Huffman coding: Difference between revisions
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abstract type HuffmanTree end |
abstract type HuffmanTree end |
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struct HuffmanLeaf <: HuffmanTree |
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ch::Char |
ch::Char |
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freq::Int |
freq::Int |
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end |
end |
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struct HuffmanNode <: HuffmanTree |
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freq::Int |
freq::Int |
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left::HuffmanTree |
left::HuffmanTree |
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Revision as of 13:27, 30 January 2019
You are encouraged to solve this task according to the task description, using any language you may know.
Huffman encoding is a way to assign binary codes to symbols that reduces the overall number of bits used to encode a typical string of those symbols.
For example, if you use letters as symbols and have details of the frequency of occurrence of those letters in typical strings, then you could just encode each letter with a fixed number of bits, such as in ASCII codes. You can do better than this by encoding more frequently occurring letters such as e and a, with smaller bit strings; and less frequently occurring letters such as q and x with longer bit strings.
Any string of letters will be encoded as a string of bits that are no-longer of the same length per letter. To successfully decode such as string, the smaller codes assigned to letters such as 'e' cannot occur as a prefix in the larger codes such as that for 'x'.
- If you were to assign a code 01 for 'e' and code 011 for 'x', then if the bits to decode started as 011... then you would not know if you should decode an 'e' or an 'x'.
The Huffman coding scheme takes each symbol and its weight (or frequency of occurrence), and generates proper encodings for each symbol taking account of the weights of each symbol, so that higher weighted symbols have fewer bits in their encoding. (See the WP article for more information).
A Huffman encoding can be computed by first creating a tree of nodes:
- Create a leaf node for each symbol and add it to the priority queue.
- While there is more than one node in the queue:
- Remove the node of highest priority (lowest probability) twice to get two nodes.
- Create a new internal node with these two nodes as children and with probability equal to the sum of the two nodes' probabilities.
- Add the new node to the queue.
- The remaining node is the root node and the tree is complete.
Traverse the constructed binary tree from root to leaves assigning and accumulating a '0' for one branch and a '1' for the other at each node. The accumulated zeros and ones at each leaf constitute a Huffman encoding for those symbols and weights:
- Task
Using the characters and their frequency from the string:
- this is an example for huffman encoding
create a program to generate a Huffman encoding for each character as a table.
Ada
huffman.ads: <lang Ada>with Ada.Containers.Indefinite_Ordered_Maps; with Ada.Containers.Ordered_Maps; with Ada.Finalization; generic
type Symbol_Type is private;
with function "<" (Left, Right : Symbol_Type) return Boolean is <>;
with procedure Put (Item : Symbol_Type);
type Symbol_Sequence is array (Positive range <>) of Symbol_Type;
type Frequency_Type is private;
with function "+" (Left, Right : Frequency_Type) return Frequency_Type
is <>;
with function "<" (Left, Right : Frequency_Type) return Boolean is <>;
package Huffman is
-- bits = booleans (true/false = 1/0) type Bit_Sequence is array (Positive range <>) of Boolean; Zero_Sequence : constant Bit_Sequence (1 .. 0) := (others => False); -- output the sequence procedure Put (Code : Bit_Sequence);
-- type for freqency map
package Frequency_Maps is new Ada.Containers.Ordered_Maps
(Element_Type => Frequency_Type,
Key_Type => Symbol_Type);
type Huffman_Tree is private;
-- create a huffman tree from frequency map
procedure Create_Tree
(Tree : out Huffman_Tree;
Frequencies : Frequency_Maps.Map);
-- encode a single symbol
function Encode
(Tree : Huffman_Tree;
Symbol : Symbol_Type)
return Bit_Sequence;
-- encode a symbol sequence
function Encode
(Tree : Huffman_Tree;
Symbols : Symbol_Sequence)
return Bit_Sequence;
-- decode a bit sequence
function Decode
(Tree : Huffman_Tree;
Code : Bit_Sequence)
return Symbol_Sequence;
-- dump the encoding table
procedure Dump_Encoding (Tree : Huffman_Tree);
private
-- type for encoding map
package Encoding_Maps is new Ada.Containers.Indefinite_Ordered_Maps
(Element_Type => Bit_Sequence,
Key_Type => Symbol_Type);
type Huffman_Node;
type Node_Access is access Huffman_Node;
-- a node is either internal (left_child/right_child used)
-- or a leaf (left_child/right_child are null)
type Huffman_Node is record
Frequency : Frequency_Type;
Left_Child : Node_Access := null;
Right_Child : Node_Access := null;
Symbol : Symbol_Type;
end record;
-- create a leaf node
function Create_Node
(Symbol : Symbol_Type;
Frequency : Frequency_Type)
return Node_Access;
-- create an internal node
function Create_Node (Left, Right : Node_Access) return Node_Access;
-- fill the encoding map
procedure Fill
(The_Node : Node_Access;
Map : in out Encoding_Maps.Map;
Prefix : Bit_Sequence);
-- huffman tree has a tree and an encoding map
type Huffman_Tree is new Ada.Finalization.Controlled with record
Tree : Node_Access := null;
Map : Encoding_Maps.Map := Encoding_Maps.Empty_Map;
end record;
-- free memory after finalization
overriding procedure Finalize (Object : in out Huffman_Tree);
end Huffman;</lang>
huffman.adb: <lang Ada>with Ada.Text_IO; with Ada.Unchecked_Deallocation; with Ada.Containers.Vectors; package body Huffman is
package Node_Vectors is new Ada.Containers.Vectors
(Element_Type => Node_Access,
Index_Type => Positive);
function "<" (Left, Right : Node_Access) return Boolean is
begin
-- compare frequency
if Left.Frequency < Right.Frequency then
return True;
elsif Right.Frequency < Left.Frequency then
return False;
end if;
-- same frequency, choose leaf node
if Left.Left_Child = null and then Right.Left_Child /= null then
return True;
elsif Left.Left_Child /= null and then Right.Left_Child = null then
return False;
end if;
-- same frequency, same node type (internal/leaf)
if Left.Left_Child /= null then
-- for internal nodes, compare left children, then right children
if Left.Left_Child < Right.Left_Child then
return True;
elsif Right.Left_Child < Left.Left_Child then
return False;
else
return Left.Right_Child < Right.Right_Child;
end if;
else
-- for leaf nodes, compare symbol
return Left.Symbol < Right.Symbol;
end if;
end "<";
package Node_Vector_Sort is new Node_Vectors.Generic_Sorting;
procedure Create_Tree
(Tree : out Huffman_Tree;
Frequencies : Frequency_Maps.Map) is
Node_Queue : Node_Vectors.Vector := Node_Vectors.Empty_Vector;
begin
-- insert all leafs into the queue
declare
use Frequency_Maps;
Position : Cursor := Frequencies.First;
The_Node : Node_Access := null;
begin
while Position /= No_Element loop
The_Node :=
Create_Node
(Symbol => Key (Position),
Frequency => Element (Position));
Node_Queue.Append (The_Node);
Next (Position);
end loop;
end;
-- sort by frequency (see "<")
Node_Vector_Sort.Sort (Node_Queue);
-- iterate over all elements
while not Node_Queue.Is_Empty loop
declare
First : constant Node_Access := Node_Queue.First_Element;
begin
Node_Queue.Delete_First;
-- if we only have one node left, it is the root node of the tree
if Node_Queue.Is_Empty then
Tree.Tree := First;
else
-- create new internal node with two smallest frequencies
declare
Second : constant Node_Access := Node_Queue.First_Element;
begin
Node_Queue.Delete_First;
Node_Queue.Append (Create_Node (First, Second));
end;
Node_Vector_Sort.Sort (Node_Queue);
end if;
end;
end loop;
-- fill encoding map
Fill (The_Node => Tree.Tree, Map => Tree.Map, Prefix => Zero_Sequence);
end Create_Tree;
-- create leaf node
function Create_Node
(Symbol : Symbol_Type;
Frequency : Frequency_Type)
return Node_Access
is
Result : Node_Access := new Huffman_Node;
begin
Result.Frequency := Frequency;
Result.Symbol := Symbol;
return Result;
end Create_Node;
-- create internal node
function Create_Node (Left, Right : Node_Access) return Node_Access is
Result : Node_Access := new Huffman_Node;
begin
Result.Frequency := Left.Frequency + Right.Frequency;
Result.Left_Child := Left;
Result.Right_Child := Right;
return Result;
end Create_Node;
-- fill encoding map
procedure Fill
(The_Node : Node_Access;
Map : in out Encoding_Maps.Map;
Prefix : Bit_Sequence) is
begin
if The_Node.Left_Child /= null then
-- append false (0) for left child
Fill (The_Node.Left_Child, Map, Prefix & False);
-- append true (1) for right child
Fill (The_Node.Right_Child, Map, Prefix & True);
else
-- leaf node reached, prefix = code for symbol
Map.Insert (The_Node.Symbol, Prefix);
end if;
end Fill;
-- free memory after finalization
overriding procedure Finalize (Object : in out Huffman_Tree) is
procedure Free is new Ada.Unchecked_Deallocation
(Name => Node_Access,
Object => Huffman_Node);
-- recursively free all nodes
procedure Recursive_Free (The_Node : in out Node_Access) is
begin
-- free node if it is a leaf
if The_Node.Left_Child = null then
Free (The_Node);
else
-- free left and right child if node is internal
Recursive_Free (The_Node.Left_Child);
Recursive_Free (The_Node.Right_Child);
-- free node afterwards
Free (The_Node);
end if;
end Recursive_Free;
begin
-- recursively free root node
Recursive_Free (Object.Tree);
end Finalize;
-- encode single symbol
function Encode
(Tree : Huffman_Tree;
Symbol : Symbol_Type)
return Bit_Sequence
is
begin
-- simply lookup in map
return Tree.Map.Element (Symbol);
end Encode;
-- encode symbol sequence
function Encode
(Tree : Huffman_Tree;
Symbols : Symbol_Sequence)
return Bit_Sequence
is
begin
-- only one element
if Symbols'Length = 1 then
-- see above
return Encode (Tree, Symbols (Symbols'First));
else
-- encode first element, append result of recursive call
return Encode (Tree, Symbols (Symbols'First)) &
Encode (Tree, Symbols (Symbols'First + 1 .. Symbols'Last));
end if;
end Encode;
-- decode a bit sequence
function Decode
(Tree : Huffman_Tree;
Code : Bit_Sequence)
return Symbol_Sequence
is
-- maximum length = code length
Result : Symbol_Sequence (1 .. Code'Length);
-- last used index of result
Last : Natural := 0;
The_Node : Node_Access := Tree.Tree;
begin
-- iterate over the code
for I in Code'Range loop
-- if current element is true, descent the right branch
if Code (I) then
The_Node := The_Node.Right_Child;
else
-- false: descend left branch
The_Node := The_Node.Left_Child;
end if;
if The_Node.Left_Child = null then
-- reached leaf node: append symbol to result
Last := Last + 1;
Result (Last) := The_Node.Symbol;
-- reset current node to root
The_Node := Tree.Tree;
end if;
end loop;
-- return subset of result array
return Result (1 .. Last);
end Decode;
-- output a bit sequence
procedure Put (Code : Bit_Sequence) is
package Int_IO is new Ada.Text_IO.Integer_IO (Integer);
begin
for I in Code'Range loop
if Code (I) then
-- true = 1
Int_IO.Put (1, 0);
else
-- false = 0
Int_IO.Put (0, 0);
end if;
end loop;
Ada.Text_IO.New_Line;
end Put;
-- dump encoding map
procedure Dump_Encoding (Tree : Huffman_Tree) is
use type Encoding_Maps.Cursor;
Position : Encoding_Maps.Cursor := Tree.Map.First;
begin
-- iterate map
while Position /= Encoding_Maps.No_Element loop
-- key
Put (Encoding_Maps.Key (Position));
Ada.Text_IO.Put (" = ");
-- code
Put (Encoding_Maps.Element (Position));
Encoding_Maps.Next (Position);
end loop;
end Dump_Encoding;
end Huffman;</lang>
example main.adb: <lang Ada>with Ada.Text_IO; with Huffman; procedure Main is
package Char_Natural_Huffman_Tree is new Huffman
(Symbol_Type => Character,
Put => Ada.Text_IO.Put,
Symbol_Sequence => String,
Frequency_Type => Natural);
Tree : Char_Natural_Huffman_Tree.Huffman_Tree;
Frequencies : Char_Natural_Huffman_Tree.Frequency_Maps.Map;
Input_String : constant String :=
"this is an example for huffman encoding";
begin
-- build frequency map
for I in Input_String'Range loop
declare
use Char_Natural_Huffman_Tree.Frequency_Maps;
Position : constant Cursor := Frequencies.Find (Input_String (I));
begin
if Position = No_Element then
Frequencies.Insert (Key => Input_String (I), New_Item => 1);
else
Frequencies.Replace_Element
(Position => Position,
New_Item => Element (Position) + 1);
end if;
end;
end loop;
-- create huffman tree
Char_Natural_Huffman_Tree.Create_Tree
(Tree => Tree,
Frequencies => Frequencies);
-- dump encodings Char_Natural_Huffman_Tree.Dump_Encoding (Tree => Tree);
-- encode example string
declare
Code : constant Char_Natural_Huffman_Tree.Bit_Sequence :=
Char_Natural_Huffman_Tree.Encode
(Tree => Tree,
Symbols => Input_String);
begin
Char_Natural_Huffman_Tree.Put (Code);
Ada.Text_IO.Put_Line
(Char_Natural_Huffman_Tree.Decode (Tree => Tree, Code => Code));
end;
end Main;</lang>
- Output:
= 101 a = 1001 c = 01010 d = 01011 e = 1100 f = 1101 g = 01100 h = 11111 i = 1110 l = 01101 m = 0010 n = 000 o = 0011 p = 01110 r = 01111 s = 0100 t = 10000 u = 10001 x = 11110 1000011111111001001011110010010110010001011100111101001001001110011011100101110100110111110111111100011101110100101001000101110000001010001101011111000001100 this is an example for huffman encoding
BBC BASIC
<lang bbcbasic> INSTALL @lib$+"SORTSALIB"
SortUp% = FN_sortSAinit(0,0) : REM Ascending
SortDn% = FN_sortSAinit(1,0) : REM Descending
Text$ = "this is an example for huffman encoding"
DIM tree{(127) ch&, num%, lkl%, lkr%}
FOR i% = 1 TO LEN(Text$)
c% = ASCMID$(Text$,i%)
tree{(c%)}.ch& = c%
tree{(c%)}.num% += 1
NEXT
C% = DIM(tree{()},1) + 1
CALL SortDn%, tree{()}, tree{(0)}.num%
FOR i% = 0 TO DIM(tree{()},1)
IF tree{(i%)}.num% = 0 EXIT FOR
NEXT
size% = i%
linked% = 0
REPEAT
C% = size%
CALL SortUp%, tree{()}, tree{(0)}.num%
i% = 0 : WHILE tree{(i%)}.lkl% OR tree{(i%)}.lkr% i% += 1 : ENDWHILE
tree{(i%)}.lkl% = size%
j% = 0 : WHILE tree{(j%)}.lkl% OR tree{(j%)}.lkr% j% += 1 : ENDWHILE
tree{(j%)}.lkr% = size%
linked% += 2
tree{(size%)}.num% = tree{(i%)}.num% + tree{(j%)}.num%
size% += 1
UNTIL linked% = (size% - 1)
FOR i% = size% - 1 TO 0 STEP -1
IF tree{(i%)}.ch& THEN
h$ = ""
j% = i%
REPEAT
CASE TRUE OF
WHEN tree{(j%)}.lkl% <> 0:
h$ = "0" + h$
j% = tree{(j%)}.lkl%
WHEN tree{(j%)}.lkr% <> 0:
h$ = "1" + h$
j% = tree{(j%)}.lkr%
OTHERWISE:
EXIT REPEAT
ENDCASE
UNTIL FALSE
VDU tree{(i%)}.ch& : PRINT " " h$
ENDIF
NEXT
END</lang>
- Output:
101 n 000 e 1110 f 1101 a 1100 i 1011 s 0110 m 0101 h 0100 o 0011 c 0010 l 0001 r 0000 x 11111 p 11110 d 11101 u 11100 g 11011 t 11010
Bracmat
<lang bracmat>( "this is an example for huffman encoding":?S & 0:?chars & 0:?p & ( @( !S
: ?
( [!p %?char [?p ?
& !char+!chars:?chars
& ~
)
)
|
)
& 0:?prioritized & whl
' ( !chars:?n*%@?w+?chars & (!n.!w)+!prioritized:?prioritized )
& whl
' ( !prioritized:(?p.?x)+(?q.?y)+?nprioritized & (!p+!q.(!p.0,!x)+(!q.1,!y))+!nprioritized:?prioritized )
& 0:?L & ( walk
= bits tree bit subtree
. !arg:(?bits.?tree)
& whl
' ( !tree:(?p.?bit,?subtree)+?tree
& ( !subtree:@
& (!subtree.str$(!bits !bit))+!L:?L
| walk$(!bits !bit.!subtree)
)
)
)
& !prioritized:(?.?prioritized) & walk$(.!prioritized) & lst$L & :?encoded & 0:?p & ( @( !S
: ?
( [!p %?char [?p ?
& !L:?+(!char.?code)+?
& !encoded !code:?encoded
& ~
)
)
| out$(str$!encoded)
)
& ( decode
= char bits
. !L
: ?+(?char.?bits&@(!arg:!bits ?arg))+?
& !char decode$!arg
| !arg
)
& out$("decoded:" str$(decode$(str$!encoded)));</lang>
- Output:
(L=
(" ".101)
+ (a.1001)
+ (c.01010)
+ (d.01011)
+ (e.1100)
+ (f.1101)
+ (g.01100)
+ (h.11111)
+ (i.1110)
+ (l.01101)
+ (m.0010)
+ (n.000)
+ (o.0011)
+ (p.01110)
+ (r.01111)
+ (s.0100)
+ (t.10000)
+ (u.10001)
+ (x.11110));
1000011111111001001011110010010110010001011100111101001001001110011011100101110100110111110111111100011101110100101001000101110000001010001101011111000001100
decoded: this is an example for huffman encoding
C
This code lacks a lot of needed checkings, especially for memory allocation.
<lang c>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
- define BYTES 256
struct huffcode {
int nbits; int code;
}; typedef struct huffcode huffcode_t;
struct huffheap {
int *h; int n, s, cs; long *f;
}; typedef struct huffheap heap_t;
/* heap handling funcs */ static heap_t *_heap_create(int s, long *f) {
heap_t *h; h = malloc(sizeof(heap_t)); h->h = malloc(sizeof(int)*s); h->s = h->cs = s; h->n = 0; h->f = f; return h;
}
static void _heap_destroy(heap_t *heap) {
free(heap->h); free(heap);
}
- define swap_(I,J) do { int t_; t_ = a[(I)]; \
a[(I)] = a[(J)]; a[(J)] = t_; } while(0)
static void _heap_sort(heap_t *heap) {
int i=1, j=2; /* gnome sort */ int *a = heap->h;
while(i < heap->n) { /* smaller values are kept at the end */
if ( heap->f[a[i-1]] >= heap->f[a[i]] ) {
i = j; j++;
} else {
swap_(i-1, i);
i--;
i = (i==0) ? j++ : i;
}
}
}
- undef swap_
static void _heap_add(heap_t *heap, int c) {
if ( (heap->n + 1) > heap->s ) {
heap->h = realloc(heap->h, heap->s + heap->cs);
heap->s += heap->cs;
}
heap->h[heap->n] = c;
heap->n++;
_heap_sort(heap);
}
static int _heap_remove(heap_t *heap) {
if ( heap->n > 0 ) {
heap->n--;
return heap->h[heap->n];
}
return -1;
}
/* huffmann code generator */ huffcode_t **create_huffman_codes(long *freqs) {
huffcode_t **codes; heap_t *heap; long efreqs[BYTES*2]; int preds[BYTES*2]; int i, extf=BYTES; int r1, r2;
memcpy(efreqs, freqs, sizeof(long)*BYTES); memset(&efreqs[BYTES], 0, sizeof(long)*BYTES);
heap = _heap_create(BYTES*2, efreqs); if ( heap == NULL ) return NULL;
for(i=0; i < BYTES; i++) if ( efreqs[i] > 0 ) _heap_add(heap, i);
while( heap->n > 1 )
{
r1 = _heap_remove(heap);
r2 = _heap_remove(heap);
efreqs[extf] = efreqs[r1] + efreqs[r2];
_heap_add(heap, extf);
preds[r1] = extf;
preds[r2] = -extf;
extf++;
}
r1 = _heap_remove(heap);
preds[r1] = r1;
_heap_destroy(heap);
codes = malloc(sizeof(huffcode_t *)*BYTES);
int bc, bn, ix;
for(i=0; i < BYTES; i++) {
bc=0; bn=0;
if ( efreqs[i] == 0 ) { codes[i] = NULL; continue; }
ix = i;
while( abs(preds[ix]) != ix ) {
bc |= ((preds[ix] >= 0) ? 1 : 0 ) << bn;
ix = abs(preds[ix]);
bn++;
}
codes[i] = malloc(sizeof(huffcode_t));
codes[i]->nbits = bn;
codes[i]->code = bc;
}
return codes;
}
void free_huffman_codes(huffcode_t **c) {
int i;
for(i=0; i < BYTES; i++) free(c[i]); free(c);
}
- define MAXBITSPERCODE 100
void inttobits(int c, int n, char *s) {
s[n] = 0;
while(n > 0) {
s[n-1] = (c%2) + '0';
c >>= 1; n--;
}
}
const char *test = "this is an example for huffman encoding";
int main() {
huffcode_t **r; int i; char strbit[MAXBITSPERCODE]; const char *p; long freqs[BYTES];
memset(freqs, 0, sizeof freqs);
p = test; while(*p != '\0') freqs[*p++]++;
r = create_huffman_codes(freqs);
for(i=0; i < BYTES; i++) {
if ( r[i] != NULL ) {
inttobits(r[i]->code, r[i]->nbits, strbit);
printf("%c (%d) %s\n", i, r[i]->code, strbit);
}
}
free_huffman_codes(r);
return 0;
}</lang>
Alternative
Using a simple heap-based priority queue. Heap is an array, while ndoe tree is done by binary links. <lang c>#include <stdio.h>
- include <string.h>
typedef struct node_t { struct node_t *left, *right; int freq; char c; } *node;
struct node_t pool[256] = Template:0; node qqq[255], *q = qqq - 1; int n_nodes = 0, qend = 1; char *code[128] = {0}, buf[1024];
node new_node(int freq, char c, node a, node b) { node n = pool + n_nodes++; if (freq) n->c = c, n->freq = freq; else { n->left = a, n->right = b; n->freq = a->freq + b->freq; } return n; }
/* priority queue */ void qinsert(node n) { int j, i = qend++; while ((j = i / 2)) { if (q[j]->freq <= n->freq) break; q[i] = q[j], i = j; } q[i] = n; }
node qremove() { int i, l; node n = q[i = 1];
if (qend < 2) return 0; qend--; while ((l = i * 2) < qend) { if (l + 1 < qend && q[l + 1]->freq < q[l]->freq) l++; q[i] = q[l], i = l; } q[i] = q[qend]; return n; }
/* walk the tree and put 0s and 1s */ void build_code(node n, char *s, int len) { static char *out = buf; if (n->c) { s[len] = 0; strcpy(out, s); code[n->c] = out; out += len + 1; return; }
s[len] = '0'; build_code(n->left, s, len + 1); s[len] = '1'; build_code(n->right, s, len + 1); }
void init(const char *s) { int i, freq[128] = {0}; char c[16];
while (*s) freq[(int)*s++]++;
for (i = 0; i < 128; i++) if (freq[i]) qinsert(new_node(freq[i], i, 0, 0));
while (qend > 2) qinsert(new_node(0, 0, qremove(), qremove()));
build_code(q[1], c, 0); }
void encode(const char *s, char *out) { while (*s) { strcpy(out, code[*s]); out += strlen(code[*s++]); } }
void decode(const char *s, node t) { node n = t; while (*s) { if (*s++ == '0') n = n->left; else n = n->right;
if (n->c) putchar(n->c), n = t; }
putchar('\n'); if (t != n) printf("garbage input\n"); }
int main(void) { int i; const char *str = "this is an example for huffman encoding";
char buf[1024];
init(str); for (i = 0; i < 128; i++) if (code[i]) printf("'%c': %s\n", i, code[i]);
encode(str, buf); printf("encoded: %s\n", buf);
printf("decoded: "); decode(buf, q[1]);
return 0; }</lang>
- Output:
' ': 000 'a': 1000 'c': 01101 'd': 01100 'e': 0101 'f': 0010 'g': 010000 'h': 1101 'i': 0011 'l': 010001 'm': 1111 'n': 101 'o': 1110 'p': 10011 'r': 10010 's': 1100 't': 01111 'u': 01110 'x': 01001 encoded: 0111111010011110000000111100000100010100001010100110001111100110100010101000001011101001000011010111000100010111110001010000101101011011110011000011101010000 decoded: this is an example for huffman encoding
C#
<lang csharp>using System; using System.Collections.Generic;
namespace Huffman_Encoding {
public class PriorityQueue<T> where T : IComparable
{
protected List<T> LstHeap = new List<T>();
public virtual int Count
{
get { return LstHeap.Count; }
}
public virtual void Add(T val)
{
LstHeap.Add(val);
SetAt(LstHeap.Count - 1, val);
UpHeap(LstHeap.Count - 1);
}
public virtual T Peek()
{
if (LstHeap.Count == 0)
{
throw new IndexOutOfRangeException("Peeking at an empty priority queue");
}
return LstHeap[0];
}
public virtual T Pop()
{
if (LstHeap.Count == 0)
{
throw new IndexOutOfRangeException("Popping an empty priority queue");
}
T valRet = LstHeap[0];
SetAt(0, LstHeap[LstHeap.Count - 1]);
LstHeap.RemoveAt(LstHeap.Count - 1);
DownHeap(0);
return valRet;
}
protected virtual void SetAt(int i, T val)
{
LstHeap[i] = val;
}
protected bool RightSonExists(int i)
{
return RightChildIndex(i) < LstHeap.Count;
}
protected bool LeftSonExists(int i)
{
return LeftChildIndex(i) < LstHeap.Count;
}
protected int ParentIndex(int i)
{
return (i - 1) / 2;
}
protected int LeftChildIndex(int i)
{
return 2 * i + 1;
}
protected int RightChildIndex(int i)
{
return 2 * (i + 1);
}
protected T ArrayVal(int i)
{
return LstHeap[i];
}
protected T Parent(int i)
{
return LstHeap[ParentIndex(i)];
}
protected T Left(int i)
{
return LstHeap[LeftChildIndex(i)];
}
protected T Right(int i)
{
return LstHeap[RightChildIndex(i)];
}
protected void Swap(int i, int j)
{
T valHold = ArrayVal(i);
SetAt(i, LstHeap[j]);
SetAt(j, valHold);
}
protected void UpHeap(int i)
{
while (i > 0 && ArrayVal(i).CompareTo(Parent(i)) > 0)
{
Swap(i, ParentIndex(i));
i = ParentIndex(i);
}
}
protected void DownHeap(int i)
{
while (i >= 0)
{
int iContinue = -1;
if (RightSonExists(i) && Right(i).CompareTo(ArrayVal(i)) > 0)
{
iContinue = Left(i).CompareTo(Right(i)) < 0 ? RightChildIndex(i) : LeftChildIndex(i);
}
else if (LeftSonExists(i) && Left(i).CompareTo(ArrayVal(i)) > 0)
{
iContinue = LeftChildIndex(i);
}
if (iContinue >= 0 && iContinue < LstHeap.Count)
{
Swap(i, iContinue);
}
i = iContinue;
}
}
}
internal class HuffmanNode<T> : IComparable
{
internal HuffmanNode(double probability, T value)
{
Probability = probability;
LeftSon = RightSon = Parent = null;
Value = value;
IsLeaf = true;
}
internal HuffmanNode(HuffmanNode<T> leftSon, HuffmanNode<T> rightSon)
{
LeftSon = leftSon;
RightSon = rightSon;
Probability = leftSon.Probability + rightSon.Probability;
leftSon.IsZero = true;
rightSon.IsZero = false;
leftSon.Parent = rightSon.Parent = this;
IsLeaf = false;
}
internal HuffmanNode<T> LeftSon { get; set; }
internal HuffmanNode<T> RightSon { get; set; }
internal HuffmanNode<T> Parent { get; set; }
internal T Value { get; set; }
internal bool IsLeaf { get; set; }
internal bool IsZero { get; set; }
internal int Bit
{
get { return IsZero ? 0 : 1; }
}
internal bool IsRoot
{
get { return Parent == null; }
}
internal double Probability { get; set; }
public int CompareTo(object obj)
{
return -Probability.CompareTo(((HuffmanNode<T>) obj).Probability);
}
}
public class Huffman<T> where T : IComparable
{
private readonly Dictionary<T, HuffmanNode<T>> _leafDictionary = new Dictionary<T, HuffmanNode<T>>();
private readonly HuffmanNode<T> _root;
public Huffman(IEnumerable<T> values)
{
var counts = new Dictionary<T, int>();
var priorityQueue = new PriorityQueue<HuffmanNode<T>>();
int valueCount = 0;
foreach (T value in values)
{
if (!counts.ContainsKey(value))
{
counts[value] = 0;
}
counts[value]++;
valueCount++;
}
foreach (T value in counts.Keys)
{
var node = new HuffmanNode<T>((double) counts[value] / valueCount, value);
priorityQueue.Add(node);
_leafDictionary[value] = node;
}
while (priorityQueue.Count > 1)
{
HuffmanNode<T> leftSon = priorityQueue.Pop();
HuffmanNode<T> rightSon = priorityQueue.Pop();
var parent = new HuffmanNode<T>(leftSon, rightSon);
priorityQueue.Add(parent);
}
_root = priorityQueue.Pop();
_root.IsZero = false;
}
public List<int> Encode(T value)
{
var returnValue = new List<int>();
Encode(value, returnValue);
return returnValue;
}
public void Encode(T value, List<int> encoding)
{
if (!_leafDictionary.ContainsKey(value))
{
throw new ArgumentException("Invalid value in Encode");
}
HuffmanNode<T> nodeCur = _leafDictionary[value];
var reverseEncoding = new List<int>();
while (!nodeCur.IsRoot)
{
reverseEncoding.Add(nodeCur.Bit);
nodeCur = nodeCur.Parent;
}
reverseEncoding.Reverse();
encoding.AddRange(reverseEncoding);
}
public List<int> Encode(IEnumerable<T> values)
{
var returnValue = new List<int>();
foreach (T value in values)
{
Encode(value, returnValue);
}
return returnValue;
}
public T Decode(List<int> bitString, ref int position)
{
HuffmanNode<T> nodeCur = _root;
while (!nodeCur.IsLeaf)
{
if (position > bitString.Count)
{
throw new ArgumentException("Invalid bitstring in Decode");
}
nodeCur = bitString[position++] == 0 ? nodeCur.LeftSon : nodeCur.RightSon;
}
return nodeCur.Value;
}
public List<T> Decode(List<int> bitString)
{
int position = 0;
var returnValue = new List<T>();
while (position != bitString.Count)
{
returnValue.Add(Decode(bitString, ref position));
}
return returnValue;
}
}
internal class Program
{
private const string Example = "this is an example for huffman encoding";
private static void Main()
{
var huffman = new Huffman<char>(Example);
List<int> encoding = huffman.Encode(Example);
List<char> decoding = huffman.Decode(encoding);
var outString = new string(decoding.ToArray());
Console.WriteLine(outString == Example ? "Encoding/decoding worked" : "Encoding/Decoding failed");
var chars = new HashSet<char>(Example);
foreach (char c in chars)
{
encoding = huffman.Encode(c);
Console.Write("{0}: ", c);
foreach (int bit in encoding)
{
Console.Write("{0}", bit);
}
Console.WriteLine();
}
Console.ReadKey();
}
}
}</lang> File:CSharpHuffman.jpg
C++
This code builds a tree to generate huffman codes, then prints the codes.
<lang cpp>#include <iostream>
- include <queue>
- include <map>
- include <climits> // for CHAR_BIT
- include <iterator>
- include <algorithm>
const int UniqueSymbols = 1 << CHAR_BIT; const char* SampleString = "this is an example for huffman encoding";
typedef std::vector<bool> HuffCode; typedef std::map<char, HuffCode> HuffCodeMap;
class INode { public:
const int f;
virtual ~INode() {}
protected:
INode(int f) : f(f) {}
};
class InternalNode : public INode { public:
INode *const left; INode *const right;
InternalNode(INode* c0, INode* c1) : INode(c0->f + c1->f), left(c0), right(c1) {}
~InternalNode()
{
delete left;
delete right;
}
};
class LeafNode : public INode { public:
const char c;
LeafNode(int f, char c) : INode(f), c(c) {}
};
struct NodeCmp {
bool operator()(const INode* lhs, const INode* rhs) const { return lhs->f > rhs->f; }
};
INode* BuildTree(const int (&frequencies)[UniqueSymbols]) {
std::priority_queue<INode*, std::vector<INode*>, NodeCmp> trees;
for (int i = 0; i < UniqueSymbols; ++i)
{
if(frequencies[i] != 0)
trees.push(new LeafNode(frequencies[i], (char)i));
}
while (trees.size() > 1)
{
INode* childR = trees.top();
trees.pop();
INode* childL = trees.top();
trees.pop();
INode* parent = new InternalNode(childR, childL);
trees.push(parent);
}
return trees.top();
}
void GenerateCodes(const INode* node, const HuffCode& prefix, HuffCodeMap& outCodes) {
if (const LeafNode* lf = dynamic_cast<const LeafNode*>(node))
{
outCodes[lf->c] = prefix;
}
else if (const InternalNode* in = dynamic_cast<const InternalNode*>(node))
{
HuffCode leftPrefix = prefix;
leftPrefix.push_back(false);
GenerateCodes(in->left, leftPrefix, outCodes);
HuffCode rightPrefix = prefix;
rightPrefix.push_back(true);
GenerateCodes(in->right, rightPrefix, outCodes);
}
}
int main() {
// Build frequency table
int frequencies[UniqueSymbols] = {0};
const char* ptr = SampleString;
while (*ptr != '\0')
++frequencies[*ptr++];
INode* root = BuildTree(frequencies); HuffCodeMap codes; GenerateCodes(root, HuffCode(), codes); delete root;
for (HuffCodeMap::const_iterator it = codes.begin(); it != codes.end(); ++it)
{
std::cout << it->first << " ";
std::copy(it->second.begin(), it->second.end(),
std::ostream_iterator<bool>(std::cout));
std::cout << std::endl;
}
return 0;
}</lang>
- Output:
110 a 1001 c 101010 d 10001 e 1111 f 1011 g 101011 h 0101 i 1110 l 01110 m 0011 n 000 o 0010 p 01000 r 01001 s 0110 t 01111 u 10100 x 10000
Clojure
(Updated to 1.6 & includes pretty-printing). Uses Java PriorityQueue <lang clojure>(require '[clojure.pprint :refer :all])
(defn probs [s]
(let [freqs (frequencies s) sum (apply + (vals freqs))]
(into {} (map (fn k v [k (/ v sum)]) freqs))))
(defn init-pq [weighted-items]
(let [comp (proxy [java.util.Comparator] []
(compare [a b] (compare (:priority a) (:priority b))))
pq (java.util.PriorityQueue. (count weighted-items) comp)]
(doseq [[item prob] weighted-items] (.add pq { :symbol item, :priority prob }))
pq))
(defn huffman-tree [pq]
(while (> (.size pq) 1) (let [a (.poll pq) b (.poll pq)
new-node {:priority (+ (:priority a) (:priority b)) :left a :right b}]
(.add pq new-node))) (.poll pq))
(defn symbol-map
([t] (symbol-map t ""))
([{:keys [symbol priority left right] :as t} code]
(if symbol [{:symbol symbol :weight priority :code code}]
(concat (symbol-map left (str code \0))
(symbol-map right (str code \1))))))
(defn huffman-encode [items]
(-> items probs init-pq huffman-tree symbol-map))
(defn display-huffman-encode [s]
(->> s huffman-encode (sort-by :weight >) print-table))
(display-huffman-encode "this is an example for huffman encoding")</lang>
- Output:
| :symbol | :weight | :code | |---------+---------+--------| | | 2/13 | 111 | | n | 4/39 | 011 | | a | 1/13 | 1001 | | e | 1/13 | 1011 | | i | 1/13 | 1100 | | f | 1/13 | 1101 | | h | 2/39 | 0001 | | s | 2/39 | 0010 | | m | 2/39 | 0100 | | o | 2/39 | 0101 | | d | 1/39 | 00000 | | t | 1/39 | 00001 | | c | 1/39 | 00110 | | x | 1/39 | 00111 | | u | 1/39 | 10000 | | l | 1/39 | 10001 | | r | 1/39 | 10100 | | g | 1/39 | 101010 | | p | 1/39 | 101011 |
Alternate Version
Uses c.d.priority-map. Creates a more shallow tree but appears to meet the requirements. <lang clojure>(require '[clojure.data.priority-map :refer [priority-map-keyfn-by]]) (require '[clojure.pprint :refer [print-table]])
(defn init-pq [s]
(let [c (count s)] (->> s frequencies
(map (fn k v [k {:sym k :weight (/ v c)}])) (into (priority-map-keyfn-by :weight <)))))
(defn huffman-tree [pq]
(letfn [(build-step
[pq] (let [a (second (peek pq)) b (second (peek (pop pq))) nn {:sym (str (:sym a) (:sym b)) :weight (+ (:weight a) (:weight b)) :left a :right b}] (assoc (pop (pop pq)) (:sym nn) nn)))]
(->> (iterate build-step pq)
(drop-while #(> (count %) 1)) first vals first)))
(defn symbol-map [m]
(letfn [(sym-step
[{:keys [sym weight left right] :as m} code] (cond (and left right) #(vector (trampoline sym-step left (str code \0)) (trampoline sym-step right (str code \1))) left #(sym-step left (str code \0)) right #(sym-step right (str code \1)) :else {:sym sym :weight weight :code code}))]
(trampoline sym-step m "")))
(defn huffman-encode [s]
(->> s init-pq huffman-tree symbol-map flatten))
(defn display-huffman-encode [s]
(->> s huffman-encode (sort-by :weight >) print-table))
(display-huffman-encode "this is an example for huffman encoding")</lang>
- Output:
| :sym | :weight | :code | |------+---------+-------| | | 2/13 | 101 | | n | 4/39 | 010 | | a | 1/13 | 1001 | | i | 1/13 | 1101 | | e | 1/13 | 1110 | | f | 1/13 | 1111 | | m | 2/39 | 0000 | | o | 2/39 | 0001 | | s | 2/39 | 0010 | | h | 2/39 | 11001 | | g | 1/39 | 00110 | | l | 1/39 | 00111 | | t | 1/39 | 01100 | | u | 1/39 | 01101 | | c | 1/39 | 01110 | | d | 1/39 | 01111 | | p | 1/39 | 10000 | | r | 1/39 | 10001 | | x | 1/39 | 11000 |
CoffeeScript
<lang coffeescript> huffman_encoding_table = (counts) ->
# counts is a hash where keys are characters and
# values are frequencies;
# return a hash where keys are codes and values
# are characters
build_huffman_tree = ->
# returns a Huffman tree. Each node has
# cnt: total frequency of all chars in subtree
# c: character to be encoded (leafs only)
# children: children nodes (branches only)
q = min_queue()
for c, cnt of counts
q.enqueue cnt,
cnt: cnt
c: c
while q.size() >= 2
a = q.dequeue()
b = q.dequeue()
cnt = a.cnt + b.cnt
node =
cnt: cnt
children: [a, b]
q.enqueue cnt, node
root = q.dequeue()
root = build_huffman_tree()
codes = {}
encode = (node, code) ->
if node.c?
codes[code] = node.c
else
encode node.children[0], code + "0"
encode node.children[1], code + "1"
encode(root, "")
codes
min_queue = ->
# This is very non-optimized; you could use a binary heap for better
# performance. Items with smaller priority get dequeued first.
arr = []
enqueue: (priority, data) ->
i = 0
while i < arr.length
if priority < arr[i].priority
break
i += 1
arr.splice i, 0,
priority: priority
data: data
dequeue: ->
arr.shift().data
size: -> arr.length
_internal: ->
arr
freq_count = (s) ->
cnts = {}
for c in s
cnts[c] ?= 0
cnts[c] += 1
cnts
rpad = (s, n) ->
while s.length < n s += ' ' s
examples = [
"this is an example for huffman encoding" "abcd" "abbccccddddddddeeeeeeeee"
]
for s in examples
console.log "---- #{s}"
counts = freq_count(s)
huffman_table = huffman_encoding_table(counts)
codes = (code for code of huffman_table).sort()
for code in codes
c = huffman_table[code]
console.log "#{rpad(code, 5)}: #{c} (#{counts[c]})"
console.log()
</lang>
- Output:
> coffee huffman.coffee ---- this is an example for huffman encoding 000 : n (4) 0010 : s (2) 0011 : m (2) 0100 : o (2) 01010: t (1) 01011: x (1) 01100: p (1) 01101: l (1) 01110: r (1) 01111: u (1) 10000: c (1) 10001: d (1) 1001 : i (3) 101 : (6) 1100 : a (3) 1101 : e (3) 1110 : f (3) 11110: g (1) 11111: h (2) ---- abcd 00 : a (1) 01 : b (1) 10 : c (1) 11 : d (1) ---- abbccccddddddddeeeeeeeee 0 : e (9) 1000 : a (1) 1001 : b (2) 101 : c (4) 11 : d (8)
Common Lisp
This implementation uses a tree built of huffman-nodes,
and a hash table mapping from elements of the input sequence to huffman-nodes.
The priority queue is implemented as a sorted list.
(For a more efficient implementation of a priority queue, see the Heapsort task.)
<lang lisp>(defstruct huffman-node
(weight 0 :type number) (element nil :type t) (encoding nil :type (or null bit-vector)) (left nil :type (or null huffman-node)) (right nil :type (or null huffman-node)))
(defun initial-huffman-nodes (sequence &key (test 'eql))
(let* ((length (length sequence))
(increment (/ 1 length))
(nodes (make-hash-table :size length :test test))
(queue '()))
(map nil #'(lambda (element)
(multiple-value-bind (node presentp) (gethash element nodes)
(if presentp
(incf (huffman-node-weight node) increment)
(let ((node (make-huffman-node :weight increment
:element element)))
(setf (gethash element nodes) node
queue (list* node queue))))))
sequence)
(values nodes (sort queue '< :key 'huffman-node-weight))))
(defun huffman-tree (sequence &key (test 'eql))
(multiple-value-bind (nodes queue)
(initial-huffman-nodes sequence :test test)
(do () ((endp (rest queue)) (values nodes (first queue)))
(destructuring-bind (n1 n2 &rest queue-rest) queue
(let ((n3 (make-huffman-node
:left n1
:right n2
:weight (+ (huffman-node-weight n1)
(huffman-node-weight n2)))))
(setf queue (merge 'list (list n3) queue-rest '<
:key 'huffman-node-weight)))))))1
(defun huffman-codes (sequence &key (test 'eql))
(multiple-value-bind (nodes tree)
(huffman-tree sequence :test test)
(labels ((hc (node length bits)
(let ((left (huffman-node-left node))
(right (huffman-node-right node)))
(cond
((and (null left) (null right))
(setf (huffman-node-encoding node)
(make-array length :element-type 'bit
:initial-contents (reverse bits))))
(t (hc left (1+ length) (list* 0 bits))
(hc right (1+ length) (list* 1 bits)))))))
(hc tree 0 '())
nodes)))
(defun print-huffman-code-table (nodes &optional (out *standard-output*))
(format out "~&Element~10tWeight~20tCode")
(loop for node being each hash-value of nodes
do (format out "~&~s~10t~s~20t~s"
(huffman-node-element node)
(huffman-node-weight node)
(huffman-node-encoding node))))</lang>
Example:
> (print-huffman-code-table (huffman-codes "this is an example for huffman encoding")) Element Weight Code #\t 1/39 #*10010 #\d 1/39 #*01101 #\m 2/39 #*0100 #\f 1/13 #*1100 #\o 2/39 #*0111 #\x 1/39 #*100111 #\h 2/39 #*1000 #\a 1/13 #*1010 #\s 2/39 #*0101 #\c 1/39 #*00010 #\l 1/39 #*00001 #\u 1/39 #*00011 #\e 1/13 #*1101 #\n 4/39 #*001 #\g 1/39 #*01100 #\p 1/39 #*100110 #\i 1/13 #*1011 #\r 1/39 #*00000 #\Space 2/13 #*111
D
<lang d>import std.stdio, std.algorithm, std.typecons, std.container, std.array;
auto encode(alias eq, R)(Group!(eq, R) sf) /*pure nothrow @safe*/ {
auto heap = sf.map!(s => tuple(s[1], [tuple(s[0], "")]))
.array.heapify!q{b < a};
while (heap.length > 1) {
auto lo = heap.front; heap.removeFront;
auto hi = heap.front; heap.removeFront;
lo[1].each!((ref pair) => pair[1] = '0' ~ pair[1]);
hi[1].each!((ref pair) => pair[1] = '1' ~ pair[1]);
heap.insert(tuple(lo[0] + hi[0], lo[1] ~ hi[1]));
}
return heap.front[1].schwartzSort!q{ tuple(a[1].length, a[0]) };
}
void main() /*@safe*/ {
immutable s = "this is an example for huffman encoding"d;
foreach (const p; s.dup.sort().group.encode)
writefln("'%s' %s", p[]);
}</lang>
- Output:
' ' 101 'n' 010 'a' 1001 'e' 1100 'f' 1101 'h' 0001 'i' 1110 'm' 0010 'o' 0011 's' 0111 'g' 00000 'l' 00001 'p' 01100 'r' 01101 't' 10000 'u' 10001 'x' 11110 'c' 111110 'd' 111111
Eiffel
Adapted C# solution. <lang eiffel> class HUFFMAN_NODE[T -> COMPARABLE] inherit COMPARABLE redefine three_way_comparison end create leaf_node, inner_node feature {NONE} leaf_node (a_probability: REAL_64; a_value: T) do probability := a_probability value := a_value is_leaf := true
left := void right := void parent := void end
inner_node (a_left, a_right: HUFFMAN_NODE[T]) do left := a_left right := a_right
a_left.parent := Current a_right.parent := Current a_left.is_zero := true a_right.is_zero := false
probability := a_left.probability + a_right.probability is_leaf := false end
feature probability: REAL_64 value: detachable T
is_leaf: BOOLEAN
is_zero: BOOLEAN assign set_is_zero
set_is_zero (a_value: BOOLEAN) do is_zero := a_value end
left: detachable HUFFMAN_NODE[T] right: detachable HUFFMAN_NODE[T] parent: detachable HUFFMAN_NODE[T] assign set_parent
set_parent (a_parent: detachable HUFFMAN_NODE[T]) do parent := a_parent end
is_root: BOOLEAN do Result := parent = void end
bit_value: INTEGER do if is_zero then Result := 0 else Result := 1 end end feature -- comparable implementation is_less alias "<" (other: like Current): BOOLEAN do Result := three_way_comparison (other) = -1 end
three_way_comparison (other: like Current): INTEGER do Result := -probability.three_way_comparison (other.probability) end end
class HUFFMAN create make feature {NONE} make(a_string: STRING) require non_empty_string: a_string.count > 0 local l_queue: HEAP_PRIORITY_QUEUE[HUFFMAN_NODE[CHARACTER]] l_counts: HASH_TABLE[INTEGER, CHARACTER] l_node: HUFFMAN_NODE[CHARACTER] l_left, l_right: HUFFMAN_NODE[CHARACTER] do create l_queue.make (a_string.count) create l_counts.make (10)
across a_string as char loop if not l_counts.has (char.item) then l_counts.put (0, char.item) end l_counts.replace (l_counts.at (char.item) + 1, char.item) end
create leaf_dictionary.make(l_counts.count)
across l_counts as kv loop create l_node.leaf_node ((kv.item * 1.0) / a_string.count, kv.key) l_queue.put (l_node) leaf_dictionary.put (l_node, kv.key) end
from until l_queue.count <= 1 loop l_left := l_queue.item l_queue.remove l_right := l_queue.item l_queue.remove
create l_node.inner_node (l_left, l_right) l_queue.put (l_node) end
root := l_queue.item root.is_zero := false end feature root: HUFFMAN_NODE[CHARACTER] leaf_dictionary: HASH_TABLE[HUFFMAN_NODE[CHARACTER], CHARACTER]
encode(a_value: CHARACTER): STRING require encodable: leaf_dictionary.has (a_value) local l_node: HUFFMAN_NODE[CHARACTER] do Result := "" if attached leaf_dictionary.item (a_value) as attached_node then l_node := attached_node from
until l_node.is_root loop Result.append_integer (l_node.bit_value) if attached l_node.parent as parent then l_node := parent end end
Result.mirror end end end
class APPLICATION create make
feature {NONE} make -- entry point local l_str: STRING huff: HUFFMAN chars: BINARY_SEARCH_TREE_SET[CHARACTER] do l_str := "this is an example for huffman encoding"
create huff.make (l_str)
create chars.make chars.fill (l_str)
from chars.start until chars.off loop print (chars.item.out + ": " + huff.encode (chars.item) + "%N") chars.forth end end end </lang>
- Output:
: 101 a: 1001 c: 01110 d: 01111 e: 1111 f: 1100 g: 01001 h: 11101 i: 1101 l: 10001 m: 0010 n: 000 o: 0011 p: 10000 r: 11100 s: 0110 t: 01000 u: 01011 x: 01010
Erlang
The main part of the code used here is extracted from Michel Rijnders' GitHubGist. See also his blog, for a complete description of the original module. <lang erlang>-module(huffman).
-export([encode/1, decode/2, main/0]).
encode(Text) ->
Tree = tree(freq_table(Text)),
Dict = dict:from_list(codewords(Tree)),
Code = << <<(dict:fetch(Char, Dict))/bitstring>> || Char <- Text >>,
{Code, Tree, Dict}.
decode(Code, Tree) ->
decode(Code, Tree, Tree, []).
main() ->
{Code, Tree, Dict} = encode("this is an example for huffman encoding"),
[begin
io:format("~s: ",Key),
print_bits(Value)
end || {Key, Value} <- lists:sort(dict:to_list(Dict))],
io:format("encoded: "),
print_bits(Code),
io:format("decoded: "),
io:format("~s\n",[decode(Code, Tree)]).
decode(<<>>, _, _, Result) ->
lists:reverse(Result);
decode(<<0:1, Rest/bits>>, Tree, {L = {_, _}, _R}, Result) ->
decode(<<Rest/bits>>, Tree, L, Result);
decode(<<0:1, Rest/bits>>, Tree, {L, _R}, Result) ->
decode(<<Rest/bits>>, Tree, Tree, [L | Result]);
decode(<<1:1, Rest/bits>>, Tree, {_L, R = {_, _}}, Result) ->
decode(<<Rest/bits>>, Tree, R, Result);
decode(<<1:1, Rest/bits>>, Tree, {_L, R}, Result) ->
decode(<<Rest/bits>>, Tree, Tree, [R | Result]).
codewords({L, R}) ->
codewords(L, <<0:1>>) ++ codewords(R, <<1:1>>).
codewords({L, R}, <<Bits/bits>>) ->
codewords(L, <<Bits/bits, 0:1>>) ++ codewords(R, <<Bits/bits, 1:1>>);
codewords(Symbol, <<Bits/bitstring>>) ->
[{Symbol, Bits}].
tree([{N, _} | []]) ->
N;
tree(Ns) ->
[{N1, C1}, {N2, C2} | Rest] = lists:keysort(2, Ns),
tree([{{N1, N2}, C1 + C2} | Rest]).
freq_table(Text) ->
freq_table(lists:sort(Text), []).
freq_table([], Acc) ->
Acc;
freq_table([S | Rest], Acc) ->
{Block, MoreBlocks} = lists:splitwith(fun (X) -> X == S end, Rest),
freq_table(MoreBlocks, [{S, 1 + length(Block)} | Acc]).
print_bits(<<>>) ->
io:format("\n");
print_bits(<<Bit:1, Rest/bitstring>>) ->
io:format("~w", [Bit]),
print_bits(Rest).</lang>
- Output:
: 111 a: 1011 c: 10010 d: 100111 e: 1010 f: 1101 g: 100110 h: 1000 i: 1100 l: 00001 m: 0101 n: 001 o: 0100 p: 00000 r: 00011 s: 0111 t: 00010 u: 01101 x: 01100 encoded: 0001010001100011111111000111111101100111110100110010110101000000000110101111101010000011111100001101110111010101101100111110100011001001001001111100001100110 decoded: this is an example for huffman encoding
F#
<lang fsharp>type 'a HuffmanTree =
| Leaf of int * 'a | Node of int * 'a HuffmanTree * 'a HuffmanTree
let freq = function Leaf (f, _) | Node (f, _, _) -> f let freqCompare a b = compare (freq a) (freq b)
let buildTree charFreqs =
let leaves = List.map (fun (c,f) -> Leaf (f,c)) charFreqs
let freqSort = List.sortWith freqCompare
let rec aux = function
| [] -> failwith "empty list"
| [a] -> a
| a::b::tl ->
let node = Node(freq a + freq b, a, b)
aux (freqSort(node::tl))
aux (freqSort leaves)
let rec printTree = function
| code, Leaf (f, c) ->
printfn "%c\t%d\t%s" c f (String.concat "" (List.rev code));
| code, Node (_, l, r) ->
printTree ("0"::code, l);
printTree ("1"::code, r)
let () =
let str = "this is an example for huffman encoding"
let charFreqs =
str |> Seq.groupBy id
|> Seq.map (fun (c, vals) -> (c, Seq.length vals))
|> Map.ofSeq
let tree = charFreqs |> Map.toList |> buildTree
printfn "Symbol\tWeight\tHuffman code";
printTree ([], tree)</lang>
- Output:
Symbol Weight Huffman code p 1 00000 r 1 00001 g 1 00010 l 1 00011 n 4 001 m 2 0100 o 2 0101 c 1 01100 d 1 01101 h 2 0111 s 2 1000 x 1 10010 t 1 100110 u 1 100111 f 3 1010 i 3 1011 a 3 1100 e 3 1101 6 111
Fantom
<lang fantom> class Node {
Float probability := 0.0f
}
class Leaf : Node {
Int character
new make (Int character, Float probability)
{
this.character = character
this.probability = probability
}
}
class Branch : Node {
Node left Node right
new make (Node left, Node right)
{
this.left = left
this.right = right
probability = this.left.probability + this.right.probability
}
}
class Huffman {
Node[] queue := [,] Str:Str table := [:]
new make (Int[] items)
{
uniqueItems := items.dup.unique
uniqueItems.each |Int item|
{
num := items.findAll { it == item }.size
queue.add (Leaf(item, num.toFloat / items.size))
}
createTree
createTable
}
Void createTree ()
{
while (queue.size > 1)
{
queue.sort |a,b| {a.probability <=> b.probability}
node1 := queue.removeAt (0)
node2 := queue.removeAt (0)
queue.add (Branch (node1, node2))
}
}
Void traverse (Node node, Str encoding)
{
if (node is Leaf)
{
table[(node as Leaf).character.toChar] = encoding
}
else // (node is Branch)
{
traverse ((node as Branch).left, encoding + "0")
traverse ((node as Branch).right, encoding + "1")
}
}
Void createTable ()
{
if (queue.size != 1) return // error!
traverse (queue.first, "")
}
override Str toStr ()
{
result := "Huffman Encoding Table:\n"
table.keys.sort.each |Str key|
{
result += "$key -> ${table[key]}\n"
}
return result
}
}
class Main {
public static Void main ()
{
example := "this is an example for huffman encoding"
huffman := Huffman (example.chars)
echo ("From \"$example\"")
echo (huffman)
}
} </lang>
- Output:
From "this is an example for huffman encoding" Huffman Encoding Table: -> 101 a -> 1100 c -> 10000 d -> 10001 e -> 1101 f -> 1110 g -> 11110 h -> 11111 i -> 1001 l -> 01101 m -> 0011 n -> 000 o -> 0100 p -> 01100 r -> 01110 s -> 0010 t -> 01010 u -> 01111 x -> 01011
Fortran
<lang fortran>! output: ! d-> 00000, t-> 00001, h-> 0001, s-> 0010, ! c-> 00110, x-> 00111, m-> 0100, o-> 0101, ! n-> 011, u-> 10000, l-> 10001, a-> 1001, ! r-> 10100, g-> 101010, p-> 101011, ! e-> 1011, i-> 1100, f-> 1101, -> 111 ! ! 00001|0001|1100|0010|111|1100|0010|111|1001|011| ! 111|1011|00111|1001|0100|101011|10001|1011|111| ! 1101|0101|10100|111|0001|10000|1101|1101|0100| ! 1001|011|111|1011|011|00110|0101|00000|1100|011|101010| ! module huffman implicit none type node
character (len=1 ), allocatable :: sym(:) character (len=10), allocatable :: code(:) integer :: freq
contains
procedure :: show => show_node
end type
type queue
type(node), allocatable :: buf(:) integer :: n = 0
contains
procedure :: extractmin procedure :: append procedure :: siftdown
end type
contains
subroutine siftdown(this, a)
class (queue) :: this
integer :: a, parent, child
associate (x => this%buf)
parent = a
do while(parent*2 <= this%n)
child = parent*2
if (child + 1 <= this%n) then
if (x(child+1)%freq < x(child)%freq ) then
child = child +1
end if
end if
if (x(parent)%freq > x(child)%freq) then
x([child, parent]) = x([parent, child])
parent = child
else
exit
end if
end do
end associate
end subroutine
function extractmin(this) result (res)
class(queue) :: this type(node) :: res res = this%buf(1) this%buf(1) = this%buf(this%n) this%n = this%n - 1 call this%siftdown(1)
end function
subroutine append(this, x)
class(queue), intent(inout) :: this type(node) :: x type(node), allocatable :: tmp(:) integer :: i this%n = this%n +1 if (.not.allocated(this%buf)) allocate(this%buf(1)) if (size(this%buf)<this%n) then allocate(tmp(2*size(this%buf))) tmp(1:this%n-1) = this%buf call move_alloc(tmp, this%buf) end if this%buf(this%n) = x i = this%n do i = i / 2 if (i==0) exit call this%siftdown(i) end do
end subroutine
function join(a, b) result(c)
type(node) :: a, b, c integer :: i, n, n1 n1 = size(a%sym) n = n1 + size(b%sym) c%freq = a%freq + b%freq allocate (c%sym(n), c%code(n)) do i = 1, n1 c%sym(i) = a%sym(i) c%code(i) = "0" // trim(a%code(i)) end do do i = 1, size(b%sym) c%sym(i+n1) = b%sym(i) c%code(i+n1) = "1" // trim(b%code(i)) end do
end function
subroutine show_node(this)
class(node) :: this integer :: i write(*, "(*(g0,'-> ',g0,:,', '))", advance="no") & (this%sym(i), trim(this%code(i)), i=1,size(this%sym)) print *
end subroutine
function create(letter, freq) result (this)
character :: letter integer :: freq type(node) :: this allocate(this%sym(1), this%code(1)) this%sym(1) = letter ; this%code(1) = "" this%freq = freq
end function end module
program main
use huffman
character (len=*), parameter :: txt = &
"this is an example for huffman encoding"
integer :: i, freq(0:255) = 0
type(queue) :: Q
type(node) :: x
do i = 1, len(txt)
freq(ichar(txt(i:i))) = freq(ichar(txt(i:i))) + 1
end do
do i = 0, 255
if (freq(i)>0) then
call Q%append(create(char(i), freq(i)))
end if
end do
do i = 1, Q%n-1
call Q%append(join(Q%extractmin(),Q%extractmin()))
end do
x = Q%extractmin()
call x%show()
do i = 1, len(txt)
do k = 1, size(x%sym)
if (x%sym(k)==txt(i:i)) exit
end do
write (*, "(a,'|')", advance="no") trim(x%code(k))
end do
print *
end program </lang>
Go
<lang go>package main
import (
"container/heap" "fmt"
)
type HuffmanTree interface {
Freq() int
}
type HuffmanLeaf struct {
freq int value rune
}
type HuffmanNode struct {
freq int left, right HuffmanTree
}
func (self HuffmanLeaf) Freq() int {
return self.freq
}
func (self HuffmanNode) Freq() int {
return self.freq
}
type treeHeap []HuffmanTree
func (th treeHeap) Len() int { return len(th) } func (th treeHeap) Less(i, j int) bool {
return th[i].Freq() < th[j].Freq()
} func (th *treeHeap) Push(ele interface{}) {
*th = append(*th, ele.(HuffmanTree))
} func (th *treeHeap) Pop() (popped interface{}) {
popped = (*th)[len(*th)-1] *th = (*th)[:len(*th)-1] return
} func (th treeHeap) Swap(i, j int) { th[i], th[j] = th[j], th[i] }
func buildTree(symFreqs map[rune]int) HuffmanTree {
var trees treeHeap
for c, f := range symFreqs {
trees = append(trees, HuffmanLeaf{f, c})
}
heap.Init(&trees)
for trees.Len() > 1 {
// two trees with least frequency
a := heap.Pop(&trees).(HuffmanTree)
b := heap.Pop(&trees).(HuffmanTree)
// put into new node and re-insert into queue
heap.Push(&trees, HuffmanNode{a.Freq() + b.Freq(), a, b})
}
return heap.Pop(&trees).(HuffmanTree)
}
func printCodes(tree HuffmanTree, prefix []byte) {
switch i := tree.(type) {
case HuffmanLeaf:
// print out symbol, frequency, and code for this
// leaf (which is just the prefix)
fmt.Printf("%c\t%d\t%s\n", i.value, i.freq, string(prefix))
case HuffmanNode:
// traverse left
prefix = append(prefix, '0')
printCodes(i.left, prefix)
prefix = prefix[:len(prefix)-1]
// traverse right
prefix = append(prefix, '1')
printCodes(i.right, prefix)
prefix = prefix[:len(prefix)-1]
}
}
func main() {
test := "this is an example for huffman encoding"
symFreqs := make(map[rune]int)
// read each symbol and record the frequencies
for _, c := range test {
symFreqs[c]++
}
// build tree tree := buildTree(symFreqs)
// print out results
fmt.Println("SYMBOL\tWEIGHT\tHUFFMAN CODE")
printCodes(tree, []byte{})
}</lang>
- Output:
SYMBOL WEIGHT HUFFMAN CODE n 4 000 m 2 0010 o 2 0011 s 2 0100 u 1 01010 p 1 01011 h 2 0110 d 1 01110 c 1 01111 t 1 10000 l 1 10001 x 1 10010 r 1 100110 g 1 100111 i 3 1010 e 3 1011 6 110 f 3 1110 a 3 1111
<lang go>package main
import (
"container/heap" "fmt"
)
type coded struct {
sym rune code string
}
type counted struct {
total int syms []coded
}
type cHeap []counted
// satisfy heap.Interface func (c cHeap) Len() int { return len(c) } func (c cHeap) Less(i, j int) bool { return c[i].total < c[j].total } func (c cHeap) Swap(i, j int) { c[i], c[j] = c[j], c[i] } func (c *cHeap) Push(ele interface{}) {
*c = append(*c, ele.(counted))
} func (c *cHeap) Pop() (popped interface{}) {
popped = (*c)[len(*c)-1] *c = (*c)[:len(*c)-1] return
}
func encode(sym2freq map[rune]int) []coded {
var ch cHeap
for sym, freq := range sym2freq {
ch = append(ch, counted{freq, []codedTemplate:Sym: sym})
}
heap.Init(&ch)
for len(ch) > 1 {
a := heap.Pop(&ch).(counted)
b := heap.Pop(&ch).(counted)
for i, c := range a.syms {
a.syms[i].code = "0" + c.code
}
for i, c := range b.syms {
b.syms[i].code = "1" + c.code
}
heap.Push(&ch, counted{a.total + b.total, append(a.syms, b.syms...)})
}
return heap.Pop(&ch).(counted).syms
}
const txt = "this is an example for huffman encoding"
func main() {
sym2freq := make(map[rune]int)
for _, c := range txt {
sym2freq[c]++
}
table := encode(sym2freq)
fmt.Println("Symbol Weight Huffman Code")
for _, c := range table {
fmt.Printf(" %c %d %s\n", c.sym, sym2freq[c.sym], c.code)
}
}</lang>
Groovy
Implemented and tested with Groovy 2.3.
<lang groovy> import groovy.transform.*
@Canonical @Sortable(includes = ['freq', 'letter']) class Node {
String letter
int freq
Node left
Node right
boolean isLeaf() { left == null && right == null }
}
Map correspondance(Node n, Map corresp = [:], String prefix = ) {
if (n.isLeaf()) {
corresp[n.letter] = prefix ?: '0'
} else {
correspondance(n.left, corresp, prefix + '0')
correspondance(n.right, corresp, prefix + '1')
}
return corresp
}
Map huffmanCode(String message) {
def queue = message.toList().countBy { it } // char frequencies
.collect { String letter, int freq -> // transformed into tree nodes
new Node(letter, freq)
} as TreeSet // put in a queue that maintains ordering
while(queue.size() > 1) {
def (nodeLeft, nodeRight) = [queue.pollFirst(), queue.pollFirst()]
queue << new Node(
freq: nodeLeft.freq + nodeRight.freq,
letter: nodeLeft.letter + nodeRight.letter,
left: nodeLeft, right: nodeRight
)
}
return correspondance(queue.pollFirst())
}
String encode(CharSequence msg, Map codeTable) {
msg.collect { codeTable[it] }.join()
}
String decode(String codedMsg, Map codeTable, String decoded = ) {
def pair = codeTable.find { k, v -> codedMsg.startsWith(v) }
pair ? pair.key + decode(codedMsg.substring(pair.value.size()), codeTable)
: decoded
} </lang> Usage: <lang groovy> def message = "this is an example for huffman encoding"
def codeTable = huffmanCode(message) codeTable.each { k, v -> println "$k: $v" }
def encoded = encode(message, codeTable) println encoded
def decoded = decode(encoded, codeTable) println decoded </lang>
- Output:
g: 00000 l: 00001 h: 0001 m: 0010 o: 0011 n: 010 p: 01100 r: 01101 s: 0111 t: 10000 u: 10001 a: 1001 : 101 e: 1100 f: 1101 i: 1110 x: 11110 c: 111110 d: 111111 1000000011110011110111100111101100101010111001111010010010011000000111001011101001101101101000110001110111010010100101010111000101111100011111111111001000000 this is an example for huffman encoding
Haskell
Credits go to huffman where you'll also find a non-tree solution. Uses sorted list as a priority queue. <lang haskell>import Data.List import Control.Arrow import Data.Ord
data HTree a
= Leaf a
| Branch (HTree a)
(HTree a)
deriving (Show, Eq, Ord)
test :: String -> IO () test =
mapM_ (\(a, b) -> putStrLn ('\ : a : "\' : " ++ b)) .
serialize . huffmanTree . freq
serialize :: HTree a -> [(a, String)] serialize (Branch l r) =
(second ('0' :) <$> serialize l) ++ (second ('1' :) <$> serialize r)
serialize (Leaf x) = [(x, "")]
huffmanTree
:: (Ord w, Num w) => [(w, a)] -> HTree a
huffmanTree =
snd . head . until (null . tail) hstep . sortBy (comparing fst) . (second Leaf <$>)
hstep
:: (Ord a, Num a) => [(a, HTree b)] -> [(a, HTree b)]
hstep ((w1, t1):(w2, t2):wts) =
insertBy (comparing fst) (w1 + w2, Branch t1 t2) wts
freq
:: Ord a => [a] -> [(Int, a)]
freq = ((length &&& head) <$>) . group . sort</lang>
- Output:
<lang haskell>*Main> test "this is an example for huffman encoding" 'p' : 00000 'r' : 00001 'g' : 00010 'l' : 00011 'n' : 001 'm' : 0100 'o' : 0101 'c' : 01100 'd' : 01101 'h' : 0111 's' : 1000 'x' : 10010 't' : 100110 'u' : 100111 'f' : 1010 'i' : 1011 'a' : 1100 'e' : 1101 ' ' : 111</lang>
Using Set as a priority queue
(might be worth it for bigger alphabets): <lang haskell>import qualified Data.Set as S
htree :: (Ord t, Num t, Ord a) => S.Set (t, HTree a) -> HTree a htree ts | S.null ts_1 = t1
| otherwise = htree ts_3
where
((w1,t1), ts_1) = S.deleteFindMin ts
((w2,t2), ts_2) = S.deleteFindMin ts_1
ts_3 = S.insert (w1 + w2, Branch t1 t2) ts_2
huffmanTree :: (Ord w, Num w, Ord a) => [(w, a)] -> HTree a huffmanTree = htree . S.fromList . map (second Leaf)</lang>
A non-tree version
This produces the output required without building the Huffman tree at all, by building all the trace strings directly while reducing the histogram: <lang haskell>import Data.List (sortBy, insertBy, sort, group) import Control.Arrow (second, (&&&)) import Data.Ord (comparing)
freq :: Ord a => [a] -> [(Int, a)] freq = map (length &&& head) . group . sort
huffman :: [(Int, Char)] -> [(Char, String)] huffman = reduce . map (\(p, c) -> (p, [(c ,"")])) . sortBy (comparing fst)
where add (p1, xs1) (p2, xs2) = (p1 + p2, map (second ('0':)) xs1 ++ map (second ('1':)) xs2)
reduce [(_, ys)] = sortBy (comparing fst) ys
reduce (x1:x2:xs) = reduce $ insertBy (comparing fst) (add x1 x2) xs
test s = mapM_ (\(a, b) -> putStrLn ('\ : a : "\' : " ++ b)) . huffman . freq $ s
main = do
test "this is an example for huffman encoding"</lang>
Icon and Unicon
<lang Icon>record huffnode(l,r,n,c) # internal and leaf nodes record huffcode(c,n,b,i) # encoding table char, freq, bitstring, bits (int)
procedure main()
s := "this is an example for huffman encoding"
Count := huffcount(s) # frequency count Tree := huffTree(Count) # heap and tree
Code := [] # extract encodings CodeT := table() every x := huffBits(Tree) do
put( Code, CodeT[c] := huffcode( c := x[-1], Count[c].n, b := x[1:-1], integer("2r"||b) ) )
Code := sortf( Code, 1 ) # show table in char order
write("Input String : ",image(s))
write(right("char",5), right("freq",5), " encoding" )
every write(right(image((x := !Code).c),5), right(x.n,5), " ", x.b )
end
procedure huffBits(N) # generates huffman bitcodes with trailing character if \N.c then return N.c # . append leaf char code suspend "0" || huffBits(N.l) # . left suspend "1" || huffBits(N.r) # . right end
procedure huffTree(T) # two queue huffman tree method
local Q1,Q2,x,n1,n2
Q1 := [] # queue of characters and weights every x := !T do # ensure all are huffnodes
if type(x) == "huffnode" then put(Q1,x) else runerr(205,x)
Q1 := sortf(Q1,3) # sort by weight ( 3 means by .n )
if *Q1 > 1 then Q2 := [] while *Q1+*\Q2 > 1 do { # While there is more than one node ...
n1 := if Q1[1] & ( ( Q1[1].n <= Q2[1].n ) | not Q2[1] ) then get(Q1) else get(Q2) # lowest weight from Q1 or Q2 n2 := if Q1[1] & ( ( Q1[1].n <= Q2[1].n ) | not Q2[1] ) then get(Q1) else get(Q2) # lowest weight from Q1 or Q2
put( Q2, huffnode( n1, n2, n1.n + n2.n ) ) # new weighted node to end of Q2
}
return (\Q2 | Q1)[1] # return the root node end
procedure huffcount(s) # return characters and frequencies in a table of huffnodes by char local c,T
T := table() every c := !s do {
/T[c] := huffnode(,,0,c) T[c].n +:= 1 }
return T end</lang>
- Output:
Input String : "this is an example for huffman encoding" char freq encoding " " 6 101 "a" 3 1100 "c" 1 10000 "d" 1 10001 "e" 3 1101 "f" 3 1110 "g" 1 11110 "h" 2 11111 "i" 3 1001 "l" 1 01101 "m" 2 0011 "n" 4 000 "o" 2 0100 "p" 1 01100 "r" 1 01110 "s" 2 0010 "t" 1 01010 "u" 1 01111 "x" 1 01011
The following Unicon specific solution takes advantage of the Heap priority queue implementation found in the UniLib Collections package and implements the algorithm given in the problem description. The program produces Huffman codes based on each line of input. <lang Unicon>import Collections
procedure main(A)
every line := !&input do {
every (t := table(0))[!line] +:= 1 # Frequency table
heap := Heap(sort(t), field, "<") # Initial priority queue
while heap.size() > 1 do { # Tree construction
every (p1|p2) := heap.get()
heap.add([&null, p1[2]+p2[2], p1, p2])
}
codes := treeWalk(heap.get(),"") # Get codes from tree
write("Huffman encoding:") # Display codes
every pair := !sort(codes) do
write("\t'",\pair[1],"'-> ",pair[2])
}
end
procedure field(node) # selector function for Heap
return node[2] # field to use for priority ordering
end
procedure treeWalk(node, prefix, codeMap)
/codeMap := table("")
if /node[1] then { # interior node
treeWalk(node[3], prefix||"0", codeMap)
treeWalk(node[4], prefix||"1", codeMap)
}
else codeMap[node[1]] := prefix
return codeMap
end</lang>
A sample run:
->huffman
this is an example for huffman encoding
Huffman encoding:
' '-> 111
'a'-> 1001
'c'-> 00110
'd'-> 00000
'e'-> 1011
'f'-> 1101
'g'-> 101010
'h'-> 0001
'i'-> 1100
'l'-> 10001
'm'-> 0100
'n'-> 011
'o'-> 0101
'p'-> 101011
'r'-> 10100
's'-> 0010
't'-> 00001
'u'-> 10000
'x'-> 00111
aardvarks are ant eaters
Huffman encoding:
' '-> 011
'a'-> 10
'd'-> 0010
'e'-> 010
'k'-> 0011
'n'-> 0001
'r'-> 110
's'-> 1111
't'-> 1110
'v'-> 0000
->
HuffStuff provides huffman encoding routines
J
Solution (drawn from the J wiki):
<lang j>hc=: 4 : 0
if. 1=#x do. y
else. ((i{x),+/j{x) hc (i{y),<j{y [ i=. (i.#x) -. j=. 2{./:x end.
)
hcodes=: 4 : 0
assert. x -:&$ y NB. weights and words have same shape
assert. (0<:x) *. 1=#$x NB. weights are non-negative
assert. 1 >: L.y NB. words are boxed not more than once
w=. ,&.> y NB. standardized words
assert. w -: ~.w NB. words are unique
t=. 0 {:: x hc w NB. minimal weight binary tree
((< S: 0 t) i. w) { <@(1&=)@; S: 1 {:: t
)</lang>
Example:<lang j> ;"1":L:0(#/.~ (],.(<' '),.hcodes) ,&.>@~.)'this is an example for huffman encoding'
t 0 1 0 1 0
h 1 1 1 1 1
i 1 0 0 1
s 0 0 1 0
1 0 1
a 1 1 0 0
n 0 0 0
e 1 1 0 1
x 0 1 0 1 1
m 0 0 1 1
p 0 1 1 0 0
l 0 1 1 0 1
f 1 1 1 0
o 0 1 0 0
r 0 1 1 1 0
u 0 1 1 1 1
c 1 0 0 0 0
d 1 0 0 0 1
g 1 1 1 1 0</lang>
Java
This implementation creates an actual tree structure, and then traverses the tree to recover the code. <lang java>import java.util.*;
abstract class HuffmanTree implements Comparable<HuffmanTree> {
public final int frequency; // the frequency of this tree
public HuffmanTree(int freq) { frequency = freq; }
// compares on the frequency
public int compareTo(HuffmanTree tree) {
return frequency - tree.frequency;
}
}
class HuffmanLeaf extends HuffmanTree {
public final char value; // the character this leaf represents
public HuffmanLeaf(int freq, char val) {
super(freq);
value = val;
}
}
class HuffmanNode extends HuffmanTree {
public final HuffmanTree left, right; // subtrees
public HuffmanNode(HuffmanTree l, HuffmanTree r) {
super(l.frequency + r.frequency);
left = l;
right = r;
}
}
public class HuffmanCode {
// input is an array of frequencies, indexed by character code
public static HuffmanTree buildTree(int[] charFreqs) {
PriorityQueue<HuffmanTree> trees = new PriorityQueue<HuffmanTree>();
// initially, we have a forest of leaves
// one for each non-empty character
for (int i = 0; i < charFreqs.length; i++)
if (charFreqs[i] > 0)
trees.offer(new HuffmanLeaf(charFreqs[i], (char)i));
assert trees.size() > 0;
// loop until there is only one tree left
while (trees.size() > 1) {
// two trees with least frequency
HuffmanTree a = trees.poll();
HuffmanTree b = trees.poll();
// put into new node and re-insert into queue
trees.offer(new HuffmanNode(a, b));
}
return trees.poll();
}
public static void printCodes(HuffmanTree tree, StringBuffer prefix) {
assert tree != null;
if (tree instanceof HuffmanLeaf) {
HuffmanLeaf leaf = (HuffmanLeaf)tree;
// print out character, frequency, and code for this leaf (which is just the prefix)
System.out.println(leaf.value + "\t" + leaf.frequency + "\t" + prefix);
} else if (tree instanceof HuffmanNode) {
HuffmanNode node = (HuffmanNode)tree;
// traverse left
prefix.append('0');
printCodes(node.left, prefix);
prefix.deleteCharAt(prefix.length()-1);
// traverse right
prefix.append('1');
printCodes(node.right, prefix);
prefix.deleteCharAt(prefix.length()-1);
}
}
public static void main(String[] args) {
String test = "this is an example for huffman encoding";
// we will assume that all our characters will have
// code less than 256, for simplicity
int[] charFreqs = new int[256];
// read each character and record the frequencies
for (char c : test.toCharArray())
charFreqs[c]++;
// build tree
HuffmanTree tree = buildTree(charFreqs);
// print out results
System.out.println("SYMBOL\tWEIGHT\tHUFFMAN CODE");
printCodes(tree, new StringBuffer());
}
}</lang>
- Output:
SYMBOL WEIGHT HUFFMAN CODE d 1 00000 t 1 00001 h 2 0001 s 2 0010 c 1 00110 x 1 00111 m 2 0100 o 2 0101 n 4 011 u 1 10000 l 1 10001 a 3 1001 r 1 10100 g 1 101010 p 1 101011 e 3 1011 i 3 1100 f 3 1101 6 111
JavaScript
for the print() function.
First, use the Binary Heap implementation from here: http://eloquentjavascript.net/appendix2.html
The Huffman encoder <lang javascript>function HuffmanEncoding(str) {
this.str = str;
var count_chars = {};
for (var i = 0; i < str.length; i++)
if (str[i] in count_chars)
count_chars[str[i]] ++;
else
count_chars[str[i]] = 1;
var pq = new BinaryHeap(function(x){return x[0];});
for (var ch in count_chars)
pq.push([count_chars[ch], ch]);
while (pq.size() > 1) {
var pair1 = pq.pop();
var pair2 = pq.pop();
pq.push([pair1[0]+pair2[0], [pair1[1], pair2[1]]]);
}
var tree = pq.pop();
this.encoding = {};
this._generate_encoding(tree[1], "");
this.encoded_string = ""
for (var i = 0; i < this.str.length; i++) {
this.encoded_string += this.encoding[str[i]];
}
}
HuffmanEncoding.prototype._generate_encoding = function(ary, prefix) {
if (ary instanceof Array) {
this._generate_encoding(ary[0], prefix + "0");
this._generate_encoding(ary[1], prefix + "1");
}
else {
this.encoding[ary] = prefix;
}
}
HuffmanEncoding.prototype.inspect_encoding = function() {
for (var ch in this.encoding) {
print("'" + ch + "': " + this.encoding[ch])
}
}
HuffmanEncoding.prototype.decode = function(encoded) {
var rev_enc = {};
for (var ch in this.encoding)
rev_enc[this.encoding[ch]] = ch;
var decoded = "";
var pos = 0;
while (pos < encoded.length) {
var key = ""
while (!(key in rev_enc)) {
key += encoded[pos];
pos++;
}
decoded += rev_enc[key];
}
return decoded;
}</lang>
And, using the Huffman encoder <lang javascript>var s = "this is an example for huffman encoding"; print(s);
var huff = new HuffmanEncoding(s); huff.inspect_encoding();
var e = huff.encoded_string; print(e);
var t = huff.decode(e); print(t);
print("is decoded string same as original? " + (s==t));</lang>
- Output:
this is an example for huffman encoding 'n': 000 's': 0010 'm': 0011 'o': 0100 't': 01010 'x': 01011 'p': 01100 'l': 01101 'r': 01110 'u': 01111 'c': 10000 'd': 10001 'i': 1001 ' ': 101 'a': 1100 'e': 1101 'f': 1110 'g': 11110 'h': 11111 0101011111100100101011001001010111000001011101010111100001101100011011101101111001000111010111111011111110111000111100000101110100010000010010001100100011110 this is an example for huffman encoding is decoded string same as original? true
Julia
<lang julia> abstract type HuffmanTree end
struct HuffmanLeaf <: HuffmanTree
ch::Char freq::Int
end
struct HuffmanNode <: HuffmanTree
freq::Int left::HuffmanTree right::HuffmanTree
end
function makefreqdict(s::String)
d = Dict{Char, Int}()
for c in s
if !haskey(d, c)
d[c] = 1
else
d[c] += 1
end
end
d
end
function huffmantree(ftable::Dict)
trees::Vector{HuffmanTree} = [HuffmanLeaf(ch, fq) for (ch, fq) in ftable]
while length(trees) > 1
sort!(trees, lt = (x, y) -> x.freq < y.freq, rev = true)
least = pop!(trees)
nextleast = pop!(trees)
push!(trees, HuffmanNode(least.freq + nextleast.freq, least, nextleast))
end
trees[1]
end
printencoding(lf::HuffmanLeaf, code) = println(lf.ch == ' ' ? "space" : lf.ch, "\t", lf.freq, "\t", code)
function printencoding(nd::HuffmanNode, code)
code *= '0' printencoding(nd.left, code) code = code[1:end-1]
code *= '1' printencoding(nd.right, code) code = code[1:end-1]
end
const msg = "this is an example for huffman encoding"
println("Char\tFreq\tHuffman code")
printencoding(huffmantree(makefreqdict(msg)), "")
</lang>
- Output:
Char Freq Huffman code p 1 00000 c 1 00001 g 1 00010 x 1 00011 n 4 001 s 2 0100 h 2 0101 u 1 01100 l 1 01101 m 2 0111 o 2 1000 d 1 10010 r 1 100110 t 1 100111 e 3 1010 f 3 1011 a 3 1100 i 3 1101 space 6 111
Kotlin
This implementation creates an actual tree structure, and then traverses the tree to recover the code. <lang kotlin>import java.util.*
abstract class HuffmanTree(var freq: Int) : Comparable<HuffmanTree> {
override fun compareTo(other: HuffmanTree) = freq - other.freq
}
class HuffmanLeaf(freq: Int, var value: Char) : HuffmanTree(freq)
class HuffmanNode(var left: HuffmanTree, var right: HuffmanTree) : HuffmanTree(left.freq + right.freq)
fun buildTree(charFreqs: IntArray) : HuffmanTree {
val trees = PriorityQueue<HuffmanTree>()
charFreqs.forEachIndexed { index, freq ->
if(freq > 0) trees.offer(HuffmanLeaf(freq, index.toChar()))
}
assert(trees.size > 0)
while (trees.size > 1) {
val a = trees.poll()
val b = trees.poll()
trees.offer(HuffmanNode(a, b))
}
return trees.poll()
}
fun printCodes(tree: HuffmanTree, prefix: StringBuffer) {
when(tree) {
is HuffmanLeaf -> println("${tree.value}\t${tree.freq}\t$prefix")
is HuffmanNode -> {
//traverse left
prefix.append('0')
printCodes(tree.left, prefix)
prefix.deleteCharAt(prefix.lastIndex)
//traverse right
prefix.append('1')
printCodes(tree.right, prefix)
prefix.deleteCharAt(prefix.lastIndex)
}
}
}
fun main(args: Array<String>) {
val test = "this is an example for huffman encoding"
val maxIndex = test.max()!!.toInt() + 1
val freqs = IntArray(maxIndex) //256 enough for latin ASCII table, but dynamic size is more fun
test.forEach { freqs[it.toInt()] += 1 }
val tree = buildTree(freqs)
println("SYMBOL\tWEIGHT\tHUFFMAN CODE")
printCodes(tree, StringBuffer())
}</lang>
- Output:
SYMBOL WEIGHT HUFFMAN CODE d 1 00000 t 1 00001 h 2 0001 s 2 0010 c 1 00110 x 1 00111 m 2 0100 o 2 0101 n 4 011 u 1 10000 l 1 10001 a 3 1001 r 1 10100 g 1 101010 p 1 101011 e 3 1011 i 3 1100 f 3 1101 6 111
Lua
This implementation proceeds in three steps: determine word frequencies, construct the Huffman tree, and finally fold the tree into the codes while outputting them. <lang lua>local build_freqtable = function (data)
local freq = { }
for i = 1, #data do local cur = string.sub (data, i, i) local count = freq [cur] or 0 freq [cur] = count + 1 end
local nodes = { }
for w, f in next, freq do
nodes [#nodes + 1] = { word = w, freq = f }
end
table.sort (nodes, function (a, b) return a.freq > b.freq end) --- reverse order!
return nodes
end
local build_hufftree = function (nodes)
while true do local n = #nodes local left = nodes [n] nodes [n] = nil
local right = nodes [n - 1] nodes [n - 1] = nil
local new = { freq = left.freq + right.freq, left = left, right = right }
if n == 2 then return new end
--- insert new node at correct priority
local prio = 1
while prio < #nodes and nodes [prio].freq > new.freq do
prio = prio + 1
end
table.insert (nodes, prio, new)
end
end
local print_huffcodes do
local rec_build_huffcodes
rec_build_huffcodes = function (node, bits, acc)
if node.word == nil then
rec_build_huffcodes (node.left, bits .. "0", acc)
rec_build_huffcodes (node.right, bits .. "1", acc)
return acc
else --- leaf
acc [#acc + 1] = { node.freq, node.word, bits }
end
return acc
end
print_huffcodes = function (root)
local codes = rec_build_huffcodes (root, "", { })
table.sort (codes, function (a, b) return a [1] < b [1] end)
print ("frequency\tword\thuffman code")
for i = 1, #codes do
print (string.format ("%9d\t‘%s’\t“%s”", table.unpack (codes [i])))
end
end
end
local huffcode = function (data)
local nodes = build_freqtable (data) local huff = build_hufftree (nodes) print_huffcodes (huff) return 0
end
return huffcode "this is an example for huffman encoding"
</lang>
frequency word huffman code
1 ‘g’ “01111”
1 ‘p’ “01011”
1 ‘d’ “01100”
1 ‘c’ “01101”
1 ‘t’ “01010”
1 ‘r’ “10000”
1 ‘u’ “11110”
1 ‘x’ “10001”
1 ‘l’ “01110”
2 ‘o’ “11111”
2 ‘m’ “0011”
2 ‘h’ “0010”
2 ‘s’ “0100”
3 ‘i’ “1101”
3 ‘f’ “1110”
3 ‘a’ “1100”
3 ‘e’ “1001”
4 ‘n’ “000”
6 ‘ ’ “101”
M2000 Interpreter
<lang M2000 Interpreter> Module Huffman {
comp=lambda (a, b) ->{
=array(a, 0)<array(b, 0)
}
module InsertPQ (a, n, &comp) {
if len(a)=0 then stack a {data n} : exit
if comp(n, stackitem(a)) then stack a {push n} : exit
stack a {
push n
t=2: b=len(a)
m=b
While t<=b {
t1=m
m=(b+t) div 2
if m=0 then m=t1 : exit
If comp(stackitem(m),n) then t=m+1: continue
b=m-1
m=b
}
if m>1 then shiftback m
}
}
a$="this is an example for huffman encoding"
inventory queue freq
For i=1 to len(a$) {
b$=mid$(a$,i,1)
if exist(freq, b$) then Return freq, b$:=freq(b$)+1 : continue
append freq, b$:=1
}
sort ascending freq
b=stack
K=each(freq)
LenA=len(a$)
While k {
InsertPQ b, (Round(Eval(k)/lenA, 4), eval$(k, k^)), &comp
}
While len(b)>1 {
Stack b {
Read m1, m2
InsertPQ b, (Array(m1)+Array(m2), (m1, m2) ), &comp
}
}
Print "Size of stack object (has only Root):"; len(b)
Print "Root probability:";Round(Array(Stackitem(b)), 3)
inventory encode, decode
Traverse(stackitem(b), "")
message$=""
For i=1 to len(a$)
message$+=encode$(mid$(a$, i, 1))
Next i
Print message$
j=1
check$=""
For i=1 to len(a$)
d=each(encode)
While d {
code$=eval$(d)
if mid$(message$, j, len(code$))=code$ then {
check$+=decode$(code$)
Print decode$(code$); : j+=len(code$)
}
}
Next i
Print
Print len(message$);" bits ", if$(a$=check$->"Encoding/decoding worked", "Encoding/Decoding failed")
Sub Traverse(a, a$)
local b=array(a,1)
if type$(b)="mArray" Else {
Print @(10); quote$(array$(a, 1));" "; a$,@(20),array(a)
Append decode, a$ :=array$(a, 1)
Append encode, array$(a, 1):=a$
Exit Sub
}
traverse(array(b), a$+"0")
traverse(array(b,1), a$+"1")
End Sub
} Huffman </lang>
- Output:
"p" 00000 0,0256
"l" 00001 0,0256
"t" 00010 0,0256
"r" 00011 0,0256
"x" 00100 0,0256
"u" 00101 0,0256
"s" 0011 0,0513
"o" 0100 0,0513
"m" 0101 0,0513
"n" 011 0,1026
"h" 1000 0,0513
"c" 10010 0,0256
"g" 100110 0,0256
"d" 100111 0,0256
"e" 1010 0,0769
"a" 1011 0,0769
"i" 1100 0,0769
"f" 1101 0,0769
" " 111 0,1538
0001010001100001111111000011111101101111110100010010110101000000000110101111101010000011111100000101110111010101101101111110100111001001001001111100011100110
this is an example for huffman encoding
157 bits Encoding/decoding worked
Mathematica / Wolfram Language
<lang mathematica>huffman[s_String] := huffman[Characters[s]]; huffman[l_List] := Module[{merge, structure, rules},
(*merge front two branches. list is assumed to be sorted*)
merge[k_] := Replace[k, {{a_, aC_}, {b_, bC_}, rest___} :> {{{a, b}, aC + bC}, rest}];
structure = FixedPoint[
Composition[merge, SortBy[#, Last] &],
Tally[l]]1, 1;
rules = (# -> Flatten[Position[structure, #] - 1]) & /@ DeleteDuplicates[l];
{Flatten[l /. rules], rules}];</lang>
Nim
<lang nim>import tables, seqUtils
const sampleString = "this is an example for huffman encoding"
type
# Following range can be changed to produce Huffman codes on arbitrary alphabet (e.g. ternary codes)
CodeSymbol = range[0..1]
HuffCode = seq[CodeSymbol]
Node = ref object
f: int
parent: Node
case isLeaf: bool
of true:
c: char
else:
childs: array[CodeSymbol, Node]
proc `<`(a: Node, b: Node): bool =
# For min operator a.f < b.f
proc `$`(hc: HuffCode): string =
result = ""
for symbol in hc:
result &= $symbol
proc freeChildList(tree: seq[Node], parent: Node = nil): seq[Node] =
# Constructs a sequence of nodes which can be adopted
# Optional parent parameter can be set to ensure node will not adopt itself
result = @[]
for node in tree:
if node.parent == nil and node != parent:
result.add(node)
proc connect(parent: Node, child: Node) =
# Only call this proc when sure that parent has a free child slot
child.parent = parent
parent.f += child.f
for i in parent.childs.low..parent.childs.high:
if parent.childs[i] == nil:
parent.childs[i] = child
return
proc generateCodes(codes: TableRef[char, HuffCode], currentNode: Node, currentCode: HuffCode = @[]) =
if currentNode.isLeaf:
let key = currentNode.c
codes[key] = currentCode
return
for i in currentNode.childs.low..currentNode.childs.high:
if currentNode.childs[i] != nil:
let newCode = currentCode & i
generateCodes(codes, currentNode.childs[i], newCode)
proc buildTree(frequencies: CountTable[char]): seq[Node] =
result = newSeq[Node](frequencies.len)
for i in result.low..result.high:
let key = toSeq(frequencies.keys)[i]
result[i] = Node(f: frequencies[key], isLeaf: true, c: key)
while result.freeChildList.len > 1:
let currentNode = new Node
result.add(currentNode)
for c in currentNode.childs:
currentNode.connect(min(result.freeChildList(currentNode)))
if result.freeChildList.len <= 1:
break
var sampleFrequencies = initCountTable[char]() for c in sampleString:
sampleFrequencies.inc(c)
let
tree = buildTree(sampleFrequencies) root = tree.freeChildList[0]
var huffCodes = newTable[char, HuffCode]() generateCodes(huffCodes, root) echo huffCodes</lang>
- Output:
{ : 101, a: 1001, c: 01010, d: 01011, e: 1100, f: 1101, g: 01100, h: 11111, i: 1110, l: 01101, m: 0010, n: 000, o: 0011, p: 01110, r: 01111, s: 0100, t: 10000, u: 10001, x: 11110}
Oberon-2
<lang oberon2> MODULE HuffmanEncoding; IMPORT
Object, PriorityQueue, Strings, Out;
TYPE
Leaf = POINTER TO LeafDesc; LeafDesc = RECORD (Object.ObjectDesc) c: CHAR; END;
Inner = POINTER TO InnerDesc; InnerDesc = RECORD (Object.ObjectDesc) left,right: Object.Object; END;
VAR
str: ARRAY 128 OF CHAR; i: INTEGER; f: ARRAY 96 OF INTEGER; q: PriorityQueue.Queue; a: PriorityQueue.Node; b: PriorityQueue.Node; c: PriorityQueue.Node; h: ARRAY 64 OF CHAR;
PROCEDURE NewLeaf(c: CHAR): Leaf; VAR
x: Leaf;
BEGIN
NEW(x);x.c := c; RETURN x
END NewLeaf;
PROCEDURE NewInner(l,r: Object.Object): Inner; VAR
x: Inner;
BEGIN
NEW(x); x.left := l; x.right := r; RETURN x
END NewInner;
PROCEDURE Preorder(n: Object.Object; VAR x: ARRAY OF CHAR);
BEGIN
IF n IS Leaf THEN
Out.Char(n(Leaf).c);Out.String(": ");Out.String(h);Out.Ln
ELSE
IF n(Inner).left # NIL THEN
Strings.Append("0",x);
Preorder(n(Inner).left,x);
Strings.Delete(x,(Strings.Length(x) - 1),1)
END;
IF n(Inner).right # NIL THEN
Strings.Append("1",x);
Preorder(n(Inner).right,x);
Strings.Delete(x,(Strings.Length(x) - 1),1)
END
END
END Preorder;
BEGIN
str := "this is an example for huffman encoding";
(* Collect letter frecuencies *)
i := 0;
WHILE str[i] # 0X DO INC(f[ORD(CAP(str[i])) - ORD(' ')]);INC(i) END;
(* Create Priority Queue *)
NEW(q);q.Clear();
(* Insert into the queue *)
i := 0;
WHILE (i < LEN(f)) DO
IF f[i] # 0 THEN
q.Insert(f[i]/Strings.Length(str),NewLeaf(CHR(i + ORD(' '))))
END;
INC(i)
END;
(* create tree *)
WHILE q.Length() > 1 DO
q.Remove(a);q.Remove(b);
q.Insert(a.w + b.w,NewInner(a.d,b.d));
END;
(* tree traversal *) h[0] := 0X;q.Remove(c);Preorder(c.d,h);
END HuffmanEncoding. </lang>
- Output:
D: 00000 T: 00001 H: 0001 S: 0010 C: 00110 X: 00111 M: 0100 O: 0101 N: 011 U: 10000 L: 10001 A: 1001 R: 10100 G: 101010 P: 101011 E: 1011 I: 1100 F: 1101 : 111
Objective-C
This is not purely Objective-C. It uses Apple's Core Foundation library for its binary heap, which admittedly is very ugly. Thus, this only builds on Mac OS X, not GNUstep. <lang objc>#import <Foundation/Foundation.h>
@interface HuffmanTree : NSObject {
int freq;
}
-(instancetype)initWithFreq:(int)f;
@property (nonatomic, readonly) int freq;
@end
@implementation HuffmanTree @synthesize freq; // the frequency of this tree -(instancetype)initWithFreq:(int)f { if (self = [super init]) { freq = f; } return self; } @end
const void *HuffmanRetain(CFAllocatorRef allocator, const void *ptr) {
return (__bridge_retained const void *)(__bridge id)ptr;
}
void HuffmanRelease(CFAllocatorRef allocator, const void *ptr) {
(void)(__bridge_transfer id)ptr;
}
CFComparisonResult HuffmanCompare(const void *ptr1, const void *ptr2, void *unused) {
int f1 = ((__bridge HuffmanTree *)ptr1).freq;
int f2 = ((__bridge HuffmanTree *)ptr2).freq;
if (f1 == f2)
return kCFCompareEqualTo;
else if (f1 > f2)
return kCFCompareGreaterThan;
else
return kCFCompareLessThan;
}
@interface HuffmanLeaf : HuffmanTree {
char value; // the character this leaf represents
}
@property (readonly) char value;
-(instancetype)initWithFreq:(int)f character:(char)c;
@end
@implementation HuffmanLeaf @synthesize value; -(instancetype)initWithFreq:(int)f character:(char)c { if (self = [super initWithFreq:f]) { value = c; } return self; } @end
@interface HuffmanNode : HuffmanTree {
HuffmanTree *left, *right; // subtrees
}
@property (readonly) HuffmanTree *left, *right;
-(instancetype)initWithLeft:(HuffmanTree *)l right:(HuffmanTree *)r;
@end
@implementation HuffmanNode @synthesize left, right; -(instancetype)initWithLeft:(HuffmanTree *)l right:(HuffmanTree *)r { if (self = [super initWithFreq:l.freq+r.freq]) { left = l; right = r; } return self; } @end
HuffmanTree *buildTree(NSCountedSet *chars) {
CFBinaryHeapCallBacks callBacks = {0, HuffmanRetain, HuffmanRelease, NULL, HuffmanCompare}; CFBinaryHeapRef trees = CFBinaryHeapCreate(NULL, 0, &callBacks, NULL);
// initially, we have a forest of leaves // one for each non-empty character for (NSNumber *ch in chars) { int freq = [chars countForObject:ch]; if (freq > 0) CFBinaryHeapAddValue(trees, (__bridge const void *)[[HuffmanLeaf alloc] initWithFreq:freq character:(char)[ch intValue]]); }
NSCAssert(CFBinaryHeapGetCount(trees) > 0, @"String must have at least one character"); // loop until there is only one tree left while (CFBinaryHeapGetCount(trees) > 1) { // two trees with least frequency HuffmanTree *a = (__bridge HuffmanTree *)CFBinaryHeapGetMinimum(trees); CFBinaryHeapRemoveMinimumValue(trees); HuffmanTree *b = (__bridge HuffmanTree *)CFBinaryHeapGetMinimum(trees); CFBinaryHeapRemoveMinimumValue(trees);
// put into new node and re-insert into queue CFBinaryHeapAddValue(trees, (__bridge const void *)[[HuffmanNode alloc] initWithLeft:a right:b]); } HuffmanTree *result = (__bridge HuffmanTree *)CFBinaryHeapGetMinimum(trees); CFRelease(trees); return result; }
void printCodes(HuffmanTree *tree, NSMutableString *prefix) { NSCAssert(tree != nil, @"tree must not be nil"); if ([tree isKindOfClass:[HuffmanLeaf class]]) { HuffmanLeaf *leaf = (HuffmanLeaf *)tree;
// print out character, frequency, and code for this leaf (which is just the prefix) NSLog(@"%c\t%d\t%@", leaf.value, leaf.freq, prefix);
} else if ([tree isKindOfClass:[HuffmanNode class]]) { HuffmanNode *node = (HuffmanNode *)tree;
// traverse left [prefix appendString:@"0"]; printCodes(node.left, prefix); [prefix deleteCharactersInRange:NSMakeRange([prefix length]-1, 1)];
// traverse right [prefix appendString:@"1"]; printCodes(node.right, prefix); [prefix deleteCharactersInRange:NSMakeRange([prefix length]-1, 1)]; } }
int main(int argc, const char * argv[]) {
@autoreleasepool {
NSString *test = @"this is an example for huffman encoding";
// read each character and record the frequencies NSCountedSet *chars = [[NSCountedSet alloc] init]; int n = [test length]; for (int i = 0; i < n; i++) [chars addObject:@([test characterAtIndex:i])];
// build tree HuffmanTree *tree = buildTree(chars);
// print out results NSLog(@"SYMBOL\tWEIGHT\tHUFFMAN CODE"); printCodes(tree, [NSMutableString string]);
} return 0;
}</lang>
- Output:
SYMBOL WEIGHT HUFFMAN CODE g 1 00000 x 1 00001 m 2 0001 d 1 00100 u 1 00101 t 1 00110 r 1 00111 n 4 010 s 2 0110 o 2 0111 p 1 10000 l 1 10001 a 3 1001 6 101 f 3 1100 e 3 1101 c 1 11100 h 2 11101 i 3 1111
OCaml
We use a Set (which is automatically sorted) as a priority queue.
<lang ocaml>type 'a huffman_tree =
| Leaf of 'a | Node of 'a huffman_tree * 'a huffman_tree
module HSet = Set.Make
(struct
type t = int * char huffman_tree (* pair of frequency and the tree *)
let compare = compare
(* We can use the built-in compare function to order this: it will order
first by the first element (frequency) and then by the second (the tree),
the latter of which we don't care about but which helps prevent elements
from being equal, since Set does not allow duplicate elements *)
end);;
let build_tree charFreqs =
let leaves = HSet.of_list (List.map (fun (c,f) -> (f, Leaf c)) charFreqs) in
let rec aux trees =
let f1, a = HSet.min_elt trees in
let trees' = HSet.remove (f1,a) trees in
if HSet.is_empty trees' then
a
else
let f2, b = HSet.min_elt trees' in
let trees = HSet.remove (f2,b) trees' in
let trees' = HSet.add (f1 + f2, Node (a, b)) trees in
aux trees
in
aux leaves
let rec print_tree code = function
| Leaf c ->
Printf.printf "%c\t%s\n" c (String.concat "" (List.rev code));
| Node (l, r) ->
print_tree ("0"::code) l;
print_tree ("1"::code) r
let () =
let str = "this is an example for huffman encoding" in
let charFreqs = Hashtbl.create 42 in
String.iter (fun c ->
let old =
try Hashtbl.find charFreqs c
with Not_found -> 0 in
Hashtbl.replace charFreqs c (old+1)
) str;
let charFreqs = Hashtbl.fold (fun c f acc -> (c,f)::acc) charFreqs [] in let tree = build_tree charFreqs in print_string "Symbol\tHuffman code\n"; print_tree [] tree</lang>
Perl
<lang perl>use 5.10.0; use strict;
- produce encode and decode dictionary from a tree
sub walk { my ($node, $code, $h, $rev_h) = @_;
my $c = $node->[0]; if (ref $c) { walk($c->[$_], $code.$_, $h, $rev_h) for 0,1 } else { $h->{$c} = $code; $rev_h->{$code} = $c }
$h, $rev_h }
- make a tree, and return resulting dictionaries
sub mktree { my (%freq, @nodes); $freq{$_}++ for split , shift; @nodes = map([$_, $freq{$_}], keys %freq);
do { # poor man's priority queue @nodes = sort {$a->[1] <=> $b->[1]} @nodes; my ($x, $y) = splice @nodes, 0, 2; push @nodes, [[$x, $y], $x->[1] + $y->[1]] } while (@nodes > 1);
walk($nodes[0], , {}, {}) }
sub encode { my ($str, $dict) = @_; join , map $dict->{$_}//die("bad char $_"), split , $str }
sub decode { my ($str, $dict) = @_; my ($seg, @out) = ("");
# append to current segment until it's in the dictionary for (split , $str) { $seg .= $_; my $x = $dict->{$seg} // next; push @out, $x; $seg = ; } die "bad code" if length($seg); join , @out }
my $txt = 'this is an example for huffman encoding'; my ($h, $rev_h) = mktree($txt); for (keys %$h) { print "'$_': $h->{$_}\n" }
my $enc = encode($txt, $h); print "$enc\n";
print decode($enc, $rev_h), "\n";</lang>
- Output:
'u': 10000 'd': 01111 'a': 1101 'l': 10001 'i': 1110 'g': 11110 'h': 0100 'r': 01110 ' ': 101 'p': 01100 't': 01101 'n': 000 'm': 0011 'x': 01011 'f': 1100 'c': 01010 'o': 0010 's': 11111 'e': 1001 0110101001110111111011110111111011101000101100101011110100110110010001100110111000010011101010100100001100110000111101000101100100001010001001111111000011110 this is an example for huffman encoding
Perl 6
By building a tree
This version uses nested Arrays to build a tree like shown in this diagram, and then recursively traverses the finished tree to accumulate the prefixes.
<lang perl6>sub huffman (%frequencies) {
my @queue = %frequencies.map({ [.value, .key] }).sort;
while @queue > 1 {
given @queue.splice(0, 2) -> ([$freq1, $node1], [$freq2, $node2]) {
@queue = (|@queue, [$freq1 + $freq2, [$node1, $node2]]).sort;
}
}
hash gather walk @queue[0][1], ;
}
multi walk ($node, $prefix) { take $node => $prefix; } multi walk ([$node1, $node2], $prefix) { walk $node1, $prefix ~ '0';
walk $node2, $prefix ~ '1'; }</lang>
Without building a tree
This version uses an Array of Pairs to implement a simple priority queue. Each value of the queue is a Hash mapping from letters to prefixes, and when the queue is reduced the hashes are merged on-the-fly, so that the last one remaining is the wanted Huffman table.
<lang perl6>sub huffman (%frequencies) {
my @queue = %frequencies.map: { .value => (hash .key => ) };
while @queue > 1 {
@queue.=sort;
my $x = @queue.shift;
my $y = @queue.shift;
@queue.push: ($x.key + $y.key) => hash $x.value.deepmap('0' ~ *),
$y.value.deepmap('1' ~ *);
}
@queue[0].value;
}
- Testing
for huffman 'this is an example for huffman encoding'.comb.Bag {
say "'{.key}' : {.value}";
}
- To demonstrate that the table can do a round trip:
say ; my $original = 'this is an example for huffman encoding';
my %encode-key = huffman $original.comb.Bag; my %decode-key = %encode-key.invert; my @codes = %decode-key.keys;
my $encoded = $original.subst: /./, { %encode-key{$_} }, :g; my $decoded = $encoded .subst: /@codes/, { %decode-key{$_} }, :g;
.say for $original, $encoded, $decoded;</lang>
- Output:
'x' : 11000 'p' : 01100 'h' : 0001 'g' : 00000 'a' : 1001 'e' : 1101 'd' : 110011 's' : 0111 'f' : 1110 'c' : 110010 'm' : 0010 ' ' : 101 'n' : 010 'o' : 0011 'u' : 10001 't' : 10000 'i' : 1111 'r' : 01101 'l' : 00001 this is an example for huffman encoding 1000000011111011110111110111101100101010111011100010010010011000000111011011110001101101101000110001111011100010100101010111010101100100011110011111101000000 this is an example for huffman encoding
Phix
<lang Phix>function store_nodes(object key, object data, integer nodes)
setd({data,key},0,nodes)
return 1
end function constant r_store_nodes = routine_id("store_nodes")
function build_freqtable(string data) integer freq = new_dict(),
nodes = new_dict()
for i=1 to length(data) do
integer di = data[i]
setd(di,getd(di,freq)+1,freq)
end for
traverse_dict(r_store_nodes, nodes, freq)
destroy_dict(freq)
return nodes
end function
function build_hufftree(integer nodes) sequence lkey, rkey, node integer lfreq, rfreq
while true do
lkey = getd_partial_key({0,0},nodes)
lfreq = lkey[1]
deld(lkey,nodes)
rkey = getd_partial_key({0,0},nodes)
rfreq = rkey[1]
deld(rkey,nodes)
node = {lfreq+rfreq,{lkey,rkey}}
if dict_size(nodes)=0 then exit end if
setd(node,0,nodes)
end while
destroy_dict(nodes)
return node
end function
procedure build_huffcodes(object node, string bits, integer d)
{integer freq, object data} = node
if sequence(data) then
build_huffcodes(data[1],bits&'0',d)
build_huffcodes(data[2],bits&'1',d)
else
setd(data,{freq,bits},d)
end if
end procedure
function print_huffcode(integer key, sequence data, integer /*user_data*/)
printf(1,"'%c' [%d] %s\n",key&data) return 1
end function constant r_print_huffcode = routine_id("print_huffcode")
procedure print_huffcodes(integer d)
traverse_dict(r_print_huffcode, 0, d)
end procedure
function invert_huffcode(integer key, sequence data, integer rd)
setd(data[2],key,rd) return 1
end function constant r_invert_huffcode = routine_id("invert_huffcode")
procedure main(string data)
if length(data)<2 then ?9/0 end if integer nodes = build_freqtable(data) sequence huff = build_hufftree(nodes) integer d = new_dict() build_huffcodes(huff, "", d) print_huffcodes(d)
string encoded = ""
for i=1 to length(data) do
encoded &= getd(data[i],d)[2]
end for
?encoded
integer rd = new_dict()
traverse_dict(r_invert_huffcode, rd, d)
string decoded = ""
integer done = 0
while done<length(encoded) do
string key = ""
integer node = 0
while node=0 do
done += 1
key &= encoded[done]
node = getd_index(key, rd)
end while
decoded &= getd_by_index(node,rd)
end while
?decoded
end procedure
main("this is an example for huffman encoding")</lang>
- Output:
' ' [6] 101 'a' [3] 1001 'c' [1] 01010 'd' [1] 01011 'e' [3] 1100 'f' [3] 1101 'g' [1] 01100 'h' [2] 11111 'i' [3] 1110 'l' [1] 01101 'm' [2] 0010 'n' [4] 000 'o' [2] 0011 'p' [1] 01110 'r' [1] 01111 's' [2] 0100 't' [1] 10000 'u' [1] 10001 'x' [1] 11110 "1000011111111001001011110010010110010001011100111101001001001110011011100101110100110111110111111100011101110100101001000101110000001010001101011111000001100" "this is an example for huffman encoding"
PHP
(not exactly)
<lang php><?php function encode($symb2freq) {
$heap = new SplPriorityQueue;
$heap->setExtractFlags(SplPriorityQueue::EXTR_BOTH);
foreach ($symb2freq as $sym => $wt)
$heap->insert(array($sym => ), -$wt);
while ($heap->count() > 1) {
$lo = $heap->extract();
$hi = $heap->extract();
foreach ($lo['data'] as &$x)
$x = '0'.$x;
foreach ($hi['data'] as &$x)
$x = '1'.$x;
$heap->insert($lo['data'] + $hi['data'],
$lo['priority'] + $hi['priority']);
}
$result = $heap->extract();
return $result['data'];
}
$txt = 'this is an example for huffman encoding'; $symb2freq = array_count_values(str_split($txt)); $huff = encode($symb2freq); echo "Symbol\tWeight\tHuffman Code\n"; foreach ($huff as $sym => $code)
echo "$sym\t$symb2freq[$sym]\t$code\n";
?></lang>
- Output:
Symbol Weight Huffman Code n 4 000 m 2 0010 o 2 0011 t 1 01000 g 1 01001 x 1 01010 u 1 01011 s 2 0110 c 1 01110 d 1 01111 p 1 10000 l 1 10001 a 3 1001 6 101 f 3 1100 i 3 1101 r 1 11100 h 2 11101 e 3 1111
PicoLisp
Using a cons cells (freq . char) for leaves, and two cells (freq left . right) for nodes. <lang PicoLisp>(de prio (Idx)
(while (cadr Idx) (setq Idx @)) (car Idx) )
(let (A NIL P NIL L NIL)
(for C (chop "this is an example for huffman encoding")
(accu 'A C 1) ) # Count characters
(for X A # Build index tree as priority queue
(idx 'P (cons (cdr X) (car X)) T) )
(while (or (cadr P) (cddr P)) # Remove entries, insert as nodes
(let (A (car (idx 'P (prio P) NIL)) B (car (idx 'P (prio P) NIL)))
(idx 'P (cons (+ (car A) (car B)) A B) T) ) )
(setq P (car P))
(recur (P L) # Traverse and print
(if (atom (cdr P))
(prinl (cdr P) " " L)
(recurse (cadr P) (cons 0 L))
(recurse (cddr P) (cons 1 L)) ) ) )</lang>
- Output:
n 000 m 0100 o 1100 s 0010 c 01010 d 11010 g 00110 l 10110 p 01110 r 11110 t 00001 u 10001 a 1001 101 e 0011 f 1011 i 0111 x 01111 h 11111
PL/I
<lang pli>*process source attributes xref or(!);
hencode: Proc Options(main);
/*--------------------------------------------------------------------
* 28.12.013 Walter Pachl translated from REXX
*-------------------------------------------------------------------*/
Dcl debug Bit(1) Init('0'b);
Dcl (i,j,k) Bin Fixed(15);
Dcl c Char(1);
Dcl s Char(100) Var Init('this is an example for huffman encoding');
Dcl sc Char(1000) Var Init();
Dcl sr Char(100) Var Init();
Dcl 1 cocc(100),
2 c Char(1),
2 occ Bin Fixed(31);
Dcl cocc_n Bin Fixed(15) Init(0);
dcl 1 node,
2 id Bin Fixed(15), /* Node id */
2 c Char(1), /* character */
2 occ Bin Fixed(15), /* number of occurrences */
2 left Bin Fixed(15), /* left child */
2 rite Bin Fixed(15), /* right child */
2 father Bin Fixed(15), /* father */
2 digit Pic'9', /* digit (0 or 1) */
2 term Pic'9'; /* 1=terminal node */
node=;
Dcl 1 m(100) Like node;
Dcl m_n Bin Fixed(15) Init(0);
Dcl father(100) Bin Fixed(15);
Dcl 1 t(100),
2 char Char(1),
2 code Char(20) Var;
Dcl t_n Bin Fixed(15) Init(0);
Do i=1 To length(s); /* first collect used characters */
c=substr(s,i,1); /* and number of occurrences */
Do j=1 To cocc_n;
If cocc(j).c=c Then Leave;
End;
If j<= cocc_n Then
cocc(j).occ+=1;
Else Do;
cocc(j).c=c;
cocc(j).occ=1;
cocc_n+=1;
End;
End;
Do j=1 To cocc_n; /* create initial node list */ node.id+=1; node.c=cocc(j).c; node.occ=cocc(j).occ; node.term=1; Call add_node; End;
If debug Then Call show;
Do While(pairs()); /* while there is more than one fatherless node */
Call mk_node; /* create a father node */
If debug Then
Call show;
End;
Call show; /* show the node table */
Call mk_trans; /* create the translate table */
Put Edit('The translate table:')(Skip,a);
Do i=1 To t_n; /* show it */
Put Edit(t(i).char,' -> ',t(i).code)(Skip,a,a,a);
End;
Call encode; /* encode the string s -> sc */
Put Edit('length(sc)=',length(sc)) /* show it */
(Skip,a,f(3));
Do i=1 By 70 To length(sc);
Put Edit(substr(sc,i,70))(Skip,a);
End;
Call decode; /* decode the string sc -> sr */
Put Edit('input : ',s)(skip,a,a);
Put Edit('result: ',sr)(skip,a,a);
Return;
add_node: Proc;
/*--------------------------------------------------------------------
* Insert the node according to increasing occurrences
*-------------------------------------------------------------------*/
il:
Do i=1 To m_n;
If m(i).occ>=node.occ Then Do;
Do k=m_n To i By -1;
m(k+1)=m(k);
End;
Leave il;
End;
End;
m(i)=node;
m_n+=1;
End;
show: Proc;
/*--------------------------------------------------------------------
* Show the contents of the node table
*-------------------------------------------------------------------*/
Put Edit('The list of nodes:')(Skip,a);
Put Edit('id c oc l r f d t')(Skip,a);
Do i=1 To m_n;
Put Edit(m(i).id,m(i).c,m(i).occ,
m(i).left,m(i).rite,m(i).father,m(i).digit,m(i).term)
(Skip,f(2),x(1),a,4(f(3)),f(2),f(3));
End;
End;
mk_node: Proc;
/*--------------------------------------------------------------------
* construct and store a new intermediate node or the top node
*-------------------------------------------------------------------*/
Dcl z Bin Fixed(15);
node=;
node.id=m_n+1; /* the next node id */
node.c='*';
ni=m_n+1;
loop:
Do i=1 To m_n; /* loop over node lines */
If m(i).father=0 Then Do; /* a fatherless node */
z=m(i).id; /* its id */
If node.left=0 Then Do; /* new node has no left child */
node.left=z; /* make this the lect child */
node.occ=m(i).occ; /* occurrences */
m(i).father=ni; /* store father info */
m(i).digit=0; /* digit 0 to be used */
father(z)=ni; /* remember z's father (redundant) */
End;
Else Do; /* New node has already left child */
node.rite=z; /* make this the right child */
node.occ=node.occ+m(i).occ; /* add in the occurrences */
m(i).father=ni; /* store father info */
m(i).digit=1; /* digit 1 to be used */
father(z)=ni; /* remember z's father (redundant) */
Leave loop;
End;
End;
End;
Call add_node;
End;
pairs: Proc Returns(Bit(1));
/*--------------------------------------------------------------------
* Return true if there are at least 2 fatherless nodes
*-------------------------------------------------------------------*/
Dcl i Bin Fixed(15);
Dcl cnt Bin Fixed(15) Init(0);
Do i=1 To m_n;
If m(i).father=0 Then Do;
cnt+=1;
If cnt>1 Then
Return('1'b);
End;
End;
Return('0'b);
End;
mk_trans: Proc;
/*--------------------------------------------------------------------
* Compute the codes for all terminal nodes (characters)
* and store the relation char -> code in array t(*)
*-------------------------------------------------------------------*/
Dcl (i,fi,fid,fidz,node,z) Bin Fixed(15);
Dcl code Char(20) Var;
Do i=1 To m_n; /* now we loop over all lines representing nodes */
If m(i).term Then Do; /* for each terminal node */
code=m(i).digit; /* its digit is the last code digit */
node=m(i).id; /* its id */
Do fi=1 To 1000; /* actually Forever */
fid=father(node); /* id of father */
If fid>0 Then Do; /* father exists */
fidz=zeile(fid); /* line that contains the father */
code=m(fidz).digit!!code; /* prepend the digit */
node=fid; /* look for next father */
End;
Else /* no father (we reached the top */
Leave;
End;
If length(code)>1 Then /* more than one character in input */
code=substr(code,2); /* remove the the top node's 0 */
call dbg(m(i).c!!' -> '!!code); /* character is encoded this way*/
ti_loop:
Do ti=1 To t_n;
If t(ti).char>m(i).c Then Do;
Do tj=t_n To ti By -1
t(tj+1)=t(tj);
End;
Leave ti_loop;
End;
End;
t(ti).char=m(i).c;
t(ti).code=code;
t_n+=1;
Call dbg(t(ti).char!!' -> '!!t(ti).code);
End;
End;
End;
zeile: Proc(nid) Returns(Bin Fixed(15));
/*--------------------------------------------------------------------
* find and return line number containing node-id
*-------------------------------------------------------------------*/
Dcl (nid,i) Bin Fixed(15);
do i=1 To m_n;
If m(i).id=nid Then
Return(i);
End;
Stop;
End;
dbg: Proc(txt); /*-------------------------------------------------------------------- * Show text if debug is enabled *-------------------------------------------------------------------*/ Dcl txt Char(*); If debug Then Put Skip List(txt); End;
encode: Proc;
/*--------------------------------------------------------------------
* encode the string s -> sc
*-------------------------------------------------------------------*/
Dcl (i,j) Bin Fixed(15);
Do i=1 To length(s);
c=substr(s,i,1);
Do j=1 To t_n;
If c=t(j).char Then
Leave;
End;
sc=sc!!t(j).code;
End;
End;
decode: Proc;
/*--------------------------------------------------------------------
* decode the string sc -> sr
*-------------------------------------------------------------------*/
Dcl (i,j) Bin Fixed(15);
Do While(sc>);
Do j=1 To t_n;
If substr(sc,1,length(t(j).code))=t(j).code Then
Leave;
End;
sr=sr!!t(j).char;
sc=substr(sc,length(t(j).code)+1);
End;
End;
End;</lang>
- Output:
The list of nodes: id c oc l r f d t 19 g 1 0 0 20 0 1 18 d 1 0 0 20 1 1 17 c 1 0 0 21 0 1 16 u 1 0 0 21 1 1 15 r 1 0 0 22 0 1 12 l 1 0 0 22 1 1 11 p 1 0 0 23 0 1 9 x 1 0 0 23 1 1 1 t 1 0 0 24 0 1 23 * 2 11 9 24 1 0 22 * 2 15 12 25 0 0 21 * 2 17 16 25 1 0 20 * 2 19 18 26 0 0 14 o 2 0 0 26 1 1 10 m 2 0 0 27 0 1 4 s 2 0 0 27 1 1 2 h 2 0 0 28 0 1 24 * 3 1 23 28 1 0 13 f 3 0 0 29 0 1 8 e 3 0 0 29 1 1 6 a 3 0 0 30 0 1 3 i 3 0 0 30 1 1 27 * 4 10 4 31 0 0 26 * 4 20 14 31 1 0 25 * 4 22 21 32 0 0 7 n 4 0 0 32 1 1 28 * 5 2 24 33 0 0 30 * 6 6 3 33 1 0 29 * 6 13 8 34 0 0 5 6 0 0 34 1 1 32 * 8 25 7 35 0 0 31 * 8 27 26 35 1 0 33 * 11 28 30 36 0 0 34 * 12 29 5 36 1 0 35 * 16 32 31 37 0 0 36 * 23 33 34 37 1 0 37 * 39 35 36 0 0 0 The translate table: -> 111 a -> 1010 c -> 00010 d -> 01101 e -> 1101 f -> 1100 g -> 01100 h -> 1000 i -> 1011 l -> 00001 m -> 0100 n -> 001 o -> 0111 p -> 100110 r -> 00000 s -> 0101 t -> 10010 u -> 00011 x -> 100111 length(sc)=157 1001010001011010111110110101111101000111111011001111010010010011000001 1101111110001110000011110000001111001100010010100011111101001000100111 01101101100101100 input : this is an example for huffman encoding result: this is an example for huffman encoding
PowerShell
<lang PowerShell> function Get-HuffmanEncodingTable ( $String )
{
# Create leaf nodes
$ID = 0
$Nodes = [char[]]$String |
Group-Object |
ForEach { $ID++; $_ } |
Select @{ Label = 'Symbol' ; Expression = { $_.Name } },
@{ Label = 'Count' ; Expression = { $_.Count } },
@{ Label = 'ID' ; Expression = { $ID } },
@{ Label = 'Parent' ; Expression = { 0 } },
@{ Label = 'Code' ; Expression = { } }
# Grow stems under leafs
ForEach ( $Branch in 2..($Nodes.Count) )
{
# Get the two nodes with the lowest count
$LowNodes = $Nodes | Where Parent -eq 0 | Sort Count | Select -First 2
# Create a new stem node
$ID++
$Nodes += |
Select @{ Label = 'Symbol' ; Expression = { } },
@{ Label = 'Count' ; Expression = { $LowNodes[0].Count + $LowNodes[1].Count } },
@{ Label = 'ID' ; Expression = { $ID } },
@{ Label = 'Parent' ; Expression = { 0 } },
@{ Label = 'Code' ; Expression = { } }
# Put the two nodes in the new stem node
$LowNodes[0].Parent = $ID
$LowNodes[1].Parent = $ID
# Assign 0 and 1 to the left and right nodes
$LowNodes[0].Code = '0'
$LowNodes[1].Code = '1'
}
# Assign coding to nodes
ForEach ( $Node in $Nodes[($Nodes.Count-2)..0] )
{
$Node.Code = ( $Nodes | Where ID -eq $Node.Parent ).Code + $Node.Code
}
$EncodingTable = $Nodes | Where { $_.Symbol } | Select Symbol, Code | Sort Symbol
return $EncodingTable
}
- Get table for given string
$String = "this is an example for huffman encoding" $HuffmanEncodingTable = Get-HuffmanEncodingTable $String
- Display table
$HuffmanEncodingTable | Format-Table -AutoSize
- Encode string
$EncodedString = $String ForEach ( $Node in $HuffmanEncodingTable )
{
$EncodedString = $EncodedString.Replace( $Node.Symbol, $Node.Code )
}
$EncodedString </lang>
- Output:
Symbol Code
------ ----
101
a 1100
c 01011
d 01100
e 1101
f 1110
g 01110
h 11111
i 1001
l 11110
m 0011
n 000
o 0100
p 10001
r 01111
s 0010
t 01010
u 01101
x 10000
0101011111100100101011001001010111000001011101100001100001110001111101101101111001000111110111111011011110111000111100000101110100001011010001100100100001110
Prolog
Works with SWI-Prolog <lang Prolog>huffman :- L = 'this is an example for huffman encoding', atom_chars(L, LA), msort(LA, LS), packList(LS, PL), sort(PL, PLS), build_tree(PLS, A), coding(A, [], C), sort(C, SC), format('Symbol~t Weight~t~30|Code~n'), maplist(print_code, SC).
build_tree(R1], [V2|R2]|T], AF) :- V is V1 + V2, A = [V, [V1|R1], [V2|R2, ( T=[] -> AF=A ; sort([A|T], NT), build_tree(NT, AF) ).
coding([_A,FG,FD], Code, CF) :- ( is_node(FG) -> coding(FG, [0 | Code], C1) ; leaf_coding(FG, [0 | Code], C1) ), ( is_node(FD) -> coding(FD, [1 | Code], C2) ; leaf_coding(FD, [1 | Code], C2) ), append(C1, C2, CF).
leaf_coding([FG,FD], Code, CF) :- reverse(Code, CodeR), CF = FG, FD, CodeR .
is_node([_V, _FG, _FD]).
print_code([N, Car, Code]):- format('~w :~t~w~t~30|', [Car, N]), forall(member(V, Code), write(V)), nl.
packList([], []). packList([X], 1,X) :- !. packList([X|Rest], [XRun|Packed]):-
run(X, Rest, XRun, RRest), packList(RRest, Packed).
run(V, [], [1,V], []). run(V, [V|LRest], [N1,V], RRest):-
run(V, LRest, [N, V], RRest), N1 is N + 1.
run(V, [Other|RRest], [1,V], [Other|RRest]):-
dif(V, Other).</lang>
- Output:
?- huffman. Symbol Weight Code c : 1 01010 d : 1 01011 g : 1 01100 l : 1 01101 p : 1 01110 r : 1 01111 t : 1 10000 u : 1 10001 x : 1 11110 h : 2 11111 m : 2 0010 o : 2 0011 s : 2 0100 a : 3 1001 e : 3 1100 f : 3 1101 i : 3 1110 n : 4 000 : 6 101
PureBasic
<lang PureBasic> OpenConsole()
SampleString.s="this is an example for huffman encoding" datalen=Len(SampleString)
Structure ztree
linked.c ischar.c char.c number.l left.l right.l
EndStructure
Dim memc.c(datalen) CopyMemory(@SampleString, @memc(0), datalen * SizeOf(Character))
Dim tree.ztree(255)
For i=0 To datalen-1
tree(memc(i))\char=memc(i) tree(memc(i))\number+1 tree(memc(i))\ischar=1
Next
SortStructuredArray(tree(),#PB_Sort_Descending,OffsetOf(ztree\number),#PB_Integer)
For i=0 To 255
If tree(i)\number=0 ReDim tree(i-1) Break EndIf
Next
dimsize=ArraySize(tree()) Repeat
min1.l=0
min2.l=0
For i=0 To dimsize
If tree(i)\linked=0
If tree(i)\number<min1 Or min1=0
min1=tree(i)\number
hmin1=i
ElseIf tree(i)\number<min2 Or min2=0
min2=tree(i)\number
hmin2=i
EndIf
EndIf
Next
If min1=0 Or min2=0
Break
EndIf
dimsize+1
ReDim tree(dimsize)
tree(dimsize)\number=tree(hmin1)\number+tree(hmin2)\number
tree(hmin1)\left=dimsize
tree(hmin2)\right=dimsize
tree(hmin1)\linked=1
tree(hmin2)\linked=1
ForEver
i=0 While tree(i)\ischar=1
str.s="" k=i ZNEXT: If tree(k)\left<>0 str="0"+str k=tree(k)\left Goto ZNEXT ElseIf tree(k)\right<>0 str="1"+str k=tree(k)\right Goto ZNEXT EndIf PrintN(Chr(tree(i)\char)+" "+str) i+1
Wend Input()
CloseConsole() </lang>
- Output:
110 n 000 e 1010 f 1001 a 1011 i 1110 h 0010 s 11111 o 0011 m 0100 x 01010 u 01011 l 01100 r 01101 c 01110 g 01111 p 10000 t 10001 d 11110
Python
A slight modification of the method outlined in the task description allows the code to be accumulated as the heap is manipulated.
The output is sorted first on length of the code, then on the symbols.
<lang python>from heapq import heappush, heappop, heapify from collections import defaultdict
def encode(symb2freq):
"""Huffman encode the given dict mapping symbols to weights"""
heap = [[wt, [sym, ""]] for sym, wt in symb2freq.items()]
heapify(heap)
while len(heap) > 1:
lo = heappop(heap)
hi = heappop(heap)
for pair in lo[1:]:
pair[1] = '0' + pair[1]
for pair in hi[1:]:
pair[1] = '1' + pair[1]
heappush(heap, [lo[0] + hi[0]] + lo[1:] + hi[1:])
return sorted(heappop(heap)[1:], key=lambda p: (len(p[-1]), p))
txt = "this is an example for huffman encoding" symb2freq = defaultdict(int) for ch in txt:
symb2freq[ch] += 1
- in Python 3.1+:
- symb2freq = collections.Counter(txt)
huff = encode(symb2freq) print "Symbol\tWeight\tHuffman Code" for p in huff:
print "%s\t%s\t%s" % (p[0], symb2freq[p[0]], p[1])</lang>
- Output:
Symbol Weight Huffman Code
6 101
n 4 010
a 3 1001
e 3 1100
f 3 1101
h 2 0001
i 3 1110
m 2 0010
o 2 0011
s 2 0111
g 1 00000
l 1 00001
p 1 01100
r 1 01101
t 1 10000
u 1 10001
x 1 11110
c 1 111110
d 1 111111
An extension to the method outlined above is given here.
Racket
<lang racket>
- lang racket
(require data/heap
data/bit-vector)
- A node is either an interior, or a leaf.
- In either case, they record an item with an associated frequency.
(struct node (freq) #:transparent) (struct interior node (left right) #:transparent) (struct leaf node (val) #:transparent)
- node<=?
- node node -> boolean
- Compares two nodes by frequency.
(define (node<=? x y)
(<= (node-freq x) (node-freq y)))
- make-huffman-tree
- (listof leaf) -> interior-node
(define (make-huffman-tree leaves)
(define a-heap (make-heap node<=?))
(heap-add-all! a-heap leaves)
(for ([i (sub1 (length leaves))])
(define min-1 (heap-min a-heap))
(heap-remove-min! a-heap)
(define min-2 (heap-min a-heap))
(heap-remove-min! a-heap)
(heap-add! a-heap (interior (+ (node-freq min-1) (node-freq min-2))
min-1 min-2)))
(heap-min a-heap))
- string->huffman-tree
- string -> node
- Given a string, produces its huffman tree. The leaves hold the characters
- and their relative frequencies.
(define (string->huffman-tree str)
(define ht (make-hash))
(define n (sequence-length str))
(for ([ch str])
(hash-update! ht ch add1 (λ () 0)))
(make-huffman-tree
(for/list ([(k v) (in-hash ht)])
(leaf (/ v n) k))))
- make-encoder
- node -> (string -> bit-vector)
- Given a huffman tree, generates the encoder function.
(define (make-encoder a-tree)
(define dict (huffman-tree->dictionary a-tree)) (lambda (a-str) (list->bit-vector (apply append (for/list ([ch a-str]) (hash-ref dict ch))))))
- huffman-tree->dictionary
- node -> (hashof val (listof boolean))
- A helper for the encoder
- maps characters to their code sequences.
(define (huffman-tree->dictionary a-node)
(define ht (make-hash))
(let loop ([a-node a-node]
[path/rev '()])
(cond
[(interior? a-node)
(loop (interior-left a-node) (cons #f path/rev))
(loop (interior-right a-node) (cons #t path/rev))]
[(leaf? a-node)
(hash-set! ht (reverse path/rev) (leaf-val a-node))]))
(for/hash ([(k v) ht]) (values v k)))
- make-decoder
- interior-node -> (bit-vector -> string)
- Generates the decoder function from the tree.
(define (make-decoder a-tree)
(lambda (a-bitvector)
(define-values (decoded/rev _)
(for/fold ([decoded/rev '()]
[a-node a-tree])
([bit a-bitvector])
(define next-node
(cond
[(not bit)
(interior-left a-node)]
[else
(interior-right a-node)]))
(cond [(leaf? next-node)
(values (cons (leaf-val next-node) decoded/rev)
a-tree)]
[else
(values decoded/rev next-node)])))
(apply string (reverse decoded/rev))))
- Example application
(define msg "this is an example for huffman encoding")
(define tree (string->huffman-tree msg))
- We can print out the mapping for inspection
(huffman-tree->dictionary tree)
(define encode (make-encoder tree)) (define encoded (encode msg))
- Here's what the encoded message looks like
(bit-vector->string encoded)
(define decode (make-decoder tree))
- Here's what the decoded message looks like
(decode encoded)</lang>
Red
<lang Red>Red [file: %huffy.red]
- message to encode
msg: "this is an example for huffman encoding"
- map to collect leave knots per uniq character of message
m: make map! []
knot: make object! [ left: right: none ;; pointer to left/right sibling code: none ;; first holds char for debugging, later binary code count: depth: 1 ;;occurence of character - length of branch ]
- -----------------------------------------
set-code: func ["recursive function to generate binary code sequence" wknot wcode [string!]] [
- -----------------------------------------
either wknot/left = none [ wknot/code: wcode ] [ set-code wknot/left rejoin [wcode "1"] set-code wknot/right rejoin [wcode "0"] ] ] ;;-- end func
- -------------------------------
merge-2knots: func ["function to merge 2 knots into 1 new" t [block!]][
- -------------------------------
nknot: copy knot ;; create new knot nknot/count: t/1/count + t/2/count nknot/right: t/1 nknot/left: t/2 nknot/depth: t/1/depth + 1 tab: remove/part t 2 ;; delete first 2 knots insert t nknot ;; insert new generated knot ] ;;-- end func
- count occurence of characters, save in map
- m
foreach chr msg [ either k: select/case m chr [ k/count: k/count + 1 ][ put/case m chr nknot: copy knot nknot/code: chr ] ]
- create sortable block (=tab) for use as prio queue
foreach k keys-of m [ append tab: [] :m/:k ]
- build tree
while [ 1 < length? tab][ sort/compare tab function [a b] [ a/count < b/count or ( a/count = b/count and ( a/depth > b/depth ) ) ] merge-2knots tab ;; merge 2 knots with lowest count / max depth ]
set-code tab/1 "" ;; generate binary codes, save at leave knot
- display codes
foreach k sort keys-of m [ print [k " = " m/:k/code] append codes: "" m/:k/code ]
- encode orig message string
foreach chr msg [ k: select/case m chr append msg-new: "" k/code ]
print [ "length of encoded msg " length? msg-new] print [ "length of (binary) codes " length? codes ]
print ["orig. message: " msg newline "encoded message: " "^/" msg-new] prin "decoded: "
- decode message (destructive! )
while [ not empty? msg-new ][
foreach [k v] body-of m [
if t: find/match msg-new v/code [
prin k
msg-new: t
]
]
]
</lang>
- Output:
= 111 a = 1101 c = 00101 d = 00100 e = 1011 f = 1100 g = 10010 h = 1000 i = 1010 l = 00000 m = 0001 n = 011 o = 0101 p = 00001 r = 00111 s = 0100 t = 100111 u = 100110 x = 00110 length of encoded msg 157 length of (binary) codes 85 orig. message: this is an example for huffman encoding encoded message: 1001111000101001001111010010011111010111111011001101101000100001000001011111110001010011111110001001101100110000011101011111101101100101010100100101001110010 decoded: this is an example for huffman encoding
REXX
<lang rexx>/* REXX ---------------------------------------------------------------
- 27.12.2013 Walter Pachl
- 29.12.2013 -"- changed for test of s=xrange('00'x,'ff'x)
- 14.03.2018 -"- use format instead of right to diagnose size poblems
- Stem m contains eventually the following node data
- m.i.0id Node id
- m.i.0c character
- m.i.0o number of occurrences
- m.i.0l left child
- m.i.0r right child
- m.i.0f father
- m.i.0d digit (0 or 1)
- m.i.0t 1=a terminal node 0=an intermediate or the top node
- --------------------------------------------------------------------*/
Parse Arg s If s= Then
s='this is an example for huffman encoding'
Say 'We encode this string:' Say s debug=0 o.=0 c.=0 codel.=0 code.= father.=0 cl= /* list of characters */ do i=1 To length(s)
Call memorize substr(s,i,1) End
If debug Then Do
Do i=1 To c.0 c=c.i Say i c o.c End End
n.=0 Do i=1 To c.0
c=c.i n.i.0c=c n.i.0o=o.c n.i.0id=i Call dbg i n.i.0id n.i.0c n.i.0o End
n=c.0 /* number of nodes */ m.=0 Do i=1 To n /* construct initial array */
Do j=1 To m.0 /* sorted by occurrences */
If m.j.0o>n.i.0o Then
Leave
End
Do k=m.0 To j By -1
k1=k+1
m.k1.0id=m.k.0id
m.k1.0c =m.k.0c
m.k1.0o =m.k.0o
m.k1.0t =m.k.0t
End
m.j.0id=i
m.j.0c =n.i.0c
m.j.0o =n.i.0o
m.j.0t =1
m.0=m.0+1
End
If debug Then
Call show
Do While pairs()>1 /* while there are at least 2 fatherless nodes */
Call mknode /* create and fill a new father node */ If debug Then Call show End
Call show c.=0 Do i=1 To m.0 /* now we loop over all lines representing nodes */
If m.i.0t Then Do /* for each terminal node */
code=m.i.0d /* its digit is the last code digit */
node=m.i.0id /* its id */
Do fi=1 To 1000 /* actually Forever */
fid=father.node /* id of father */
If fid<>0 Then Do /* father exists */
fidz=zeile(fid) /* line that contains the father */
code=m.fidz.0d||code /* prepend the digit */
node=fid /* look for next father */
End
Else /* no father (we reached the top */
Leave
End
If length(code)>1 Then /* more than one character in input */
code=substr(code,2) /* remove the the top node's 0 */
call dbg m.i.0c '->' code /* character is encoded this way */
char=m.i.0c
code.char=code
z=codel.0+1
codel.z=code
codel.0=z
char.code=char
End
End
Call show_char2code /* show used characters and corresponding codes */
codes.=0 /* now we build the array of codes/characters */ Do j=1 To codel.0
z=codes.0+1 code=codel.j codes.z=code chars.z=char.code codes.0=z Call dbg codes.z '----->' chars.z End
sc= /* here we ecnode the string */ Do i=1 To length(s) /* loop over input */
c=substr(s,i,1) /* a character */ sc=sc||code.c /* append the corresponding code */ End
Say 'Length of encoded string:' length(sc) Do i=1 To length(sc) by 70
Say substr(sc,i,70) End
sr= /* now decode the string */ Do si=1 To 999 While sc<>
Do i=codes.0 To 1 By -1 /* loop over codes */
cl=length(codes.i) /* length of code */
If left(sc,cl)==codes.i Then Do /* found on top of string */
sr=sr||chars.i /* append character to result */
sc=substr(sc,cl+1) /* cut off the used code */
Leave /* this was one character */
End
End
End
Say 'Input ="'s'"' Say 'result="'sr'"'
Exit
show: /*---------------------------------------------------------------------
- show all lines representing node data
- --------------------------------------------------------------------*/
Say ' i pp id c f l r d' Do i=1 To m.0
Say format(i,3) format(m.i.0o,4) format(m.i.0id,3),
format(m.i.0f,3) format(m.i.0l,3) format(m.i.0r,3) m.i.0d m.i.0t
End
Call dbg copies('-',21) Return
pairs: Procedure Expose m. /*---------------------------------------------------------------------
- return number of fatherless nodes
- --------------------------------------------------------------------*/
res=0
Do i=1 To m.0
If m.i.0f=0 Then
res=res+1
End
Return res
mknode: /*---------------------------------------------------------------------
- construct and store a new intermediate or the top node
- --------------------------------------------------------------------*/
new.=0 ni=m.0+1 /* the next node id */ Do i=1 To m.0 /* loop over node lines */
If m.i.0f=0 Then Do /* a fatherless node */
z=m.i.0id /* its id */
If new.0l=0 Then Do /* new node has no left child */
new.0l=z /* make this the lect child */
new.0o=m.i.0o /* occurrences */
m.i.0f=ni /* store father info */
m.i.0d='0' /* digit 0 to be used */
father.z=ni /* remember z's father (redundant) */
End
Else Do /* New node has already left child */
new.0r=z /* make this the right child */
new.0o=new.0o+m.i.0o /* add in the occurrences */
m.i.0f=ni /* store father info */
m.i.0d=1 /* digit 1 to be used */
father.z=ni /* remember z's father (redundant) */
Leave
End
End
End
Do i=1 To m.0 /* Insert new node according to occurrences */
If m.i.0o>=new.0o Then Do
Do k=m.0 To i By -1
k1=k+1
m.k1.0id=m.k.0id
m.k1.0o =m.k.0o
m.k1.0c =m.k.0c
m.k1.0l =m.k.0l
m.k1.0r =m.k.0r
m.k1.0f =m.k.0f
m.k1.0d =m.k.0d
m.k1.0t =m.k.0t
End
Leave
End
End
m.i.0id=ni m.i.0c ='*' m.i.0o =new.0o m.i.0l =new.0l m.i.0r =new.0r m.i.0t =0 father.ni=0 m.0=ni Return
zeile: /*---------------------------------------------------------------------
- find and return line number containing node-id
- --------------------------------------------------------------------*/
do fidz=1 To m.0
If m.fidz.0id=arg(1) Then
Return fidz
End
Call dbg arg(1) 'not found'
Pull .
dbg: /*---------------------------------------------------------------------
- Show text if debug is enabled
- --------------------------------------------------------------------*/
If debug=1 Then Say arg(1) Return
memorize: Procedure Expose c. o.
/*---------------------------------------------------------------------
- store characters and corresponding occurrences
- --------------------------------------------------------------------*/
Parse Arg c If o.c=0 Then Do z=c.0+1 c.z=c c.0=z End o.c=o.c+1 Return
show_char2code: /*---------------------------------------------------------------------
- show used characters and corresponding codes
- --------------------------------------------------------------------*/
cl=xrange('00'x,'ff'x) Say 'char --> code' Do While cl<>
Parse Var cl c +1 cl If code.c<> Then Say ' 'c '-->' code.c End
Return</lang>
- Output:
We encode this string:
this is an example for huffman encoding
i pp id c f l r d
1 1 1 20 0 0 0 1
2 1 9 20 0 0 1 1
3 1 11 21 0 0 0 1
4 1 12 21 0 0 1 1
5 1 15 22 0 0 0 1
6 1 16 22 0 0 1 1
7 1 17 23 0 0 0 1
8 1 18 23 0 0 1 1
9 1 19 24 0 0 0 1
10 2 23 24 17 18 1 0
11 2 22 25 15 16 0 0
12 2 21 25 11 12 1 0
13 2 20 26 1 9 0 0
14 2 2 26 0 0 1 1
15 2 4 27 0 0 0 1
16 2 10 27 0 0 1 1
17 2 14 28 0 0 0 1
18 3 24 28 19 23 1 0
19 3 3 29 0 0 0 1
20 3 6 29 0 0 1 1
21 3 8 30 0 0 0 1
22 3 13 30 0 0 1 1
23 4 27 31 4 10 0 0
24 4 26 31 20 2 1 0
25 4 25 32 22 21 0 0
26 4 7 32 0 0 1 1
27 5 28 33 14 24 0 0
28 6 30 33 8 13 1 0
29 6 29 34 3 6 0 0
30 6 5 34 0 0 1 1
31 8 32 35 25 7 0 0
32 8 31 35 27 26 1 0
33 11 33 36 28 30 0 0
34 12 34 36 29 5 1 0
35 16 35 37 32 31 0 0
36 23 36 37 33 34 1 0
37 39 37 0 35 36 0 0
char --> code
--> 111
a --> 1101
c --> 100110
d --> 100111
e --> 1010
f --> 1011
g --> 10010
h --> 0111
i --> 1100
l --> 00011
m --> 0101
n --> 001
o --> 1000
p --> 00010
r --> 00000
s --> 0100
t --> 01100
u --> 00001
x --> 01101
Length of encoded string: 157
0110001111100010011111000100111110100111110100110111010101000100001110
1011110111000000001110111000011011101101011101001111101000110011010001
00111110000110010
Input ="this is an example for huffman encoding"
result="this is an example for huffman encoding"
Ruby
Uses a
package PriorityQueue
<lang ruby>require 'priority_queue'
def huffman_encoding(str)
char_count = Hash.new(0)
str.each_char {|c| char_count[c] += 1}
pq = CPriorityQueue.new
# chars with fewest count have highest priority
char_count.each {|char, count| pq.push(char, count)}
while pq.length > 1
key1, prio1 = pq.delete_min
key2, prio2 = pq.delete_min
pq.push([key1, key2], prio1 + prio2)
end
Hash[*generate_encoding(pq.min_key)]
end
def generate_encoding(ary, prefix="")
case ary
when Array
generate_encoding(ary[0], "#{prefix}0") + generate_encoding(ary[1], "#{prefix}1")
else
[ary, prefix]
end
end
def encode(str, encoding)
str.each_char.collect {|char| encoding[char]}.join
end
def decode(encoded, encoding)
rev_enc = encoding.invert
decoded = ""
pos = 0
while pos < encoded.length
key = ""
while rev_enc[key].nil?
key << encoded[pos]
pos += 1
end
decoded << rev_enc[key]
end
decoded
end
str = "this is an example for huffman encoding" encoding = huffman_encoding(str) encoding.to_a.sort.each {|x| p x}
enc = encode(str, encoding) dec = decode(enc, encoding) puts "success!" if str == dec</lang>
[" ", "111"] ["a", "1011"] ["c", "00001"] ["d", "00000"] ["e", "1101"] ["f", "1100"] ["g", "00100"] ["h", "1000"] ["i", "1001"] ["l", "01110"] ["m", "10101"] ["n", "010"] ["o", "0001"] ["p", "00101"] ["r", "00111"] ["s", "0110"] ["t", "00110"] ["u", "01111"] ["x", "10100"] success!
Rust
Adapted C++ solution.
<lang rust> use std::collections::BTreeMap; use std::collections::binary_heap::BinaryHeap;
- [derive(Debug, Eq, PartialEq)]
enum NodeKind {
Internal(Box<Node>, Box<Node>), Leaf(char),
}
- [derive(Debug, Eq, PartialEq)]
struct Node {
frequency: usize, kind: NodeKind,
}
impl Ord for Node {
fn cmp(&self, rhs: &Self) -> std::cmp::Ordering {
rhs.frequency.cmp(&self.frequency)
}
}
impl PartialOrd for Node {
fn partial_cmp(&self, rhs: &Self) -> Option<std::cmp::Ordering> {
Some(self.cmp(&rhs))
}
}
type HuffmanCodeMap = BTreeMap<char, Vec<u8>>;
fn main() {
let text = "this is an example for huffman encoding";
let mut frequencies = BTreeMap::new();
for ch in text.chars() {
*frequencies.entry(ch).or_insert(0) += 1;
}
let mut prioritized_frequencies = BinaryHeap::new();
for counted_char in frequencies {
prioritized_frequencies.push(Node {
frequency: counted_char.1,
kind: NodeKind::Leaf(counted_char.0),
});
}
while prioritized_frequencies.len() > 1 {
let left_child = prioritized_frequencies.pop().unwrap();
let right_child = prioritized_frequencies.pop().unwrap();
prioritized_frequencies.push(Node {
frequency: right_child.frequency + left_child.frequency,
kind: NodeKind::Internal(Box::new(left_child), Box::new(right_child)),
});
}
let mut codes = HuffmanCodeMap::new();
generate_codes(
prioritized_frequencies.peek().unwrap(),
vec![0u8; 0],
&mut codes,
);
for item in codes {
print!("{}: ", item.0);
for bit in item.1 {
print!("{}", bit);
}
println!();
}
}
fn generate_codes(node: &Node, prefix: Vec<u8>, out_codes: &mut HuffmanCodeMap) {
match node.kind {
NodeKind::Internal(ref left_child, ref right_child) => {
let mut left_prefix = prefix.clone();
left_prefix.push(0);
generate_codes(&left_child, left_prefix, out_codes);
let mut right_prefix = prefix;
right_prefix.push(1);
generate_codes(&right_child, right_prefix, out_codes);
}
NodeKind::Leaf(ch) => {
out_codes.insert(ch, prefix);
}
}
} </lang>
Output:
: 110 a: 1001 c: 101010 d: 10001 e: 1111 f: 1011 g: 101011 h: 0101 i: 1110 l: 01110 m: 0011 n: 000 o: 0010 p: 01000 r: 01001 s: 0110 t: 01111 u: 10100 x: 10000
Scala
<lang scala>object Huffman {
import scala.collection.mutable.{Map, PriorityQueue}
sealed abstract class Tree
case class Node(left: Tree, right: Tree) extends Tree
case class Leaf(c: Char) extends Tree
def treeOrdering(m: Map[Tree, Int]) = new Ordering[Tree] {
def compare(x: Tree, y: Tree) = m(y).compare(m(x))
}
def stringMap(text: String) = text groupBy (x => Leaf(x) : Tree) mapValues (_.length)
def buildNode(queue: PriorityQueue[Tree], map: Map[Tree,Int]) {
val right = queue.dequeue
val left = queue.dequeue
val node = Node(left, right)
map(node) = map(left) + map(right)
queue.enqueue(node)
}
def codify(tree: Tree, map: Map[Tree, Int]) = {
def recurse(tree: Tree, prefix: String): List[(Char, (Int, String))] = tree match {
case Node(left, right) => recurse(left, prefix+"0") ::: recurse(right, prefix+"1")
case leaf @ Leaf(c) => c -> ((map(leaf), prefix)) :: Nil
}
recurse(tree, "")
}
def encode(text: String) = {
val map = Map.empty[Tree,Int] ++= stringMap(text)
val queue = new PriorityQueue[Tree]()(treeOrdering(map)) ++= map.keysIterator
while(queue.size > 1) {
buildNode(queue, map)
}
codify(queue.dequeue, map)
}
def main(args: Array[String]) {
val text = "this is an example for huffman encoding"
val code = encode(text)
println("Char\tWeight\t\tEncoding")
code sortBy (_._2._1) foreach {
case (c, (weight, encoding)) => println("%c:\t%3d/%-3d\t\t%s" format (c, weight, text.length, encoding))
}
}
}</lang>
- Output:
Char Weight Encoding t: 1/39 011000 p: 1/39 011001 r: 1/39 01101 c: 1/39 01110 x: 1/39 01111 g: 1/39 10110 l: 1/39 10111 u: 1/39 11000 d: 1/39 11001 o: 2/39 1010 s: 2/39 1101 m: 2/39 1110 h: 2/39 1111 f: 3/39 0000 a: 3/39 0001 e: 3/39 0010 i: 3/39 0011 n: 4/39 100 : 6/39 010
Scala (Alternate version)
<lang scala> // this version uses immutable data only, recursive functions and pattern matching object Huffman {
sealed trait Tree[+A] case class Leaf[A](value: A) extends Tree[A] case class Branch[A](left: Tree[A], right: Tree[A]) extends Tree[A]
// recursively build the binary tree needed to Huffman encode the text
def merge(xs: List[(Tree[Char], Int)]): List[(Tree[Char], Int)] = {
if (xs.length == 1) xs else {
val l = xs.head
val r = xs.tail.head
val merged = (Branch(l._1, r._1), l._2 + r._2)
merge((merged :: xs.drop(2)).sortBy(_._2))
}
}
// recursively search the branches of the tree for the required character
def contains(tree: Tree[Char], char: Char): Boolean = tree match {
case Leaf(c) => if (c == char) true else false
case Branch(l, r) => contains(l, char) || contains(r, char)
}
// recursively build the path string required to traverse the tree to the required character
def encodeChar(tree: Tree[Char], char: Char): String = {
def go(tree: Tree[Char], char: Char, code: String): String = tree match {
case Leaf(_) => code
case Branch(l, r) => if (contains(l, char)) go(l, char, code + '0') else go(r, char, code + '1')
}
go(tree, char, "")
}
def main(args: Array[String]) {
val text = "this is an example for huffman encoding"
// transform the text into a list of tuples.
// each tuple contains a Leaf node containing a unique character and an Int representing that character's weight
val frequencies = text.groupBy(chars => chars).mapValues(group => group.length).toList.map(x => (Leaf(x._1), x._2)).sortBy(_._2)
// build the Huffman Tree for this text
val huffmanTree = merge(frequencies).head._1
// output the resulting character codes
println("Char\tWeight\tCode")
frequencies.foreach(x => println(x._1.value + "\t" + x._2 + s"/${text.length}" + s"\t${encodeChar(huffmanTree, x._1.value)}"))
}
}</lang>
Char Weight Code
x 1/39 01100
t 1/39 01101
u 1/39 00010
g 1/39 00011
l 1/39 00000
p 1/39 00001
c 1/39 100110
r 1/39 100111
d 1/39 10010
s 2/39 0111
m 2/39 0100
h 2/39 0101
o 2/39 1000
e 3/39 1100
f 3/39 1101
a 3/39 1010
i 3/39 1011
n 4/39 001
6/39 111
Scheme
<lang scheme>(define (char-freq port table)
(if (eof-object? (peek-char port)) table (char-freq port (add-char (read-char port) table))))
(define (add-char char table)
(cond ((null? table) (list (list char 1))) ((eq? (caar table) char) (cons (list char (+ (cadar table) 1)) (cdr table))) (#t (cons (car table) (add-char char (cdr table))))))
(define (nodeify table)
(map (lambda (x) (list x '() '())) table))
(define node-freq cadar)
(define (huffman-tree nodes)
(let ((queue (sort nodes (lambda (x y) (< (node-freq x) (node-freq y))))))
(if
(null? (cdr queue))
(car queue)
(huffman-tree
(cons
(list
(list 'notleaf (+ (node-freq (car queue)) (node-freq (cadr queue))))
(car queue)
(cadr queue))
(cddr queue))))))
(define (list-encodings tree chars)
(for-each (lambda (c) (format #t "~a:~a~%" c (encode c tree))) chars))
(define (encode char tree)
(cond
((null? tree) #f)
((eq? (caar tree) char) '())
(#t
(let ((left (encode char (cadr tree))) (right (encode char (caddr tree))))
(cond
((not (or left right)) #f)
(left (cons #\1 left))
(right (cons #\0 right)))))))
(define (decode digits tree)
(cond ((not (eq? (caar tree) 'notleaf)) (caar tree)) ((eq? (car digits) #\0) (decode (cdr digits) (cadr tree))) (#t (decode (cdr digits) (caddr tree)))))
(define input "this is an example for huffman encoding") (define freq-table (char-freq (open-input-string input) '())) (define tree (huffman-tree (nodeify freq-table))) (list-encodings tree (map car freq-table))</lang>
- Output:
t:(1 0 0 1 1) h:(1 0 0 0) i:(0 0 1 1) s:(1 0 1 1) :(0 0 0) a:(0 0 1 0) n:(1 1 0) e:(0 1 0 1) x:(1 0 0 1 0) m:(1 0 1 0) p:(1 1 1 0 1) l:(1 1 1 0 0) f:(0 1 0 0) o:(0 1 1 1) r:(1 1 1 1 1) u:(1 1 1 1 0) c:(0 1 1 0 0 1) d:(0 1 1 0 0 0) g:(0 1 1 0 1)
SETL
<lang SETL>var forest := {}, encTab := {};
plaintext := 'this is an example for huffman encoding';
ft := {}; (for c in plaintext)
ft(c) +:= 1;
end;
forest := {[f, c]: [c, f] in ft}; (while 1 < #forest)
[f1, n1] := getLFN(); [f2, n2] := getLFN(); forest with:= [f1+f2, [n1,n2]];
end; addToTable(, arb range forest);
(for e = encTab(c))
print(c, ft(c), e);
end;
print(+/ [encTab(c): c in plaintext]);
proc addToTable(prefix, node);
if is_tuple node then addToTable(prefix + '0', node(1)); addToTable(prefix + '1', node(2)); else encTab(node) := prefix; end;
end proc;
proc getLFN();
f := min/ domain forest;
n := arb forest{f};
forest less:= [f, n];
return [f, n];
end proc;</lang>
Sidef
<lang ruby>func walk(n, s, h) {
if (n.contains(:a)) {
h{n{:a}} = s
say "#{n{:a}}: #{s}"
return nil
}
walk(n{:0}, s+'0', h)
walk(n{:1}, s+'1', h)
}
func make_tree(text) {
var letters = Hash()
text.each { |c| letters{c} := 0 ++ }
var nodes = letters.keys.map { |l|
Hash(a => l, freq => letters{l})
}
var n = Hash()
while (nodes.sort_by!{|c| c{:freq} }.len > 1) {
n = Hash(:0 => nodes.shift, :1 => nodes.shift)
n{:freq} = (n{:0}{:freq} + n{:1}{:freq})
nodes.append(n)
}
walk(n, "", n{:tree} = Hash())
return n
}
func encode(s, t) {
t = t{:tree}
s.chars.map{|c| t{c} }.join
}
func decode (enc, tree) {
var n = tree var out = ""
enc.each {|bit|
n = n{bit}
if (n.contains(:a)) {
out += n{:a}
n = tree
}
}
return out
}
var text = "this is an example for huffman encoding" var tree = make_tree(text) var enc = encode(text, tree)
say enc say decode(enc, tree)</lang>
- Output:
n: 000 s: 0010 o: 0011 h: 0100 l: 01010 g: 01011 x: 01100 c: 01101 d: 01110 u: 01111 p: 10000 t: 10001 i: 1001 : 101 f: 1100 a: 1101 e: 1110 r: 11110 m: 11111 1000101001001001010110010010101110100010111100110011011111110000010101110101110000111111010101000111111001100111111101000101111000001101001101110100100001011 this is an example for huffman encoding
Standard ML
<lang sml>datatype 'a huffman_tree =
Leaf of 'a
| Node of 'a huffman_tree * 'a huffman_tree
structure HuffmanPriority = struct
type priority = int
(* reverse comparison to achieve min-heap *)
fun compare (a, b) = Int.compare (b, a) type item = int * char huffman_tree val priority : item -> int = #1
end
structure HPQueue = LeftPriorityQFn (HuffmanPriority)
fun buildTree charFreqs = let
fun aux trees = let
val ((f1,a), trees) = HPQueue.remove trees
in
if HPQueue.isEmpty trees then
a
else let
val ((f2,b), trees) = HPQueue.remove trees
val trees = HPQueue.insert ((f1 + f2, Node (a, b)),
trees)
in
aux trees
end
end
val trees = HPQueue.fromList (map (fn (c,f) => (f, Leaf c)) charFreqs)
in
aux trees
end
fun printCodes (revPrefix, Leaf c) =
print (String.str c ^ "\t" ^
implode (rev revPrefix) ^ "\n")
| printCodes (revPrefix, Node (l, r)) = (
printCodes (#"0"::revPrefix, l);
printCodes (#"1"::revPrefix, r)
);
let
val test = "this is an example for huffman encoding"
val charFreqs = HashTable.mkTable
(HashString.hashString o String.str, op=)
(42, Empty)
val () =
app (fn c =>
let val old = getOpt (HashTable.find charFreqs c, 0)
in HashTable.insert charFreqs (c, old+1)
end)
(explode test)
val tree = buildTree (HashTable.listItemsi charFreqs)
in
print "SYMBOL\tHUFFMAN CODE\n"; printCodes ([], tree)
end</lang>
Swift
Rather than a priority queue of subtrees, we use the strategy of two sorted lists, one for leaves and one for nodes, and "merge" them as we iterate through them, taking advantage of the fact that any new nodes we create are bigger than any previously created nodes, so go at the end of the nodes list.
<lang swift>enum HuffmanTree<T> {
case Leaf(T)
indirect case Node(HuffmanTree<T>, HuffmanTree<T>)
func printCodes(prefix: String) {
switch(self) {
case let .Leaf(c):
print("\(c)\t\(prefix)")
case let .Node(l, r):
l.printCodes(prefix + "0")
r.printCodes(prefix + "1")
}
}
}
func buildTree<T>(freqs: [(T, Int)]) -> HuffmanTree<T> {
assert(freqs.count > 0, "must contain at least one character")
// leaves sorted by increasing frequency
let leaves : [(Int, HuffmanTree<T>)] = freqs.sort { (p1, p2) in p1.1 < p2.1 }.map { (x, w) in (w, .Leaf(x)) }
// nodes sorted by increasing frequency
var nodes = [(Int, HuffmanTree<T>)]()
// iterate through leaves and nodes in order of increasing frequency
for var i = 0, j = 0; ; {
assert(i < leaves.count || j < nodes.count)
// get subtree of least frequency
var e1 : (Int, HuffmanTree<T>)
if j == nodes.count || i < leaves.count && leaves[i].0 < nodes[j].0 {
e1 = leaves[i]
i++
} else {
e1 = nodes[j]
j++
}
// if there's no subtrees left, then that one was the answer
if i == leaves.count && j == nodes.count {
return e1.1
}
// get next subtree of least frequency
var e2 : (Int, HuffmanTree<T>)
if j == nodes.count || i < leaves.count && leaves[i].0 < nodes[j].0 {
e2 = leaves[i]
i++
} else {
e2 = nodes[j]
j++
}
// create node from two subtrees
nodes.append((e1.0 + e2.0, .Node(e1.1, e2.1)))
}
}
func getFreqs(seq: S) -> [(S.Generator.Element, Int)] {
var freqs : [S.Generator.Element : Int] = [:]
for c in seq {
freqs[c] = (freqs[c] ?? 0) + 1
}
return Array(freqs)
}
let str = "this is an example for huffman encoding" let charFreqs = getFreqs(str.characters) let tree = buildTree(charFreqs) print("Symbol\tHuffman code") tree.printCodes("")</lang>
- Output:
Symbol Huffman code u 00000 t 00001 d 00010 r 00011 c 00100 l 00101 o 0011 m 0100 s 0101 n 011 h 1000 g 10010 p 100110 x 100111 f 1010 a 1011 i 1100 e 1101 111
Tcl
<lang tcl>package require Tcl 8.5 package require struct::prioqueue
proc huffmanEncode {str args} {
array set opts [concat -dump false $args]
set charcount [dict create]
foreach char [split $str ""] {
dict incr charcount $char
}
set pq [struct::prioqueue -dictionary] ;# want lower values to have higher priority
dict for {char count} $charcount {
$pq put $char $count
}
while {[$pq size] > 1} {
lassign [$pq peekpriority 2] p1 p2
$pq put [$pq get 2] [expr {$p1 + $p2}]
}
set encoding [walkTree [$pq get]]
if {$opts(-dump)} {
foreach {char huffCode} [lsort -index 1 -stride 2 -command compare $encoding] {
puts "$char\t[dict get $charcount $char]\t$huffCode"
}
}
$pq destroy
return $encoding
}
proc walkTree {tree {prefix ""}} {
if {[llength $tree] < 2} {
return [list $tree $prefix]
}
lassign $tree left right
return [concat [walkTree $left "${prefix}0"] [walkTree $right "${prefix}1"]]
}
proc compare {a b} {
if {[string length $a] < [string length $b]} {return -1}
if {[string length $a] > [string length $b]} {return 1}
return [string compare $a $b]
}
set str "this is an example for huffman encoding"
set encoding [huffmanEncode $str -dump true]
puts $str puts [string map $encoding $str]</lang>
- Output:
n 4 000 6 101 s 2 0010 m 2 0011 o 2 0100 i 3 1001 a 3 1100 e 3 1101 f 3 1110 t 1 01010 x 1 01011 p 1 01100 l 1 01101 r 1 01110 u 1 01111 c 1 10000 d 1 10001 g 1 11110 h 2 11111 this is an example for huffman encoding 0101011111100100101011001001010111000001011101010111100001101100011011101101111001000111010111111011111110111000111100000101110100010000010010001100100011110
Ursala
following the algorithm given above <lang Ursala>#import std
- import nat
- import flo
code_table = # takes a training dataset to a table <char: code...>
-+
*^ ~&v?\~&iNC @v ~&t?\~&h ~&plrDSLrnPlrmPCAS/'01', ~&itB->h fleq-<&d; ^C\~&tt @hthPX ^V\~&lrNCC plus@bd, ^V(div@rrPlX,~&rlNVNC)^*D(plus:-0.@rS,~&)+ *K2 ^/~&h float+ length+-
- cast %csAL
table = code_table 'this is an example for huffman encoding'</lang> a quick walk through the code starting from the bottom:
*K2 ^/~&h float+ lengthcompute character frequencies by partitioning the input list of characters by equality, and transforming each equivalence class to a pair containing its member and its cardinality represented as a floating point number^V(div@rrPlX,~&rlNVNC)^*D(plus:-0.@rS,~&)construct a list of unary trees, one for each character class, with its normalized frequency in the root, and the character in the leaf~&itB->hwhile the list contains more than one tree, do the following, and when done take the head of the listfleq-<&d;sort the trees in increasing order by their roots^C\~&tt @hthPX ^V\~&lrNCC plus@bdchange the first two trees in the sorted list to a single binary tree whose root is the sum of their roots*^visit the following function on each node of the tree obtained from the loop and propagate the results upward from the leaves~&v?\~&iNCif the node is a leaf, construct a singleton list containing the pair of its root (a character) and the empty string (of bits)@v ~&t?\~&hif there is only a single subtree, propagate the result already obtained for it~&plrDSLrnPlrmPCAS/'01'otherwise there are two subtrees, hence two lists previously computed results propagating upward, so insert a zero into all of the bit strings in the results on the left, and a one into all the ones on the right, concatenate the left and right results, and propagate the contatenation upward
- Output:
< `r: '00000', `l: '00001', `c: '00010', `u: '00011', `n: '001', `m: '0100', `h: '0101', `g: '01100', `d: '01101', `o: '0111', `s: '1000', `t: '10010', `p: '100110', `x: '100111', `a: '1010', `f: '1011', `i: '1100', `e: '1101', ` : '111'>
zkl
This code was adapted from Perl, Python and most of the other examples. <lang zkl>fcn buildHuffman(text){ //-->(encode dictionary, decode dictionary)
ft:=Dictionary();
foreach c in (text){ ft[c]=ft.find(c,0)+1 } // leafs w/count
// build the tree, which is a list of lists of ...
tree:=ft.pump(List,fcn([(c,cnt)]){ //-->L( (cnt, ((sym,code))), ...)
L(cnt, L(L(c,"")))
}).copy(); // make it writable
while(tree.len()>1){ // fake up a [lame] priorty queue
tree=tree.sort(fcn(a,b){ a[0]>b[0] }); //prioritize high to low
a,b:=tree.pop(-2,2); //remove 2 least frequent symbols
mc:=fcn(n,c){ n[1] = c + n[1]; }; //(sym,code),"0"|"1"
a[1].apply2(mc,"0"); b[1].apply2(mc,"1"); // mc(a[1],"0")
tree.append( L(a[0]+b[0],a[1].extend(b[1])) ); //(a,b)-->new node
}//-->L(L(39, L( L(" ","000"),L("e","0010"),L("a","0011") ...
tree=tree[0][1].pump(List,fcn(i){ // flatten rather than traverse
if(T.isType(i))return(Void.Recurse,i,self.fcn); i });
encodeTable:=tree.toDictionary(); // symbol:Huffman code decodeTable:=encodeTable.pump(Dictionary(),"reverse"); // code:symbol return(encodeTable,decodeTable);
}</lang> <lang zkl>fcn encode(text,table){ text.pump(String,table.get) } fcn decode(bits,table){ // this is a horrible decoder, for testing only
w:=bits.walker(); sink:=Sink(String);
try{ s:=""; while(1){
s+=w.next(); if(c:=table.find(s)) { sink.write(c); s=""; }
}}catch(TheEnd){}
sink.close();
}</lang> <lang zkl>text:="this is an example for huffman encoding"; encodeTable,decodeTable := buildHuffman(text); encodeTable.pump(Console.println,fcn(kv){"%s : %s".fmt(kv.xplode())});
e:=encode(text,encodeTable); "Encode %d characters (%d bits) to %d bits (%d bytes):"
.fmt(text.len(),text.len()*8,e.len(),(e.len()+7)/8).println();
println(e);
0'|Bits decoded to: "%s"|.fmt(decode(e,decodeTable)).println();</lang>
- Output:
a : 0011 c : 10101 d : 10100 e : 0010 f : 0110 g : 10111 h : 1000 i : 0101 l : 10110 m : 1001 n : 110 o : 01000 p : 11111 r : 11100 s : 0111 t : 01001 u : 11101 x : 11110 : 000 Encode 39 characters (312 bits) to 157 bits (20 bytes): 0100110000101011100001010111000001111000000101111000111001111111011000100000110010001110000010001110101100110100100111100000010110101010100010100010111010111 Bits decoded to: "this is an example for huffman encoding"
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