = stack.pop().unwrap();
res.push(node);
match node.right {
None => {}
Some(box ref n) => stack.push(n),
}
match node.left {
None => {}
Some(box ref n) => stack.push(n),
}
}
res
}
// Leftmost to rightmost
fn iterative_inorder(&self) -> Vec<&TreeNode<T>> {
let mut stack: Vec<&TreeNode<T>> = Vec::new();
let mut res: Vec<&TreeNode<T>> = Vec::new();
let mut p = self;
loop {
// Stack parents and right children while left-descending
loop {
match p.right {
None => {}
Some(box ref n) => stack.push(n),
}
stack.push(p);
match p.left {
None => break,
Some(box ref n) => p = n,
}
}
// Visit the nodes with no right child
p = stack.pop().unwrap();
while !stack.is_empty() && p.right.is_none() {
res.push(p);
p = stack.pop().unwrap();
}
// First node that can potentially have a right child:
res.push(p);
if stack.is_empty() {
break;
} else {
p = stack.pop().unwrap();
}
}
res
}
// Left-to-right postorder is same sequence as right-to-left preorder, reversed
fn iterative_postorder(&self) -> Vec<&TreeNode<T>> {
let mut stack: Vec<&TreeNode<T>> = Vec::new();
let mut res: Vec<&TreeNode<T>> = Vec::new();
stack.push(self);
while !stack.is_empty() {
let node = stack.pop().unwrap();
res.push(node);
match node.left {
None => {}
Some(box ref n) => stack.push(n),
}
match node.right {
None => {}
Some(box ref n) => stack.push(n),
}
}
let rev_iter = res.iter().rev();
let mut rev: Vec<&TreeNode<T>> = Vec::new();
for elem in rev_iter {
rev.push(elem);
}
rev
}
fn iterative_levelorder(&self) -> Vec<&TreeNode<T>> {
let mut queue: VecDeque<&TreeNode<T>> = VecDeque::new();
let mut res: Vec<&TreeNode<T>> = Vec::new();
queue.push_back(self);
while !queue.is_empty() {
let node = queue.pop_front().unwrap();
res.push(node);
match node.left {
None => {}
Some(box ref n) => queue.push_back(n),
}
match node.right {
None => {}
Some(box ref n) => queue.push_back(n),
}
}
res
}
}
fn main() {
// Array representation of task tree
let arr_tree = [[1, 2, 3],
[2, 4, 5],
[3, 6, -1],
[4, 7, -1],
[5, -1, -1],
[6, 8, 9],
[7, -1, -1],
[8, -1, -1],
[9, -1, -1]];
let root = TreeNode::<i8>::new(&arr_tree);
for method_label in [(TraversalMethod::PreOrder, "pre-order:"),
(TraversalMethod::InOrder, "in-order:"),
(TraversalMethod::PostOrder, "post-order:"),
(TraversalMethod::LevelOrder, "level-order:")]
.iter() {
print!("{}\t", method_label.1);
for n in root.traverse(&method_label.0) {
print!(" {}", n.value);
}
print!("\n");
}
} </lang> Output is same as Ruby et al.
Scala
<lang Scala>case class IntNode(value: Int, left: Option[IntNode] = None, right: Option[IntNode] = None) {
def preorder(f: IntNode => Unit) {
f(this)
left.map(_.preorder(f)) // Same as: if(left.isDefined) left.get.preorder(f)
right.map(_.preorder(f))
}
def postorder(f: IntNode => Unit) {
left.map(_.postorder(f))
right.map(_.postorder(f))
f(this)
}
def inorder(f: IntNode => Unit) {
left.map(_.inorder(f))
f(this)
right.map(_.inorder(f))
}
def levelorder(f: IntNode => Unit) {
def loVisit(ls: List[IntNode]): Unit = ls match {
case Nil => None
case node :: rest => f(node); loVisit(rest ++ node.left ++ node.right)
}
loVisit(List(this)) }
}
object TreeTraversal extends App {
implicit def intNode2SomeIntNode(n: IntNode) = Some[IntNode](n)
val tree = IntNode(1,
IntNode(2,
IntNode(4,
IntNode(7)),
IntNode(5)),
IntNode(3,
IntNode(6,
IntNode(8),
IntNode(9))))
List(
" preorder: " -> tree.preorder _, // `_` denotes the function value of type `IntNode => Unit` (returning nothing)
" inorder: " -> tree.inorder _,
" postorder: " -> tree.postorder _,
"levelorder: " -> tree.levelorder _) foreach {
case (name, func) =>
val s = new StringBuilder(name)
func(n => s ++= n.value.toString + " ")
println(s)
}
}</lang>
Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 levelorder: 1 2 3 4 5 6 7 8 9
SequenceL
<lang sequenceL> main(args(2)) :=
"preorder: " ++ toString(preOrder(testTree)) ++ "\ninoder: " ++ toString(inOrder(testTree)) ++ "\npostorder: " ++ toString(postOrder(testTree)) ++ "\nlevel-order: " ++ toString(levelOrder(testTree));
Node ::= (value : int, left : Node, right : Node);
preOrder(n) := [n.value] ++
(preOrder(n.left) when isDefined(n, left) else []) ++
(preOrder(n.right) when isDefined(n, right) else []);
inOrder(n) := (inOrder(n.left) when isDefined(n, left) else []) ++
[n.value] ++
(inOrder(n.right) when isDefined(n, right) else []);
postOrder(n) := (postOrder(n.left) when isDefined(n, left) else []) ++
(postOrder(n.right) when isDefined(n, right) else []) ++
[n.value];
levelOrder(n) := levelOrderHelper([n]); levelOrderHelper(ns(1)) :=
let
n := head(ns);
in
[] when size(ns) = 0 else
[n.value] ++ levelOrderHelper(tail(ns) ++
([n.left] when isDefined(n, left) else []) ++
([n.right] when isDefined(n, right) else []));
testTree :=
(value : 1,
left : (value : 2,
left : (value : 4,
left : (value : 7)),
right : (value : 5)),
right : (value : 3,
left : (value : 6,
left : (value : 8),
right : (value : 9))
)
);
</lang>
- Output:
Output:
preorder: [1,2,4,7,5,3,6,8,9] inoder: [7,4,2,5,1,8,6,9,3] postorder: [7,4,5,2,8,9,6,3,1] level-order: [1,2,3,4,5,6,7,8,9]
Sidef
<lang ruby>func preorder(t) {
t ? [t[0], __FUNC__(t[1])..., __FUNC__(t[2])...] : [];
}
func inorder(t) {
t ? [__FUNC__(t[1])..., t[0], __FUNC__(t[2])...] : [];
}
func postorder(t) {
t ? [__FUNC__(t[1])..., __FUNC__(t[2])..., t[0]] : [];
}
func depth(t) {
var a = [t];
var ret = [];
while (a.len > 0) {
var v = (a.shift \\ next);
ret « v[0];
a += [v[1,2]];
};
return ret;
}
var x = [1,[2,[4,[7]],[5]],[3,[6,[8],[9]]]]; say "pre: #{preorder(x)}"; say "in: #{inorder(x)}"; say "post: #{postorder(x)}"; say "depth: #{depth(x)}";</lang>
- Output:
pre: 1 2 4 7 5 3 6 8 9 in: 7 4 2 5 1 8 6 9 3 post: 7 4 5 2 8 9 6 3 1 depth: 1 2 3 4 5 6 7 8 9
Smalltalk
This solution relies on a binary tree that distinguishes between ordinary and empty nodes. Therefore, the tree can be traversed using a visitor pattern that uses a polymorphic access message. The traversal variants are implemented as subclasses of a generic visitor. The action to be performed with each (non-empty) node is provided as block to the traversal algorithm.
The code below is plain, human-readable code instead of a file-out of some specific Smalltalk dialect. It shows only the messages of each class but not its definition as they differ between dialects.
Object subclass: EmptyNode <lang smalltalk>"Protocol: visiting" EmptyNode>>accept: aVisitor
EmptyNode>>accept: aVisitor with: anObject ^anObject
"Protocol: enumerating" EmptyNode>>traverse: aVisitorClass do: aBlock ^self accept: (aVisitorClass block: aBlock) </lang>
EmptyNode subclass: Node <lang smalltalk>"Protocol: visiting" Node>>accept: aVisitor ^aVisitor visit: self
Node>>accept: aVisitor with: anObject ^aVisitor visit: self with: anObject
"Protocol: accessing" Node>>data ^data
Node>>data: anObject data := anObject
Node>>left ^left
Node>>left: aNode left := aNode
Node>>right ^right
Node>>right: aNode right := aNode
"Protocol: initialize-release" Node>>initialize super initialize. left := right := EmptyNode new
"Class side" "Protocol: instance creation" Node class>>data: anObject ^self new data: anObject </lang>
Object subclass: Visitor <lang smalltalk>"Protocol: visiting" visit: aNode self subclassResponsibility
"Protocol: accessing" Visitor>>block: anObject block := anObject
"Protocol: initialize-release" Visitor>>initialize super initialize. block := [:node | ]
"Class side" "Protocol: instance creation" Visitor class>>block: aBlock ^self new block: aBlock </lang>
Visitor subclass: InOrder <lang smalltalk>"Protocol: visiting" InOrder>>visit: aNode aNode left accept: self. block value: aNode. aNode right accept: self </lang>
Visitor subclass: LevelOrder <lang smalltalk>"Protocol: visiting" LevelOrder>>visit: aNode | queue | queue := OrderedCollection with: aNode. [(queue removeFirst accept: self with: queue) isEmpty] whileFalse
LevelOrder>>visit: aNode with: aQueue block value: aNode. ^aQueue add: aNode left; add: aNode right; yourself </lang>
Visitor subclass: PostOrder <lang smalltalk>"Protocol: visiting" PostOrder>>visit: aNode aNode left accept: self. aNode right accept: self. block value: aNode </lang>
"Visitor subclass: PreOrder" <lang smalltalk>"Protocol: visiting" PreOrder>>visit: aNode block value: aNode. aNode left accept: self. aNode right accept: self </lang>
Execute code in a Workspace: <lang smalltalk>| tree | tree := (Node data: 1) left: ((Node data: 2) left: ((Node data: 4) left: (Node data: 7)); right: (Node data: 5)); right: ((Node data: 3) left: ((Node data: 6) left: (Node data: 8); right: (Node data: 9))). tree traverse: PreOrder do: [:node | Transcript print: node data; space]. Transcript cr. tree traverse: InOrder do: [:node | Transcript print: node data; space]. Transcript cr. tree traverse: PostOrder do: [:node | Transcript print: node data; space]. Transcript cr. tree traverse: LevelOrder do: [:node | Transcript print: node data; space]. Transcript cr. </lang>
Output in Transcript:
1 2 4 7 5 3 6 8 9 7 4 2 5 1 8 6 9 3 7 4 5 2 8 9 6 3 1 1 2 3 4 5 6 7 8 9
Swift
<lang swift>class TreeNode<T> {
let value: T
let left: TreeNode?
let right: TreeNode?
init(value: T, left: TreeNode? = nil, right: TreeNode? = nil) {
self.value = value
self.left = left
self.right = right
}
func preOrder(function: (T) -> Void) {
function(value)
if left != nil {
left!.preOrder(function: function)
}
if right != nil {
right!.preOrder(function: function)
}
}
func inOrder(function: (T) -> Void) {
if left != nil {
left!.inOrder(function: function)
}
function(value)
if right != nil {
right!.inOrder(function: function)
}
}
func postOrder(function: (T) -> Void) {
if left != nil {
left!.postOrder(function: function)
}
if right != nil {
right!.postOrder(function: function)
}
function(value)
}
func levelOrder(function: (T) -> Void) {
var queue: [TreeNode] = []
queue.append(self)
while queue.count > 0 {
let node = queue.removeFirst()
function(node.value)
if node.left != nil {
queue.append(node.left!)
}
if node.right != nil {
queue.append(node.right!)
}
}
}
}
typealias Node = TreeNode<Int>
let n = Node(value: 1,
left: Node(value: 2,
left: Node(value: 4,
left: Node(value: 7)),
right: Node(value: 5)),
right: Node(value: 3,
left: Node(value: 6,
left: Node(value: 8),
right: Node(value: 9))))
let fn = { print($0, terminator: " ") }
print("pre-order: ", terminator: "") n.preOrder(function: fn) print()
print("in-order: ", terminator: "") n.inOrder(function: fn) print()
print("post-order: ", terminator: "") n.postOrder(function: fn) print()
print("level-order: ", terminator: "") n.levelOrder(function: fn) print()</lang>
- Output:
pre-order: 1 2 4 7 5 3 6 8 9 in-order: 7 4 2 5 1 8 6 9 3 post-order: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
Tcl
or
<lang tcl>oo::class create tree {
# Basic tree data structure stuff...
variable val l r
constructor {value {left {}} {right {}}} {
set val $value set l $left set r $right
}
method value {} {return $val}
method left {} {return $l}
method right {} {return $r}
destructor {
if {$l ne ""} {$l destroy} if {$r ne ""} {$r destroy}
}
# Traversal methods
method preorder {varName script {level 0}} {
upvar [incr level] $varName var set var $val uplevel $level $script if {$l ne ""} {$l preorder $varName $script $level} if {$r ne ""} {$r preorder $varName $script $level}
}
method inorder {varName script {level 0}} {
upvar [incr level] $varName var if {$l ne ""} {$l inorder $varName $script $level} set var $val uplevel $level $script if {$r ne ""} {$r inorder $varName $script $level}
}
method postorder {varName script {level 0}} {
upvar [incr level] $varName var if {$l ne ""} {$l postorder $varName $script $level} if {$r ne ""} {$r postorder $varName $script $level} set var $val uplevel $level $script
}
method levelorder {varName script} {
upvar 1 $varName var set nodes [list [self]]; # A queue of nodes to process while {[llength $nodes] > 0} { set nodes [lassign $nodes n] set var [$n value] uplevel 1 $script if {[$n left] ne ""} {lappend nodes [$n left]} if {[$n right] ne ""} {lappend nodes [$n right]} }
}
}</lang>
Note that in Tcl it is conventional to handle performing something “for each element” by evaluating a script in the caller's scope for each node after setting a caller-nominated variable to the value for that iteration. Doing this transparently while recursing requires the use of a varying ‘level’ parameter to upvar and uplevel, but makes for compact and clear code.
Demo code to satisfy the official challenge instance: <lang tcl># Helpers to make construction and listing of a whole tree simpler proc Tree nested {
lassign $nested v l r
if {$l ne ""} {set l [Tree $l]}
if {$r ne ""} {set r [Tree $r]}
tree new $v $l $r
} proc Listify {tree order} {
set list {}
$tree $order v {
lappend list $v
} return $list
}
- Make a tree, print it a few ways, and destroy the tree
set t [Tree {1 {2 {4 7} 5} {3 {6 8 9}}}] puts "preorder: [Listify $t preorder]" puts "inorder: [Listify $t inorder]" puts "postorder: [Listify $t postorder]" puts "level-order: [Listify $t levelorder]" $t destroy</lang> Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
UNIX Shell
Bash (also "sh" on most Unix systems) has arrays. We implement a node as an association between three arrays: left, right, and value. <lang bash>left=() right=() value=()
- node node#, left#, right#, value
- if value is empty, use node#
node() {
nx=${1:-'Missing node index'}
leftx=${2}
rightx=${3}
val=${4:-$1}
value[$nx]="$val"
left[$nx]="$leftx"
right[$nx]="$rightx"
}
- define the tree
node 1 2 3 node 2 4 5 node 3 6 node 4 7 node 5 node 6 8 9 node 7 node 8 node 9
- walk NODE# ORDER
walk() {
local nx=${1-"Missing index"}
shift
for branch in "$@" ; do
case "$branch" in
left) if [[ "${left[$nx]}" ]]; then walk ${left[$nx]} $@ ; fi ;;
right) if [[ "${right[$nx]}" ]]; then walk ${right[$nx]} $@ ; fi ;;
self) printf "%d " "${value[$nx]}" ;;
esac
done
}
apush() {
local var="$1"
eval "$var=( \"\${$var[@]}\" \"$2\" )"
}
showname() {
printf "%-12s " "$1:"
}
showdata() {
showname "$1" shift walk "$@" echo
}
preorder() { showdata $FUNCNAME $1 self left right ; } inorder() { showdata $FUNCNAME $1 left self right ; } postorder() { showdata $FUNCNAME $1 left right self ; } levelorder() {
showname 'level-order'
queue=( $1 )
x=0
while [[ $x < ${#queue[*]} ]]; do
value="${queue[$x]}"
printf "%d " "$value"
for more in "${left[$value]}" "${right[$value]}" ; do
if -n "$more" ; then
apush queue "$more"
fi done : $((x++)) done echo
}
preorder 1 inorder 1 postorder 1 levelorder 1</lang> The output: <lang bash>preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9</lang>
Ursala
Ursala has built-in notation for trees and is perfect for whipping up little tree walking functions. This source listing shows the tree depicted above declared as a constant, followed by declarations of four functions applicable to trees of any type. The main program applies all four of them to the tree and makes a list of their results, each of which is a list of natural numbers. The compiler directive #cast %nLL induces the compile-time side effect of displaying the result on standard output as a list of lists of naturals. <lang Ursala>tree =
1^:<
2^: <4^: <7^: <>, 0>, 5^: <>>, 3^: <6^: <8^: <>, 9^: <>>, 0>>
pre = ~&dvLPCo post = ~&vLPdNCTo in = ~&vvhPdvtL2CTiQo lev = ~&iNCaadSPfavSLiF3RTaq
- cast %nLL
main = <.pre,in,post,lev> tree</lang> output:
< <1,2,4,7,5,3,6,8,9>, <7,4,2,5,1,8,6,9,3>, <7,4,5,2,8,9,6,3,1>, <1,2,3,4,5,6,7,8,9>>
VBA
TreeItem Class Module <lang VB> Public Value As Integer Public LeftChild As TreeItem Public RightChild As TreeItem </lang> Module <lang VB> Dim tihead As TreeItem
Private Function Add(v As Integer, left As TreeItem, right As TreeItem) As TreeItem
Dim x As New TreeItem x.Value = v Set x.LeftChild = left Set x.RightChild = right Set Add = x
End Function
Private Sub Init()
Set tihead = Add(1, _
Add(2, _
Add(4, _
Add(7, Nothing, Nothing), _
Nothing), _
Add(5, Nothing, Nothing)), _
Add(3, _
Add(6, _
Add(8, Nothing, Nothing), _
Add(9, Nothing, Nothing)), _
Nothing))
End Sub
Private Sub InOrder(ti As TreeItem)
If Not ti Is Nothing Then
Call InOrder(ti.LeftChild)
Debug.Print ti.Value;
Call InOrder(ti.RightChild)
End If
End Sub
Private Sub PreOrder(ti As TreeItem)
If Not ti Is Nothing Then
Debug.Print ti.Value;
Call PreOrder(ti.LeftChild)
Call PreOrder(ti.RightChild)
End If
End Sub
Private Sub PostOrder(ti As TreeItem)
If Not ti Is Nothing Then
Call PostOrder(ti.LeftChild)
Call PostOrder(ti.RightChild)
Debug.Print ti.Value;
End If
End Sub
Private Sub LevelOrder(ti As TreeItem)
Dim queue As Object
Set queue = CreateObject("System.Collections.Queue")
queue.Enqueue ti
Do While (queue.Count > 0)
Set next_ = queue.Dequeue
Debug.Print next_.Value;
If Not next_.LeftChild Is Nothing Then queue.Enqueue next_.LeftChild
If Not next_.RightChild Is Nothing Then queue.Enqueue next_.RightChild
Loop
End Sub
Public Sub Main()
Init Debug.Print "preorder: "; Call PreOrder(tihead) Debug.Print vbCrLf; "inorder: "; Call InOrder(tihead) Debug.Print vbCrLf; "postorder: "; Call PostOrder(tihead) Debug.Print vbCrLf; "level-order: "; Call LevelOrder(tihead)
End Sub </lang>
- Output:
preorder: 1 2 4 7 5 3 6 8 9 inorder: 7 4 2 5 1 8 6 9 3 postorder: 7 4 5 2 8 9 6 3 1 level-order: 1 2 3 4 5 6 7 8 9
Wren
The object-oriented version. <lang ecmascript>class Node {
construct new(v) {
_v = v
_left = null
_right = null
}
value { _v }
left { _left }
right { _right}
left =(n) { _left = n }
right= (n) { _right = n }
preOrder() {
System.write(this)
if (_left) _left.preOrder()
if (_right) _right.preOrder()
}
inOrder() {
if ( _left) _left.inOrder()
System.write(this)
if (_right) _right.inOrder()
}
postOrder() {
if (_left) _left.postOrder()
if (_right) _right.postOrder()
System.write(this)
}
levelOrder() {
var queue = [this]
while (true) {
var node = queue.removeAt(0)
System.write(node)
if (node.left) queue.add(node.left)
if (node.right) queue.add(node.right)
if (queue.isEmpty) break
}
}
exec(name, f) {
System.write(name)
f.call(this)
System.print()
}
toString { " %(_v)" }
}
var nodes = List.filled(10, null) for (i in 0..9) nodes[i] = Node.new(i) nodes[1].left = nodes[2] nodes[1].right = nodes[3] nodes[2].left = nodes[4] nodes[2].right = nodes[5] nodes[4].left = nodes[7] nodes[3].left = nodes[6] nodes[6].left = nodes[8] nodes[6].right = nodes[9]
nodes[1].exec(" preOrder:", Fn.new { |n| n.preOrder() }) nodes[1].exec(" inOrder:", Fn.new { |n| n.inOrder() }) nodes[1].exec(" postOrder:", Fn.new { |n| n.postOrder() }) nodes[1].exec("level-order:", Fn.new { |n| n.levelOrder() })</lang>
- Output:
preOrder: 1 2 4 7 5 3 6 8 9
inOrder: 7 4 2 5 1 8 6 9 3
postOrder: 7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9
zkl
<lang zkl>class Node{ var [mixin=Node]left,right; var v;
fcn init(val,[Node]l=Void,[Node]r=Void) { v,left,right=vm.arglist }
}
class BTree{ var [mixin=Node] root;
fcn init(r){ root=r }
const VISIT=Void, LEFT="left", RIGHT="right";
fcn preOrder { traverse(VISIT,LEFT, RIGHT) }
fcn inOrder { traverse(LEFT, VISIT,RIGHT) }
fcn postOrder { traverse(LEFT, RIGHT,VISIT) }
fcn [private] traverse(order){ //--> list of Nodes
sink:=List();
fcn(sink,[Node]n,order){
if(n){ foreach o in (order){
if(VISIT==o) sink.write(n); else self.fcn(sink,n.setVar(o),order); // actually get var, eg n.left }}
}(sink,root,vm.arglist);
sink
}
fcn levelOrder{ // breadth first
sink:=List(); q:=List(root);
while(q){
n:=q.pop(0); l:=n.left; r:=n.right;
sink.write(n); if(l) q.append(l); if(r) q.append(r);
}
sink
}
}</lang> It is easy to convert to lazy by replacing "sink.write" with "vm.yield" and wrapping the traversal with a Utils.Generator. <lang zkl>t:=BTree(Node(1, Node(2, Node(4,Node(7)), Node(5)), Node(3, Node(6, Node(8),Node(9)))));
t.preOrder() .apply("v").println(" preorder"); t.inOrder() .apply("v").println(" inorder"); t.postOrder() .apply("v").println(" postorder"); t.levelOrder().apply("v").println(" level-order");</lang> The "apply("v")" extracts the contents of var v from each node.
- Output:
L(1,2,4,7,5,3,6,8,9) preorder L(7,4,2,5,1,8,6,9,3) inorder L(7,4,5,2,8,9,6,3,1) postorder L(1,2,3,4,5,6,7,8,9) level-order