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Huffman Coding using Priority Queue

  • Difficulty Level : Medium
  • Last Updated : 11 Aug, 2021

Prerequisite: Greedy Algorithms | Set 3 (Huffman Coding), priority_queue::push() and priority_queue::pop() in C++ STL 
Given a char array ch[] and frequency of each character as freq[]. The task is to find Huffman Codes for every character in ch[] using Priority Queue.

Example 

Input: ch[] = { ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, ‘f’ }, freq[] = { 5, 9, 12, 13, 16, 45 } 
Output: 
f 0 
c 100 
d 101 
a 1100 
b 1101 
e 111 
  

Approach: 

  1. Push all the characters in ch[] mapped to corresponding frequency freq[] in priority queue.
  2. To create Huffman Tree, pop two nodes from priority queue.
  3. Assign two popped node from priority queue as left and right child of new node.
  4. Push the new node formed in priority queue.
  5. Repeat all above steps until size of priority queue becomes 1.
  6. Traverse the Huffman Tree (whose root is the only node left in the priority queue) to store the Huffman Code
  7. Print all the stored Huffman Code for every character in ch[].

Below is the implementation of the above approach:  

C++




// C++ Program for Huffman Coding
// using Priority Queue
#include <iostream>
#include <queue>
using namespace std;
 
// Maximum Height of Huffman Tree.
#define MAX_SIZE 100
 
class HuffmanTreeNode {
public:
    // Stores character
    char data;
 
    // Stores frequency of
    // the character
    int freq;
 
    // Left child of the
    // current node
    HuffmanTreeNode* left;
 
    // Right child of the
    // current node
    HuffmanTreeNode* right;
 
    // Initializing the
    // current node
    HuffmanTreeNode(char character,
                    int frequency)
    {
        data = character;
        freq = frequency;
        left = right = NULL;
    }
};
 
// Custom comparator class
class Compare {
public:
    bool operator()(HuffmanTreeNode* a,
                    HuffmanTreeNode* b)
    {
        // Defining priority on
        // the basis of frequency
        return a->freq > b->freq;
    }
};
 
// Function to generate Huffman
// Encoding Tree
HuffmanTreeNode* generateTree(priority_queue<HuffmanTreeNode*,
                              vector<HuffmanTreeNode*>,
                                             Compare> pq)
{
 
    // We keep on looping till
    // only one node remains in
    // the Priority Queue
    while (pq.size() != 1) {
 
        // Node which has least
        // frequency
        HuffmanTreeNode* left = pq.top();
 
        // Remove node from
        // Priority Queue
        pq.pop();
 
        // Node which has least
        // frequency
        HuffmanTreeNode* right = pq.top();
 
        // Remove node from
        // Priority Queue
        pq.pop();
 
        // A new node is formed
        // with frequency left->freq
        // + right->freq
 
        // We take data as '$'
        // because we are only
        // concerned with the
        // frequency
        HuffmanTreeNode* node = new HuffmanTreeNode('$',
                                  left->freq + right->freq);
        node->left = left;
        node->right = right;
 
        // Push back node
        // created to the
        // Priority Queue
        pq.push(node);
    }
 
    return pq.top();
}
 
// Function to print the
// huffman code for each
// character.
 
// It uses arr to store the codes
void printCodes(HuffmanTreeNode* root,
                int arr[], int top)
{
    // Assign 0 to the left node
    // and recur
    if (root->left) {
        arr[top] = 0;
        printCodes(root->left,
                   arr, top + 1);
    }
 
    // Assign 1 to the right
    // node and recur
    if (root->right) {
        arr[top] = 1;
        printCodes(root->right, arr, top + 1);
    }
 
    // If this is a leaf node,
    // then we print root->data
 
    // We also print the code
    // for this character from arr
    if (!root->left && !root->right) {
        cout << root->data << " ";
        for (int i = 0; i < top; i++) {
            cout << arr[i];
        }
        cout << endl;
    }
}
 
void HuffmanCodes(char data[],
                  int freq[], int size)
{
 
    // Declaring priority queue
    // using custom comparator
    priority_queue<HuffmanTreeNode*,
                   vector<HuffmanTreeNode*>,
                   Compare>
        pq;
 
    // Populating the priority
    // queue
    for (int i = 0; i < size; i++) {
        HuffmanTreeNode* newNode
            = new HuffmanTreeNode(data[i], freq[i]);
        pq.push(newNode);
    }
 
    // Generate Huffman Encoding
    // Tree and get the root node
    HuffmanTreeNode* root = generateTree(pq);
 
    // Print Huffman Codes
    int arr[MAX_SIZE], top = 0;
    printCodes(root, arr, top);
}
 
// Driver Code
int main()
{
    char data[] = { 'a', 'b', 'c', 'd', 'e', 'f' };
    int freq[] = { 5, 9, 12, 13, 16, 45 };
    int size = sizeof(data) / sizeof(data[0]);
 
    HuffmanCodes(data, freq, size);
    return 0;
}
Output: 
f 0
c 100
d 101
a 1100
b 1101
e 111

 

Time Complexity: O(n*logn) where n is the number of unique characters
Auxiliary Space: O(n)


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