# Huffman coding

(Redirected from Huffman codes)
Huffman coding
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:

1. Create a leaf node for each symbol and add it to the priority queue.
2. While there is more than one node in the queue:
1. Remove the node of highest priority (lowest probability) twice to get two nodes.
2. Create a new internal node with these two nodes as children and with probability equal to the sum of the two nodes' probabilities.
3. Add the new node to the queue.
3. 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:

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.

## 11l

Translation of: Python
T Element((Int weight, [(Char, String)] symbols))
F <(other)
R (.weight, .symbols) < (other.weight, other.symbols)

F encode(symb2freq)
V heap = symb2freq.map((sym, wt) -> Element(wt, [(sym, ‘’)]))
minheap:heapify(&heap)

L heap.len > 1
V lo = minheap:pop(&heap)
V hi = minheap:pop(&heap)

L(&sym) lo.symbols
sym[1] = ‘0’sym[1]

L(&sym) hi.symbols
sym[1] = ‘1’sym[1]

minheap:push(&heap, Element(lo.weight + hi.weight, lo.symbols [+] hi.symbols))

R sorted(minheap:pop(&heap).symbols, key' p -> (p[1].len, p))

V txt = ‘this is an example for huffman encoding’
V symb2freq = DefaultDict[Char, Int]()
L(ch) txt
symb2freq[ch]++

V huff = encode(symb2freq)
print("Symbol\tWeight\tHuffman Code")
L(p) huff
print("#.\t#.\t#.".format(p[0], symb2freq[p[0]], p[1]))
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


Works with: Ada 2005

with Ada.Containers.Indefinite_Ordered_Maps;
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;


with Ada.Text_IO;
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;
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;


with Ada.Text_IO;
with Huffman;
procedure Main is
package Char_Natural_Huffman_Tree is new Huffman
(Symbol_Type => Character,
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);
(Char_Natural_Huffman_Tree.Decode (Tree => Tree, Code => Code));
end;
end Main;

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

 This example is incorrect. Please fix the code and remove this message.Details: Huffman code can not contain another code as a prefix
      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$ENDIF NEXT END  Output:  101 n 000 e 1110 f 1101 a 1100 i 1011 s 0110 m 0101 h 0100 o 0011 c 0010 l 0001 r 0000 x 11111 p 11110 d 11101 u 11100 g 11011 t 11010  ## Bracmat ( "this is an example for huffman encoding":?S & 0:?chars & 0:?p & ( @( !S : ? ( [!p %?char [?p ? & !char+!chars:?chars & ~ ) ) | ) & 0:?prioritized & whl ' ( !chars:?n*%@?w+?chars & (!n.!w)+!prioritized:?prioritized ) & whl ' ( !prioritized:(?p.?x)+(?q.?y)+?nprioritized & (!p+!q.(!p.0,!x)+(!q.1,!y))+!nprioritized:?prioritized ) & 0:?L & ( walk = bits tree bit subtree . !arg:(?bits.?tree) & whl ' ( !tree:(?p.?bit,?subtree)+?tree & ( !subtree:@ & (!subtree.str$(!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)));
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.

#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];
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;
}


### Alternative

Using a simple heap-based priority queue. Heap is an array, while ndoe tree is done by binary links.

#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] = {{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;
}

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#

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)
{
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);
_leafDictionary[value] = node;
}

while (priorityQueue.Count > 1)
{
HuffmanNode<T> leftSon = priorityQueue.Pop();
HuffmanNode<T> rightSon = priorityQueue.Pop();
var parent = new HuffmanNode<T>(leftSon, rightSon);
}

_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)
{
nodeCur = nodeCur.Parent;
}

reverseEncoding.Reverse();
}

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)
{
}
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();
}
}
}
}


## C++

This code builds a tree to generate huffman codes, then prints the codes.

#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;
}

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

(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}]
(.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")

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.

(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")

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

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()

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.)

(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))))


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

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[]);
}

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

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

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.

-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).

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#

Translation of: OCaml
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)

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

## Factor

USING: kernel sequences combinators accessors assocs math hashtables math.order
sorting.slots classes formatting prettyprint ;

IN: huffman

! -------------------------------------
! CLASSES -----------------------------
! -------------------------------------

TUPLE: huffman-node
weight element encoding left right ;

! For nodes
: <huffman-tnode> ( left right -- huffman )
huffman-node new [ left<< ] [ swap >>right ] bi ;

! For leafs
: <huffman-node> ( element -- huffman )
1 swap f f f huffman-node boa ;

! --------------------------------------
! INITIAL HASHTABLE --------------------
! --------------------------------------

<PRIVATE

! Increment node if it already exists
! Else make it and add it to the hash-table
: huffman-gen ( element nodes  -- )
2dup at
[ [ [ 1 + ] change-weight ] change-at ]
[ [ dup <huffman-node> swap ] dip set-at ] if ;

! Curry node-hash.  Then each over the seq
! to get the weighted values
: (huffman) ( nodes seq --  nodes )
dup [ [ huffman-gen ] curry each ] dip ;

! ---------------------------------------
! TREE GENERATION -----------------------
! ---------------------------------------

: (huffman-weight) ( node1 node2 -- weight )
[ weight>> ] dup bi* + ;

! Combine two nodes into the children of a parent
! node which has a weight equal to their collective
! weight
: (huffman-combine) ( node1 node2 -- node3 )
[ (huffman-weight) ]
[ <huffman-tnode> ] 2bi
swap >>weight ;

! Generate a tree by combining nodes
! in the priority queue until we're
! left with the root node
: (huffman-tree) ( nodes -- tree )
dup rest empty?
[ first ] [
{ { weight>> <=> } } sort-by
[ rest rest ] [ first ]
[ second ] tri
(huffman-combine) prefix
(huffman-tree)
] if  ; recursive

! --------------------------------------
! ENCODING -----------------------------
! --------------------------------------

: (huffman-leaf?) ( node -- bool )
[ left>>  huffman-node instance? ]
[ right>> huffman-node instance? ] bi and not ;

: (huffman-leaf) ( leaf bit -- )
swap encoding<< ;

DEFER: (huffman-encoding)

! Recursively walk the nodes left and right
: (huffman-node) ( bit nodes -- )
[ 0 suffix ] [ 1 suffix ] bi
[ [ left>> ] [ right>> ] bi ] 2dip
[ swap ] dip
[ (huffman-encoding) ] 2bi@ ;

: (huffman-encoding) ( bit nodes -- )
over (huffman-leaf?)
[ (huffman-leaf) ]
[ (huffman-node) ] if ;

PRIVATE>

! -------------------------------
! USER WORDS --------------------
! -------------------------------

: huffman-print ( nodes -- )
"Element" "Weight" "Code" "\n%10s\t%10s\t%6s\n" printf
{ { weight>> >=< } } sort-by
[  [ encoding>> ] [ element>> ] [ weight>> ] tri
"%8c\t%7d\t\t" printf  pprint "\n" printf ] each ;

: huffman ( sequence -- nodes )
H{ } clone (huffman) values
[ (huffman-tree) { } (huffman-encoding) ] keep ;

! ---------------------------------
! USAGE ---------------------------
! ---------------------------------

! { 1 2 3 4 } huffman huffman-print
! "this is an example of a huffman tree" huffman huffman-print

! Element   Weight	  Code
!      	      7		{ 0 0 0 }
!     a	      4		{ 1 1 1 }
!     e	      4		{ 1 1 0 }
!     f	      3		{ 0 0 1 0 }
!     h	      2		{ 1 0 1 0 }
!     i	      2		{ 0 1 0 1 }
!     m	      2		{ 0 1 0 0 }
!     n	      2		{ 0 1 1 1 }
!     s	      2		{ 0 1 1 0 }
!     t	      2		{ 0 0 1 1 }
!     l	      1		{ 1 0 1 1 1 }
!     o	      1		{ 1 0 1 1 0 }
!     p	      1		{ 1 0 0 0 1 }
!     r	      1		{ 1 0 0 0 0 }
!     u	      1		{ 1 0 0 1 1 }
!     x	      1		{ 1 0 0 1 0 }


## 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)

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 )  Example:  ;"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  ## Java This implementation creates an actual tree structure, and then traverses the tree to recover the code. 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()); } }  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 Translation of: Ruby Works with: SpiderMonkey for the print() function. First, use the Binary Heap implementation from here: http://eloquentjavascript.net/appendix2.html The Huffman encoder 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; }  And, using the Huffman encoder 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));  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 Translation of: C class node{ constructor(freq, char, left, right){ this.left = left; this.right = right; this.freq = freq; this.c = char; } }; nodes = []; code = {}; function new_node(left, right){ return new node(left.freq + right.freq, -1, left, right);; }; function qinsert(node){ nodes.push(node); nodes.sort(compareFunction); }; function qremove(){ return nodes.pop(); }; function compareFunction(a, b){ return b.freq - a.freq; }; function build_code(node, codeString, length){ if (node.c != -1){ code[node.c] = codeString; return; }; /* Left Branch */ leftCodeString = codeString + "0"; build_code(node.left, leftCodeString, length + 1); /* Right Branch */ rightCodeString = codeString + "1"; build_code(node.right, rightCodeString, length + 1); }; function init(string){ var i; var freq = []; var codeString = ""; for (var i = 0; i < string.length; i++){ if (isNaN(freq[string.charCodeAt(i)])){ freq[string.charCodeAt(i)] = 1; } else { freq[string.charCodeAt(i)] ++; }; }; for (var i = 0; i < freq.length; i++){ if (freq[i] > 0){ qinsert(new node(freq[i], i, null, null)); }; }; while (nodes.length > 1){ qinsert(new_node(qremove(), qremove())); }; build_code(nodes[0], codeString, 0); }; function encode(string){ output = ""; for (var i = 0; i < string.length; i ++){ output += code[string.charCodeAt(i)]; }; return output; }; function decode(input){ output = ""; node = nodes[0]; for (var i = 0; i < input.length; i++){ if (input[i] == "0"){ node = node.left; } else { node = node.right; }; if (node.c != -1){ output += String.fromCharCode(node.c); node = nodes[0]; }; }; return output }; string = "this is an example of huffman encoding"; console.log("initial string: " + string); init(string); for (var i = 0; i < Object.keys(code).length; i++){ if (isNaN(code[Object.keys(code)[i]])){ } else { console.log("'" + String.fromCharCode(Object.keys(code)[i]) + "'" + ": " + code[Object.keys(code)[i]]); }; }; huffman = encode(string); console.log("encoded: " + huffman + "\n"); output = decode(huffman); console.log("decoded: " + output);  initial string: this is an example of huffman encoding ' ': 111 'a': 1011 'c': 00101 'd': 00100 'e': 1010 'f': 1101 'g': 00111 'h': 0101 'i': 1100 'l': 00110 'm': 0100 'n': 100 'o': 0111 'p': 00001 's': 0110 't': 00000 'u': 00011 'x': 00010 encoded: 000000101110001101111100011011110111001111010000101011010000001001101010111011111011110101000111101110101001011100111101010000101011100100110010000111 decoded: this is an example of huffman encoding  ## 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)), "")  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 Translation of: Java This implementation creates an actual tree structure, and then traverses the tree to recover the code. 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())
}

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.

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"

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

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 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 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}];  ## Nim import tables, sequtils 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] func <(a: Node, b: Node): bool = # For min operator. a.f < b.f func $(hc: HuffCode): string =
result = ""
for symbol in hc:
result &= $symbol func 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 for node in tree: if node.parent.isNil and node != parent: result.add(node) func 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 func 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 not currentNode.childs[i].isNil: let newCode = currentCode & i generateCodes(codes, currentNode.childs[i], newCode) func 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 when isMainModule: import algorithm, strformat const SampleString = "this is an example for huffman encoding" SampleFrequencies = SampleString.toCountTable() func <(code1, code2: HuffCode): bool = # Used to sort the result. if code1.len == code2.len: result = false for (c1, c2) in zip(code1, code2): if c1 != c2: return c1 < c2 else: result = code1.len < code2.len let tree = buildTree(SampleFrequencies) root = tree.freeChildList[0] var huffCodes = newTable[char, HuffCode]() generateCodes(huffCodes, root) for (key, value) in sortedByIt(toSeq(huffCodes.pairs), it[1]): echo &"'{key}' → {value}"  Output: 'n' → 000 ' ' → 101 's' → 0010 'h' → 0011 'm' → 0100 'f' → 1001 'i' → 1100 'a' → 1101 'e' → 1110 'd' → 01010 'x' → 01011 'g' → 01100 'r' → 01101 'c' → 01110 'u' → 01111 't' → 10000 'p' → 10001 'l' → 11110 'o' → 11111 ## Oberon-2 Works with: oo2c 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. 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 Translation of: Java 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. #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; }  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 Translation of: Standard ML We use a Set (which is automatically sorted) as a priority queue. Works with: OCaml version 4.02+ 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  ## Ol (define phrase "this is an example for huffman encoding") ; prepare initial probabilities table (define table (ff->list (fold (lambda (ff x) (put ff x (+ (ff x 0) 1))) {} (string->runes phrase)))) ; just sorter... (define (resort l) (sort (lambda (x y) (< (cdr x) (cdr y))) l)) ; ...to sort table (define table (resort table)) ; build huffman tree (define tree (let loop ((table table)) (if (null? (cdr table)) (car table) (loop (resort (cons (cons { 1 (car table) 0 (cadr table)} (+ (cdar table) (cdadr table))) (cddr table))))))) ; huffman codes (define codes (map (lambda (i) (call/cc (lambda (return) (let loop ((prefix #null) (tree tree)) (if (ff? (car tree)) (begin (loop (cons 0 prefix) ((car tree) 0)) (loop (cons 1 prefix) ((car tree) 1))) (if (eq? (car tree) i) (return (reverse prefix)))))))) (map car table)))  Output: (print "weights: ---------------------------") (for-each (lambda (ch) (print (string (car ch)) ": " (cdr ch))) (reverse table)) (print "codes: -----------------------------") (map (lambda (char code) (print (string char) ": " code)) (reverse (map car table)) (reverse codes))  weights: --------------------------- : 6 n: 4 i: 3 f: 3 e: 3 a: 3 s: 2 o: 2 m: 2 h: 2 x: 1 u: 1 t: 1 r: 1 p: 1 l: 1 g: 1 d: 1 c: 1 codes: ----------------------------- : (0 0 0) n: (1 1 0) i: (0 1 0 0) f: (0 1 0 1) e: (0 0 1 0) a: (0 0 1 1) s: (0 1 1 1) o: (1 0 1 0) m: (1 0 1 1) h: (1 0 0 0) x: (0 1 1 0 1) u: (0 1 1 0 0 0) t: (0 1 1 0 0 1) r: (1 1 1 1 0) p: (1 1 1 1 1) l: (1 1 1 0 0) g: (1 1 1 0 1) d: (1 0 0 1 0) c: (1 0 0 1 1)  ## 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";

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


## Phix

Translation of: Lua
with javascript_semantics
function store_nodes(object key, object data, integer nodes)
setd({data,key},0,nodes)
return 1
end function

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(store_nodes, nodes, freq)
destroy_dict(freq)
return nodes
end function

function build_hufftree(integer nodes)
sequence node
while true do
sequence lkey = getd_partial_key({0,0},nodes)
integer lfreq = lkey[1]
deld(lkey,nodes)
sequence rkey = getd_partial_key({0,0},nodes)
integer 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*/)
{integer i, string s} = data
printf(1,"'%c' [%d] %s\n",{key,i,s})
return 1
end function

procedure print_huffcodes(integer d)
traverse_dict(print_huffcode, 0, d)
end procedure

function invert_huffcode(integer key, sequence data, integer rd)
setd(data[2],key,rd)
return 1
end function

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
?shorten(encoded)

integer rd = new_dict()
traverse_dict(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")

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
"10000111111110010010...01101011111000001100 (157 digits)"
"this is an example for huffman encoding"


## PHP

Works with: PHP version 5.3+
Translation of: Python

(not exactly)

<?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";
?>

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


## Picat

Translation of: Prolog
go =>
huffman("this is an example for huffman encoding").

huffman(LA) :-
LS=sort(LA),
packList(LS,PL),
PLS=sort(PL).remove_dups(),
build_tree(PLS, A),
coding(A, [], C),
SC=sort(C).remove_dups(),
println("Symbol\tWeight\tCode"),
foreach(SS in SC) print_code(SS) end.

build_tree([[V1|R1], [V2|R2]|T], AF) :-
V = V1 + V2,
A = [V, [V1|R1], [V2|R2]],
(   T=[] -> AF=A ; NT=sort([A|T]), 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) :-
CodeR = reverse(Code),
CF = [[FG, FD, CodeR]] .

is_node([_V, _FG, _FD]).

print_code([N, Car, Code]) :-
printf("%w:\t%w\t", Car, N),
foreach(V in Code) print(V) end,
nl.

packList([], []).
packList([X],[[1,X]]).
packList([X|Rest], XRunPacked) :-
XRunPacked = [XRun|Packed],
run(X, Rest, XRun, RRest),
packList(RRest, Packed).

run(V, [], VV, [])  :- VV=[1,V].
run(V, [V|LRest], [N1,V], RRest) :-
run(V, LRest, [N, V], RRest),
N1 = N + 1.
run(V, [Other|RRest], [1,V], [Other|RRest]) :-
different_terms(V, Other).
Output:
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

## PicoLisp

Using a cons cells (freq . char) for leaves, and two cells (freq left . right) for nodes.

(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)) ) ) )
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

*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;
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;

/*--------------------------------------------------------------------
* 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;
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;
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

Works with: PowerShell version 2
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

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

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([[V1|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).

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

Works with: PureBasic version 4.50
OpenConsole()

SampleString.s="this is an example for huffman encoding"
datalen=Len(SampleString)

Structure ztree
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)\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
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()
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.

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])

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.

### Alternative

This implementation creates an explicit tree structure, which is used during decoding. We also make use of a "pseudo end of file" symbol and padding bits to facilitate reading and writing encoded data to from/to a file.

"""Huffman encoding and decoding. Requires Python >= 3.7."""
from __future__ import annotations

from collections import Counter

from heapq import heapify
from heapq import heappush
from heapq import heappop

from itertools import chain
from itertools import islice

from typing import BinaryIO
from typing import Dict
from typing import Iterable
from typing import Optional
from typing import Tuple

LEFT_BIT = "0"
RIGHT_BIT = "1"
WORD_SIZE = 8  # Assumed to be a multiple of 8.
READ_SIZE = WORD_SIZE // 8
P_EOF = 1 << WORD_SIZE

class Node:
"""Huffman tree node."""

def __init__(
self,
weight: int,
symbol: Optional[int] = None,
left: Optional[Node] = None,
right: Optional[Node] = None,
):
self.weight = weight
self.symbol = symbol
self.left = left
self.right = right

def is_leaf(self) -> bool:
"""Return True if this node is a leaf node, or False otherwise."""
return self.left is None and self.right is None

def __lt__(self, other: Node) -> bool:
return self.weight < other.weight

def huffman_tree(weights: Dict[int, int]) -> Node:
"""Build a prefix tree from a map of symbol frequencies."""
heap = [Node(v, k) for k, v in weights.items()]
heapify(heap)

# Pseudo end-of-file with a weight of 1.
heappush(heap, Node(1, P_EOF))

while len(heap) > 1:
left, right = heappop(heap), heappop(heap)
node = Node(weight=left.weight + right.weight, left=left, right=right)
heappush(heap, node)

return heappop(heap)

def huffman_table(tree: Node) -> Dict[int, str]:
"""Build a table of prefix codes by visiting every leaf node in tree."""
codes: Dict[int, str] = {}

def walk(node: Optional[Node], code: str = ""):
if node is None:
return

if node.is_leaf():
assert node.symbol
codes[node.symbol] = code
return

walk(node.left, code + LEFT_BIT)
walk(node.right, code + RIGHT_BIT)

walk(tree)
return codes

def huffman_encode(data: bytes) -> Tuple[Iterable[bytes], Node]:
"""Encode the given byte string using Huffman coding.

Returns the encoded byte stream and the Huffman tree required to
decode those bytes.
"""
weights = Counter(data)
tree = huffman_tree(weights)
table = huffman_table(tree)
return _encode(data, table), tree

def huffman_decode(data: Iterable[bytes], tree: Node) -> bytes:
"""Decode the given byte stream using a Huffman tree."""
return bytes(_decode(_bits_from_bytes(data), tree))

def _encode(stream: Iterable[int], codes: Dict[int, str]) -> Iterable[bytes]:
bits = chain(chain.from_iterable(codes[s] for s in stream), codes[P_EOF])

# Pack bits (stream of 1s and 0s) one word at a time.
while True:
word = "".join(islice(bits, WORD_SIZE))  # Most significant bit first.
if not word:
break

# Pad last bits if they don't align to a whole word.
if len(word) < WORD_SIZE:
word = word.ljust(WORD_SIZE, "0")

# Byte order becomes relevant when READ_SIZE > 1.
yield int(word, 2).to_bytes(READ_SIZE, byteorder="big", signed=False)

def _decode(bits: Iterable[str], tree: Node) -> Iterable[int]:
node = tree

for bit in bits:
if bit == LEFT_BIT:
assert node.left
node = node.left
else:
assert node.right
node = node.right

if node.symbol == P_EOF:
break

if node.is_leaf():
assert node.symbol
yield node.symbol
node = tree  # Back to the top of the tree.

def _word_to_bits(word: bytes) -> str:
"""Return the binary representation of a word given as a byte string,
including leading zeros up to WORD_SIZE.

For example, when WORD_SIZE is 8:
_word_to_bits(b'65') == '01000001'
"""
i = int.from_bytes(word, "big")
return bin(i)[2:].zfill(WORD_SIZE)

def _bits_from_file(file: BinaryIO) -> Iterable[str]:
"""Generate a stream of bits (strings of either "0" or "1") from file-like
object file, opened in binary mode."""
while word:
yield from _word_to_bits(word)

def _bits_from_bytes(stream: Iterable[bytes]) -> Iterable[str]:
"""Generate a stream of bits (strings of either "0" or "1") from an
iterable of single byte byte-strings."""
return chain.from_iterable(_word_to_bits(byte) for byte in stream)

def main():
"""Example usage."""
s = "this is an example for huffman encoding"
data = s.encode()  # Need a byte string
encoded, tree = huffman_encode(data)

# Pretty print the Huffman table
print(f"Symbol Code\n------ ----")
for k, v in sorted(huffman_table(tree).items(), key=lambda x: len(x[1])):
print(f"{chr(k):<6} {v}")

# Print the bit pattern of the encoded data
print("".join(_bits_from_bytes(encoded)))

# Encode then decode
decoded = huffman_decode(*huffman_encode(data))
print(decoded.decode())

if __name__ == "__main__":
main()

Output:
Symbol Code
------ ----
n      000
110
m      0010
h      0101
i      1001
f      1010
e      1011
a      1110
r      00110
l      00111
c      01000
u      01001
x      01100
d      01101
t      01110
p      01111
Ā      10000
g      10001
o      11110
s      11111
011100101100111111110100111111110111000011010110110011100010011110011110111101010111100011011001010100110101010001011100001101011000010001111001101100100010001100000000
this is an example for huffman encoding


## Quackery

To use this code you will need to load the higher-order words defined at Higher-order functions#Quackery and the priority queue words defined at Priority queue#Quackery.

The word huffmantree takes a string and generates a tree from it suitable for Huffman decoding. To decode a single character, start with the whole tree and either 0 peek or 1 peek according to the next bit in the compressed stream until you reach a number (ascii character code.)

The word huffmanlist will turn the Huffman tree into a nest of nests, each containing an ascii character code and a nest containing a Huffman code. The nests are sorted by ascii character code to facilitate binary splitting.

  [ 2dup peek 1+ unrot poke ]    is itemincr    ( [ n --> [   )

[ [ 0 128 of ] constant
swap witheach itemincr
' [ i^ join ] map
' [ 0 peek ] filter ]        is countchars  (   $--> [ ) [ 0 peek dip [ 0 peek ] < ] is fewerchars ( [ [ --> b ) [ behead rot behead rot + unrot dip nested nested join join ] is makenode ( [ [ --> [ ) [ [ dup pqsize 1 > while frompq dip frompq makenode topq again ] frompq nip 0 pluck drop ] is maketree ( [ --> [ ) [ countchars pqwith fewerchars maketree ] is huffmantree ($ --> [   )

[ stack ]                      is path.hfl    (     --> s   )

[ stack ]                      is list.hfl    (     --> s   )

forward is makelist    (   [ -->     )
[ dup size 1 = iff
[ 0 peek
nested join nested
list.hfl take
join
list.hfl put ] done
unpack
1 path.hfl put
makelist
0 path.hfl replace
makelist
path.hfl release ]     resolves makelist    (   [ -->     )

[ sortwith
[ 0 peek swap 0 peek < ] ] is charsort    (   [ --> [   )

[ [] list.hfl put
makelist
list.hfl take
charsort ]                   is huffmanlist (   [ --> [   )

[ sortwith
[ 1 peek size
swap 1 peek size < ] ]   is codesort    (   [ --> [   )

[ witheach
[ unpack swap
say ' "' emit
say '" ' echo cr ] ]    is echohuff    (   [ --> [   )

$"this is an example for huffman encoding" huffmantree huffmanlist say " Huffman codes sorted by character." cr dup echohuff cr say " Huffman codes sorted by code length." cr codesort echohuff Output:  Huffman codes sorted by character. " " [ 1 1 1 ] "a" [ 1 0 0 1 ] "c" [ 1 0 0 0 1 ] "d" [ 0 0 1 1 0 ] "e" [ 1 0 1 1 ] "f" [ 1 1 0 1 ] "g" [ 1 0 1 0 1 0 ] "h" [ 0 0 0 1 ] "i" [ 1 1 0 0 ] "l" [ 1 0 0 0 0 ] "m" [ 0 1 0 0 ] "n" [ 0 1 1 ] "o" [ 0 1 0 1 ] "p" [ 1 0 1 0 1 1 ] "r" [ 1 0 1 0 0 ] "s" [ 0 0 0 0 ] "t" [ 0 0 1 1 1 ] "u" [ 0 0 1 0 0 ] "x" [ 0 0 1 0 1 ] Huffman codes sorted by code length. " " [ 1 1 1 ] "n" [ 0 1 1 ] "a" [ 1 0 0 1 ] "e" [ 1 0 1 1 ] "f" [ 1 1 0 1 ] "h" [ 0 0 0 1 ] "i" [ 1 1 0 0 ] "m" [ 0 1 0 0 ] "o" [ 0 1 0 1 ] "s" [ 0 0 0 0 ] "c" [ 1 0 0 0 1 ] "d" [ 0 0 1 1 0 ] "l" [ 1 0 0 0 0 ] "r" [ 1 0 1 0 0 ] "t" [ 0 0 1 1 1 ] "u" [ 0 0 1 0 0 ] "x" [ 0 0 1 0 1 ] "g" [ 1 0 1 0 1 0 ] "p" [ 1 0 1 0 1 1 ] ## 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)  ## Raku (formerly 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. Works with: rakudo version 2015-12-17 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'; }


### 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.

Works with: rakudo version 2015-12-17
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;  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 ## 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 ] ] ]  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 /* 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  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 Library: RubyGems package PriorityQueue 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  [" ", "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. 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); } } }  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 Works with: scala version 2.8 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)) } } }  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) Works with: scala version 2.11.7 // 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)}")) } }  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 (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))  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 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; ## Sidef 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)  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 Works with: SML/NJ 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  ## 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. Works with: Swift version 2+ 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<S : SequenceType where S.Generator.Element : Hashable>(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("")  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 Library: Tcllib (Package: struct::prioqueue) 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 $str]  Output: n 4 000 6 101 s 2 0010 m 2 0011 o 2 0100 i 3 1001 a 3 1100 e 3 1101 f 3 1110 t 1 01010 x 1 01011 p 1 01100 l 1 01101 r 1 01110 u 1 01111 c 1 10000 d 1 10001 g 1 11110 h 2 11111 this is an example for huffman encoding 0101011111100100101011001001010111000001011101010111100001101100011011101101111001000111010111111011111110111000111100000101110100010000010010001100100011110 ## UNIX Shell Works with: Bourne Again SHell #!/bin/bash set -eu # make scratch directory t="$(mktemp -d)"
cd "${t:?mktemp failed}" trap 'rm -r -- "$t"' EXIT

# get character frequencies
declare -a freq=()
for c in $line; do :$((freq[8#$c]++)) done done < <(od -b -v) # convert freqs into a bucket queue declare -i i=0 for c in${!freq[@]}; do
fn="${freq[c]}.$((i++))"
echo "$c:${freq[c]}" >"\$fn"
top2() { ls </