Huffman Coding

Data StructureAnalysis of AlgorithmsAlgorithms

Huffman coding is lossless data compression algorithm. In this algorithm a variable-length code is assigned to input different characters. The code length is related with how frequently characters are used. Most frequent characters have smallest codes, and longer codes for least frequent characters.

There are mainly two parts. First one to create Huffman tree, and another one to traverse the tree to find codes.

For an example, consider some strings “YYYZXXYYX”, the frequency of character Y is larger than X and the character Z has least frequency. So the length of code for Y is smaller than X, and code for X will be smaller than Z.

  • Complexity for assigning code for each character according to their frequency is O(n log n)

Input − A string with different characters, say “ACCEBFFFFAAXXBLKE”
Output − Code for different characters:

Data: K, Frequency: 1, Code: 0000
Data: L, Frequency: 1, Code: 0001
Data: E, Frequency: 2, Code: 001
Data: F, Frequency: 4, Code: 01
Data: B, Frequency: 2, Code: 100
Data: C, Frequency: 2, Code: 101
Data: X, Frequency: 2, Code: 110
Data: A, Frequency: 3, Code: 111

Algorithm

huffmanCoding(string)

Input − A string with different characters.

Output − The codes for each individual characters.

Begin
   define a node with character, frequency, left and right child of the node for Huffman tree.
   create a list ‘freq’ to store frequency of each character, initially all are 0
   for each character c in the string do
      increase the frequency for character ch in freq list.
   done
   for all type of character ch do
      if the frequency of ch is non zero then add ch and its frequency as a node of priority queue Q.
   done
   while Q is not empty do
      remove item from Q and assign it to left child of node
      remove item from Q and assign to the right child of node
      traverse the node to find the assigned code
   done
End

traverseNode(n: node, code)

Input − The node n of Huffman tree, and code assigned from previous call 

Output − Code assigned with each character

if left child of node n ≠ φ then
   traverseNode(leftChild(n), code+’0’) //traverse through the left child
   traverseNode(rightChild(n), code+’1’) //traverse through the right child
else
   display the character and data of current node.

Example

#include<iostream>
#include<queue>
#include<string>
using namespace std;
struct node{
   int freq;
   char data;
   const node *child0, *child1;
   node(char d, int f = -1){ //assign values in the node
      data = d;
      freq = f;
      child0 = NULL;
      child1 = NULL;
   }
   node(const node *c0, const node *c1){
      data = 0;
      freq = c0->freq + c1->freq;
      child0=c0;
      child1=c1;
   }
   bool operator<( const node &a ) const { //< operator performs to find priority in queue
      return freq >a.freq;
   }
   void traverse(string code = "")const{
      if(child0!=NULL){
         child0->traverse(code+'0'); //add 0 with the code as left child
         child1->traverse(code+'1'); //add 1 with the code as right child
      }else{
         cout << "Data: " << data<< ", Frequency: "<<freq << ", Code: " << code<<endl;
      }
   }
};
void huffmanCoding(string str){
   priority_queue<node> qu;
   int frequency[256];
   for(int i = 0; i<256; i++)
      frequency[i] = 0; //clear all frequency
   for(int i = 0; i<str.size(); i++){
      frequency[int(str[i])]++; //increase frequency
   }
   for(int i = 0; i<256; i++){
      if(frequency[i]){
         qu.push(node(i, frequency[i]));
      }
   }
   while(qu.size() >1){
      node *c0 = new node(qu.top()); //get left child and remove from queue
      qu.pop();
      node *c1 = new node(qu.top()); //get right child and remove from queue
      qu.pop();
      qu.push(node(c0, c1)); //add freq of two child and add again in the queue
   }
   cout << "The Huffman Code: "<<endl;
   qu.top().traverse(); //traverse the tree to get code
}
main(){
   string str = "ACCEBFFFFAAXXBLKE"; //arbitray string to get frequency
   huffmanCoding(str);
}

Output

The Huffman Code:
Data: K, Frequency: 1, Code: 0000
Data: L, Frequency: 1, Code: 0001
Data: E, Frequency: 2, Code: 001
Data: F, Frequency: 4, Code: 01
Data: B, Frequency: 2, Code: 100
Data: C, Frequency: 2, Code: 101
Data: X, Frequency: 2, Code: 110
Data: A, Frequency: 3, Code: 111
raja
Published on 05-Aug-2019 11:14:26
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