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Huffman Decoding

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  • Difficulty Level : Hard
  • Last Updated : 21 Mar, 2023
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We have discussed Huffman Encoding in a previous post. In this post, decoding is discussed. 

Examples:

Input Data: AAAAAABCCCCCCDDEEEEE
Frequencies: A: 6, B: 1, C: 6, D: 2, E: 5

Encoded Data: 0000000000001100101010101011111111010101010

Huffman Tree: ‘#’ is the special character usedfor internal nodes as character field
                         is not needed for internal nodes. 

                    #(20)
                  /       \
          #(12)         #(8)
         /      \        /     \
     A(6)     C(6) E(5)     #(3)
                                 /     \
                             B(1)    D(2)  

Code of ‘A’ is ’00’, code of ‘C’ is ’01’, ..

Decoded Data: AAAAAABCCCCCCDDEEEEE

Input Data: GeeksforGeeks

Character With there Frequencies
e 10, f 1100, g 011, k 00, o 010, r 1101, s 111

Encoded Huffman data: 01110100011111000101101011101000111
Decoded Huffman Data: geeksforgeeks

Recommended Practice

Follow the below steps to solve the problem:

Note: To decode the encoded data we require the Huffman tree. We iterate through the binary encoded data. To find character corresponding to current bits, we use the following simple steps:

  • We start from the root and do the following until a leaf is found.
  • If the current bit is 0, we move to the left node of the tree.
  • If the bit is 1, we move to right node of the tree.
  • If during the traversal, we encounter a leaf node, we print the character of that particular leaf node and then again continue the iteration of the encoded data starting from step 1.

The below code takes a string as input, encodes it, and saves it in a variable encoded string. Then it decodes it and prints the original string. 

Below is the implementation of the above approach:

CPP




// C++ program to encode and decode a string using
// Huffman Coding.
#include <bits/stdc++.h>
#define MAX_TREE_HT 256
using namespace std;
 
// to map each character its huffman value
map<char, string> codes;
 
// To store the frequency of character of the input data
map<char, int> freq;
 
// A Huffman tree node
struct MinHeapNode {
    char data; // One of the input characters
    int freq; // Frequency of the character
    MinHeapNode *left, *right; // Left and right child
 
    MinHeapNode(char data, int freq)
    {
        left = right = NULL;
        this->data = data;
        this->freq = freq;
    }
};
 
// utility function for the priority queue
struct compare {
    bool operator()(MinHeapNode* l, MinHeapNode* r)
    {
        return (l->freq > r->freq);
    }
};
 
// utility function to print characters along with
// there huffman value
void printCodes(struct MinHeapNode* root, string str)
{
    if (!root)
        return;
    if (root->data != '$')
        cout << root->data << ": " << str << "\n";
    printCodes(root->left, str + "0");
    printCodes(root->right, str + "1");
}
 
// utility function to store characters along with
// there huffman value in a hash table, here we
// have C++ STL map
void storeCodes(struct MinHeapNode* root, string str)
{
    if (root == NULL)
        return;
    if (root->data != '$')
        codes[root->data] = str;
    storeCodes(root->left, str + "0");
    storeCodes(root->right, str + "1");
}
 
// STL priority queue to store heap tree, with respect
// to their heap root node value
priority_queue<MinHeapNode*, vector<MinHeapNode*>, compare>
    minHeap;
 
// function to build the Huffman tree and store it
// in minHeap
void HuffmanCodes(int size)
{
    struct MinHeapNode *left, *right, *top;
    for (map<char, int>::iterator v = freq.begin();
         v != freq.end(); v++)
        minHeap.push(new MinHeapNode(v->first, v->second));
    while (minHeap.size() != 1) {
        left = minHeap.top();
        minHeap.pop();
        right = minHeap.top();
        minHeap.pop();
        top = new MinHeapNode('$',
                              left->freq + right->freq);
        top->left = left;
        top->right = right;
        minHeap.push(top);
    }
    storeCodes(minHeap.top(), "");
}
 
// utility function to store map each character with its
// frequency in input string
void calcFreq(string str, int n)
{
    for (int i = 0; i < str.size(); i++)
        freq[str[i]]++;
}
 
// function iterates through the encoded string s
// if s[i]=='1' then move to node->right
// if s[i]=='0' then move to node->left
// if leaf node append the node->data to our output string
string decode_file(struct MinHeapNode* root, string s)
{
    string ans = "";
    struct MinHeapNode* curr = root;
    for (int i = 0; i < s.size(); i++) {
        if (s[i] == '0')
            curr = curr->left;
        else
            curr = curr->right;
 
        // reached leaf node
        if (curr->left == NULL and curr->right == NULL) {
            ans += curr->data;
            curr = root;
        }
    }
    // cout<<ans<<endl;
    return ans + '\0';
}
 
// Driver code
int main()
{
    string str = "geeksforgeeks";
    string encodedString, decodedString;
    calcFreq(str, str.length());
    HuffmanCodes(str.length());
    cout << "Character With there Frequencies:\n";
    for (auto v = codes.begin(); v != codes.end(); v++)
        cout << v->first << ' ' << v->second << endl;
 
    for (auto i : str)
        encodedString += codes[i];
 
    cout << "\nEncoded Huffman data:\n"
         << encodedString << endl;
 
      // Function call
    decodedString
        = decode_file(minHeap.top(), encodedString);
    cout << "\nDecoded Huffman Data:\n"
         << decodedString << endl;
    return 0;
}


Java




// Java program to encode and decode a string using
// Huffman Coding.
import java.util.*;
import java.util.Map.Entry;
 
public class HuffmanCoding {
     
    private static Map<Character, String> codes = new HashMap<>();
    private static Map<Character, Integer> freq = new HashMap<>();
    private static PriorityQueue<MinHeapNode> minHeap = new PriorityQueue<>();
     
    public static void main(String[] args) {
        String str = "geeksforgeeks";
        String encodedString = "";
        String decodedString = "";
        calcFreq(str);
        HuffmanCodes(str.length());
        System.out.println("Character With their Frequencies:");
        for (Entry<Character, String> entry : codes.entrySet()) {
            System.out.println(entry.getKey() + " " + entry.getValue());
        }
        for (char c : str.toCharArray()) {
            encodedString += codes.get(c);
        }
        System.out.println("\nEncoded Huffman data:");
        System.out.println(encodedString);
        decodedString = decodeFile(minHeap.peek(), encodedString);
        System.out.println("\nDecoded Huffman Data:");
        System.out.println(decodedString);
    }
     
    private static void HuffmanCodes(int size) {
        for (Entry<Character, Integer> entry : freq.entrySet()) {
            minHeap.add(new MinHeapNode(entry.getKey(), entry.getValue()));
        }
        while (minHeap.size() != 1) {
            MinHeapNode left = minHeap.poll();
            MinHeapNode right = minHeap.poll();
            MinHeapNode top = new MinHeapNode('$', left.freq + right.freq);
            top.left = left;
            top.right = right;
            minHeap.add(top);
        }
        storeCodes(minHeap.peek(), "");
    }
     
    private static void calcFreq(String str) {
        for (char c : str.toCharArray()) {
            freq.put(c, freq.getOrDefault(c, 0) + 1);
        }
    }
     
    private static void storeCodes(MinHeapNode root, String str) {
        if (root == null) {
            return;
        }
        if (root.data != '$') {
            codes.put(root.data, str);
        }
        storeCodes(root.left, str + "0");
        storeCodes(root.right, str + "1");
    }
     
    private static String decodeFile(MinHeapNode root, String s) {
        String ans = "";
        MinHeapNode curr = root;
        int n = s.length();
        for (int i = 0; i < n; i++) {
            if (s.charAt(i) == '0') {
                curr = curr.left;
            } else {
                curr = curr.right;
            }
            if (curr.left == null && curr.right == null) {
                ans += curr.data;
                curr = root;
            }
        }
        return ans + '\0';
    }
     
}
 
class MinHeapNode implements Comparable<MinHeapNode> {
    char data;
    int freq;
    MinHeapNode left, right;
     
    MinHeapNode(char data, int freq) {
        this.data = data;
        this.freq = freq;
    }
     
    public int compareTo(MinHeapNode other) {
        return this.freq - other.freq;
    }
}
 
//This code is contributed by NarasingaNikhil


Python3




import heapq
from collections import defaultdict
 
# to map each character its huffman value
codes = {}
 
# To store the frequency of character of the input data
freq = defaultdict(int)
 
# A Huffman tree node
class MinHeapNode:
    def __init__(self, data, freq):
        self.left = None
        self.right = None
        self.data = data
        self.freq = freq
 
    def __lt__(self, other):
        return self.freq < other.freq
 
# utility function to print characters along with
# there huffman value
def printCodes(root, str):
    if root is None:
        return
    if root.data != '$':
        print(root.data, ":", str)
    printCodes(root.left, str + "0")
    printCodes(root.right, str + "1")
 
# utility function to store characters along with
# there huffman value in a hash table
def storeCodes(root, str):
    if root is None:
        return
    if root.data != '$':
        codes[root.data] = str
    storeCodes(root.left, str + "0")
    storeCodes(root.right, str + "1")
 
# function to build the Huffman tree and store it
# in minHeap
def HuffmanCodes(size):
    global minHeap
    for key in freq:
        minHeap.append(MinHeapNode(key, freq[key]))
    heapq.heapify(minHeap)
    while len(minHeap) != 1:
        left = heapq.heappop(minHeap)
        right = heapq.heappop(minHeap)
        top = MinHeapNode('$', left.freq + right.freq)
        top.left = left
        top.right = right
        heapq.heappush(minHeap, top)
    storeCodes(minHeap[0], "")
 
# utility function to store map each character with its
# frequency in input string
def calcFreq(str, n):
    for i in range(n):
        freq[str[i]] += 1
 
# function iterates through the encoded string s
# if s[i]=='1' then move to node->right
# if s[i]=='0' then move to node->left
# if leaf node append the node->data to our output string
def decode_file(root, s):
    ans = ""
    curr = root
    n = len(s)
    for i in range(n):
        if s[i] == '0':
            curr = curr.left
        else:
            curr = curr.right
 
        # reached leaf node
        if curr.left is None and curr.right is None:
            ans += curr.data
            curr = root
    return ans + '\0'
 
# Driver code
if __name__ == "__main__":
    minHeap = []
    str = "geeksforgeeks"
    encodedString, decodedString = "", ""
    calcFreq(str, len(str))
    HuffmanCodes(len(str))
    print("Character With there Frequencies:")
    for key in sorted(codes):
        print(key, codes[key])
 
    for i in str:
        encodedString += codes[i]
 
    print("\nEncoded Huffman data:")
    print(encodedString)
 
    # Function call
    decodedString = decode_file(minHeap[0], encodedString)
    print("\nDecoded Huffman Data:")
    print(decodedString)


Javascript




// To map each character its huffman value
let codes = {};
 
// To store the frequency of character of the input data
let freq = {};
 
// A Huffman tree node
class MinHeapNode {
    constructor(data, freq) {
        this.left = null;
        this.right = null;
        this.data = data;
        this.freq = freq;
    }
 
    // Define the comparison method for sorting the nodes in the heap
    compareTo(other) {
        return this.freq - other.freq;
    }
}
 
// Create an empty min-heap
let minHeap = [];
 
// Utility function to print characters along with their huffman value
function printCodes(root, str) {
    if (!root) {
        return;
    }
    if (root.data !== "$") {
        console.log(root.data + " : " + str);
    }
    printCodes(root.left, str + "0");
    printCodes(root.right, str + "1");
}
 
// Utility function to store characters along with their huffman value in a hash table
function storeCodes(root, str) {
    if (!root) {
        return;
    }
    if (root.data !== "$") {
        codes[root.data] = str;
    }
    storeCodes(root.left, str + "0");
    storeCodes(root.right, str + "1");
}
 
// Function to build the Huffman tree and store it in minHeap
function HuffmanCodes(size) {
    for (let key in freq) {
        minHeap.push(new MinHeapNode(key, freq[key]));
    }
    // Convert the array to a min-heap using the built-in sort method
    minHeap.sort((a, b) => a.compareTo(b));
    while (minHeap.length !== 1) {
        let left = minHeap.shift();
        let right = minHeap.shift();
        let top = new MinHeapNode("$", left.freq + right.freq);
        top.left = left;
        top.right = right;
        minHeap.push(top);
        // Sort the array to maintain the min-heap property
        minHeap.sort((a, b) => a.compareTo(b));
    }
    storeCodes(minHeap[0], "");
}
 
// Utility function to store map each character with its frequency in input string
function calcFreq(str) {
    for (let i = 0; i < str.length; i++) {
        let char = str.charAt(i);
        if (freq[char]) {
            freq[char]++;
        } else {
            freq[char] = 1;
        }
    }
}
 
// Function iterates through the encoded string s
// If s[i] == '1' then move to node.right
// If s[i] == '0' then move to node.left
// If leaf node, append the node.data to our output string
function decode_file(root, s) {
    let ans = "";
    let curr = root;
    let n = s.length;
    for (let i = 0; i < n; i++) {
        if (s.charAt(i) == "0") {
            curr = curr.left;
        } else {
            curr = curr.right;
        }
 
        // Reached leaf node
        if (!curr.left && !curr.right) {
            ans += curr.data;
            curr = root;
        }
    }
    return ans + "\0";
}
 
// Driver code
let str = "geeksforgeeks";
let encodedString = "";
let decodedString = "";
calcFreq(str);
HuffmanCodes(str.length);
console.log("Character With their Frequencies:")
let keys = Array.from(Object.keys(codes))
keys.sort()
for (var key of keys)
    console.log(key, codes[key])
 
for (var i of str)
    encodedString += codes[i]
 
console.log("\nEncoded Huffman data:")
console.log(encodedString)
 
// Function call
decodedString = decode_file(minHeap[0], encodedString)
console.log("\nDecoded Huffman Data:")
console.log(decodedString)


C#




using System;
using System.Collections.Generic;
using System.Linq;
 
namespace HuffmanEncoding
{
    // To store the frequency of character of the input data
    class FrequencyTable
    {
        private readonly Dictionary<char, int> _freq = new Dictionary<char, int>();
 
        public void Add(char c)
        {
            if (_freq.ContainsKey(c))
            {
                _freq++;
            }
            else
            {
                _freq = 1;
            }
        }
 
        public Dictionary<char, int> ToDictionary()
        {
            return _freq;
        }
    }
 
    // A Huffman tree node
    class HuffmanNode : IComparable<HuffmanNode>
    {
        public HuffmanNode Left { get; set; }
        public HuffmanNode Right { get; set; }
        public char Data { get; set; }
        public int Frequency { get; set; }
 
        public HuffmanNode(char data, int freq)
        {
            Data = data;
            Frequency = freq;
        }
 
        // Define the comparison method for sorting the nodes in the heap
        public int CompareTo(HuffmanNode other)
        {
            return Frequency - other.Frequency;
        }
    }
 
    // Utility class for creating Huffman codes
    class HuffmanEncoder
    {
        // To map each character its Huffman value
        private readonly Dictionary<char, string> _codes = new Dictionary<char, string>();
 
        // Create an empty min-heap
        private readonly List<HuffmanNode> _minHeap = new List<HuffmanNode>();
 
        // Function to build the Huffman tree and store it in minHeap
        private void BuildHuffmanTree(Dictionary<char, int> freq)
        {
            foreach (var kvp in freq)
            {
                _minHeap.Add(new HuffmanNode(kvp.Key, kvp.Value));
            }
            // Convert the list to a min-heap using the built-in sort method
            _minHeap.Sort();
            while (_minHeap.Count > 1)
            {
                var left = _minHeap.First();
                _minHeap.RemoveAt(0);
                var right = _minHeap.First();
                _minHeap.RemoveAt(0);
                var top = new HuffmanNode('$', left.Frequency + right.Frequency);
                top.Left = left;
                top.Right = right;
                _minHeap.Add(top);
                // Sort the list to maintain the min-heap property
                _minHeap.Sort();
            }
        }
 
        // Utility function to store characters along with their Huffman value in a hash table
        private void StoreCodes(HuffmanNode root, string str)
        {
            if (root == null)
            {
                return;
            }
            if (root.Data != '$')
            {
                _codes[root.Data] = str;
            }
            StoreCodes(root.Left, str + "0");
            StoreCodes(root.Right, str + "1");
        }
 
        // Utility function to print characters along with their Huffman value
        public void PrintCodes(HuffmanNode root, string str)
        {
            if (root == null)
            {
                return;
            }
            if (root.Data != '$')
            {
                Console.WriteLine(root.Data + " : " + str);
            }
            PrintCodes(root.Left, str + "0");
            PrintCodes(root.Right, str + "1");
        }
 
        // Function iterates through the encoded string s
        // If s[i] == '1' then move to node.right
        // If s[i] == '0' then move to node.left
        // If leaf node, append the node.data to our output string
        public string DecodeFile(HuffmanNode root, string s)
        {
            
            string ans = "";
            HuffmanNode curr = root;
            int n = s.Length;
            for (int i = 0; i < n; i++)
            {
                if (s[i] == '0')
                {
                    curr = curr.Left;
                }
                else
                {
                    curr = curr.Right;
                }
 
                // Reached leaf node
                if (curr.Left == null && curr.Right == null)
                {
                    ans += curr.Data;
                    curr = root;
                }
            }
            return ans + "\0";
        }
 
        // Function to build the Huffman tree and store it in minHeap
        public void BuildCodes(Dictionary<char, int> freq)
        {
            BuildHuffmanTree(freq);
            StoreCodes(_minHeap.First(), "");
        }
 
        public Dictionary<char, string> GetCodes()
        {
            return _codes;
        }
 
        public HuffmanNode GetRoot()
        {
            return _minHeap.First();
        }
    }
 
    class Program
    {
        static void Main(string[] args)
        {
            // Driver code
            string str = "geeksforgeeks";
            string encodedString = "";
            string decodedString;
            var freqTable = new FrequencyTable();
            foreach (char c in str)
            {
                freqTable.Add(c);
            }
            var huffmanEncoder = new HuffmanEncoder();
            huffmanEncoder.BuildCodes(freqTable.ToDictionary());
            Console.WriteLine("Character With their Frequencies:");
            foreach (var kvp in huffmanEncoder.GetCodes())
            {
                Console.WriteLine($"{kvp.Key} : {kvp.Value}");
            }
 
            foreach (char c in str)
            {
                encodedString += huffmanEncoder.GetCodes();
            }
 
            Console.WriteLine("\nEncoded Huffman data:");
            Console.WriteLine(encodedString);
 
            // Function call
            decodedString = huffmanEncoder.DecodeFile(huffmanEncoder.GetRoot(), encodedString);
            Console.WriteLine("\nDecoded Huffman Data:");
            Console.WriteLine(decodedString);
        }
    }
}


Output

Character With there Frequencies:
e 10
f 1100
g 011
k 00
o 010
r 1101
s 111

Encoded Huffman data:
01110100011111000101101011101000111

Decoded Huffman Data:
geeksforgeeks

Comparing Input file size and Output file size: 

Comparing the input file size and the Huffman encoded output file. We can calculate the size of the output data in a simple way. Let’s say our input is a string “geeksforgeeks” and is stored in a file input.txt. 

Input File Size:

Input: “geeksforgeeks”
Total number of character i.e. input length: 13
Size: 13 character occurrences * 8 bits = 104 bits or 13 bytes.

Output File Size:

Input: “geeksforgeeks”

————————————————
Character |  Frequency |  Binary Huffman Value |
————————————————

   e      |      4     |         10              |
   f       |      1     |         1100          |   
   g      |      2     |         011            |
   k      |      2     |         00              |
   o      |      1     |         010            |
   r       |      1     |         1101          |
   s       |      2     |         111            | 

————————————————

So to calculate output size:

e: 4 occurrences * 2 bits = 8 bits
f: 1 occurrence  * 4 bits = 4 bits
g: 2 occurrences * 3 bits = 6 bits
k: 2 occurrences * 2 bits = 4 bits
o: 1 occurrence  * 3 bits = 3 bits
r: 1 occurrence  * 4 bits = 4 bits
s: 2 occurrences * 3 bits = 6 bits

Total Sum: 35 bits approx 5 bytes

Hence, we could see that after encoding the data we saved a large amount of data. The above method can also help us to determine the value of N i.e. the length of the encoded data. 

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