Tree traversal: Difference between revisions
| Line 2,522: | Line 2,522: | ||
<code>reorder</code> 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.) |
<code>reorder</code> 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.) |
||
<code>childinds</code> extracts the child pointers which some of these results assume. |
<code>childinds</code> extracts the child pointers which some of these results assume. This implementation assumes we are working with a binary tree (which seems to be an assumption of this task). |
||
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): |
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): |
||
Revision as of 12:39, 16 July 2015
You are encouraged to solve this task according to the task description, using any language you may know.
Implement a binary tree where each node carries an integer, and implement preoder, inorder, postorder 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
This article has more information on traversing trees.
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>
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
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>
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
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>
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>
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>
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]
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
<lang haskell>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])
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 () main = do print $ preorder tree
print $ inorder tree
print $ postorder tree
print $ 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]
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 ->
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 seems to be an assumption of this task).
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
<lang java5>import java.util.Queue; import java.util.LinkedList; public class TreeTraverse {
private static class Node<T>
{
public Node<T> left;
public Node<T> right;
public T data;
public Node(T data)
{
this.data = data;
}
public Node<T> getLeft()
{
return this.left;
}
public void setLeft(Node<T> left)
{
this.left = left;
}
public Node<T> getRight()
{
return this.right;
}
public void setRight(Node<T> right)
{
this.right = right;
}
}
public static void preorder(Node<?> n)
{
if (n != null)
{
System.out.print(n.data + " ");
preorder(n.getLeft());
preorder(n.getRight());
}
}
public static void inorder(Node<?> n)
{
if (n != null)
{
inorder(n.getLeft());
System.out.print(n.data + " ");
inorder(n.getRight());
}
}
public static void postorder(Node<?> n)
{
if (n != null)
{
postorder(n.getLeft());
postorder(n.getRight());
System.out.print(n.data + " ");
}
}
public static void levelorder(Node<?> n)
{
Queue<Node<?>> nodequeue = new LinkedList<Node<?>>();
if (n != null)
nodequeue.add(n);
while (!nodequeue.isEmpty())
{
Node<?> next = nodequeue.remove();
System.out.print(next.data + " ");
if (next.getLeft() != null)
{
nodequeue.add(next.getLeft());
}
if (next.getRight() != null)
{
nodequeue.add(next.getRight());
}
}
}
public static void main(final 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.setLeft(two);
one.setRight(three);
two.setLeft(four);
two.setRight(five);
three.setLeft(six);
four.setLeft(seven);
six.setLeft(eight);
six.setRight(nine);
preorder(one);
System.out.println();
inorder(one);
System.out.println();
postorder(one);
System.out.println();
levelorder(one);
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
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>
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 = {1, {2, {4, {7, {},
{}},
{}},
{5, {},
{}}},
{3, {6, {8, {},
{}},
{9, {},
{}}},
{}}}
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
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>
Mathematica
<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}
Nim
<lang nim>import queues, sequtils
type
Node[T] = ref TNode[T] TNode[T] = 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 == nil: @[] else: @[n.data] & preorder(n.left) & preorder(n.right)
proc inorder[T](n: Node[T]): seq[T] =
if n == nil: @[] else: inorder(n.left) & @[n.data] & inorder(n.right)
proc postorder[T](n: Node[T]): seq[T] =
if n == nil: @[] else: postorder(n.left) & postorder(n.right) & @[n.data]
proc levelorder[T](n: Node[T]): seq[T] =
result = @[] var queue = initQueue[Node[T]]() queue.enqueue(n) while queue.len > 0: let next = queue.dequeue() result.add next.data if next.left != nil: queue.enqueue(next.left) if next.right != nil: queue.enqueue(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
Perl 6
<lang perl6>class TreeNode {
has TreeNode $.parent; has TreeNode $.left; has TreeNode $.right; has $.value;
method pre-order {
gather {
take $.value;
take $.left.pre-order if $.left;
take $.right.pre-order if $.right
}
}
method in-order {
gather {
take $.left.in-order if $.left;
take $.value;
take $.right.in-order if $.right;
}
}
method post-order {
gather {
take $.left.post-order if $.left;
take $.right.post-order if $.right;
take $.value;
}
}
method level-order {
my TreeNode @queue = (self);
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
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: Proceedural
<lang python>from collections import namedtuple from sys import stdout
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):
stdout.write("%i " % i)
def preorder(node, visitor = printwithspace):
if node is not None:
visitor(node.data)
preorder(node.left, visitor)
preorder(node.right, visitor)
def inorder(node, visitor = printwithspace):
if node is not None:
inorder(node.left, visitor)
visitor(node.data)
inorder(node.right, visitor)
def postorder(node, visitor = printwithspace):
if node is not None:
postorder(node.left, visitor)
postorder(node.right, visitor)
visitor(node.data)
def levelorder(node, more=None, visitor = printwithspace):
if node is not None:
if more is None:
more = []
more += [node.left, node.right]
visitor(node.data)
if more:
levelorder(more[0], more[1:], visitor)
stdout.write(' preorder: ') preorder(tree) stdout.write('\n inorder: ') inorder(tree) stdout.write('\n postorder: ') postorder(tree) stdout.write('\nlevelorder: ') levelorder(tree) stdout.write('\n')</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: 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.
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
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
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
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
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>>
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
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