Algorithme de compression de Huffman

0|011|0|100|011|0|11    adacdab
0|0|11|0|100|0|11|011   aabacabd
0|011|0|100|0|11|0|11   adacabab 

Codage Huffman

1. Créez un nœud feuille pour chaque personnage et ajoutez-les à la file d'attente prioritaire.
2. Pendant que vous êtes en ligne pour plusieurs feuilles, procédez comme suit:
   
   • Supprimez les deux nœuds avec la priorité la plus élevée (avec la fréquence la plus basse) de la file d'attente;
   • Créez un nouveau nœud interne où ces deux nœuds seront héritiers et la fréquence d'occurrence sera égale à la somme des fréquences de ces deux nœuds.
   • Ajoutez un nouveau nœud à la file d'attente prioritaire.
3. Le seul nœud restant sera la racine, ceci terminera la construction de l'arbre.

#include <iostream>
#include <string>
#include <queue>
#include <unordered_map>
using namespace std;

// A Tree node
struct Node
{
	char ch;
	int freq;
	Node *left, *right;
};

// Function to allocate a new tree node
Node* getNode(char ch, int freq, Node* left, Node* right)
{
	Node* node = new Node();

	node->ch = ch;
	node->freq = freq;
	node->left = left;
	node->right = right;

	return node;
}

// Comparison object to be used to order the heap
struct comp
{
	bool operator()(Node* l, Node* r)
	{
		// highest priority item has lowest frequency
		return l->freq > r->freq;
	}
};

// traverse the Huffman Tree and store Huffman Codes
// in a map.
void encode(Node* root, string str,
			unordered_map<char, string> &huffmanCode)
{
	if (root == nullptr)
		return;

	// found a leaf node
	if (!root->left && !root->right) {
		huffmanCode[root->ch] = str;
	}

	encode(root->left, str + "0", huffmanCode);
	encode(root->right, str + "1", huffmanCode);
}

// traverse the Huffman Tree and decode the encoded string
void decode(Node* root, int &index, string str)
{
	if (root == nullptr) {
		return;
	}

	// found a leaf node
	if (!root->left && !root->right)
	{
		cout << root->ch;
		return;
	}

	index++;

	if (str[index] =='0')
		decode(root->left, index, str);
	else
		decode(root->right, index, str);
}

// Builds Huffman Tree and decode given input text
void buildHuffmanTree(string text)
{
	// count frequency of appearance of each character
	// and store it in a map
	unordered_map<char, int> freq;
	for (char ch: text) {
		freq[ch]++;
	}

	// Create a priority queue to store live nodes of
	// Huffman tree;
	priority_queue<Node*, vector<Node*>, comp> pq;

	// Create a leaf node for each character and add it
	// to the priority queue.
	for (auto pair: freq) {
		pq.push(getNode(pair.first, pair.second, nullptr, nullptr));
	}

	// do till there is more than one node in the queue
	while (pq.size() != 1)
	{
		// Remove the two nodes of highest priority
		// (lowest frequency) from the queue
		Node *left = pq.top(); pq.pop();
		Node *right = pq.top();	pq.pop();

		// Create a new internal node with these two nodes
		// as children and with frequency equal to the sum
		// of the two nodes' frequencies. Add the new node
		// to the priority queue.
		int sum = left->freq + right->freq;
		pq.push(getNode('\0', sum, left, right));
	}

	// root stores pointer to root of Huffman Tree
	Node* root = pq.top();

	// traverse the Huffman Tree and store Huffman Codes
	// in a map. Also prints them
	unordered_map<char, string> huffmanCode;
	encode(root, "", huffmanCode);

	cout << "Huffman Codes are :\n" << '\n';
	for (auto pair: huffmanCode) {
		cout << pair.first << " " << pair.second << '\n';
	}

	cout << "\nOriginal string was :\n" << text << '\n';

	// print encoded string
	string str = "";
	for (char ch: text) {
		str += huffmanCode[ch];
	}

	cout << "\nEncoded string is :\n" << str << '\n';

	// traverse the Huffman Tree again and this time
	// decode the encoded string
	int index = -1;
	cout << "\nDecoded string is: \n";
	while (index < (int)str.size() - 2) {
		decode(root, index, str);
	}
}

// Huffman coding algorithm
int main()
{
	string text = "Huffman coding is a data compression algorithm.";

	buildHuffmanTree(text);

	return 0;
}

import java.util.HashMap;
import java.util.Map;
import java.util.PriorityQueue;

// A Tree node
class Node
{
	char ch;
	int freq;
	Node left = null, right = null;

	Node(char ch, int freq)
	{
		this.ch = ch;
		this.freq = freq;
	}

	public Node(char ch, int freq, Node left, Node right) {
		this.ch = ch;
		this.freq = freq;
		this.left = left;
		this.right = right;
	}
};

class Huffman
{
	// traverse the Huffman Tree and store Huffman Codes
	// in a map.
	public static void encode(Node root, String str,
							  Map<Character, String> huffmanCode)
	{
		if (root == null)
			return;

		// found a leaf node
		if (root.left == null && root.right == null) {
			huffmanCode.put(root.ch, str);
		}


		encode(root.left, str + "0", huffmanCode);
		encode(root.right, str + "1", huffmanCode);
	}

	// traverse the Huffman Tree and decode the encoded string
	public static int decode(Node root, int index, StringBuilder sb)
	{
		if (root == null)
			return index;

		// found a leaf node
		if (root.left == null && root.right == null)
		{
			System.out.print(root.ch);
			return index;
		}

		index++;

		if (sb.charAt(index) == '0')
			index = decode(root.left, index, sb);
		else
			index = decode(root.right, index, sb);

		return index;
	}

	// Builds Huffman Tree and huffmanCode and decode given input text
	public static void buildHuffmanTree(String text)
	{
		// count frequency of appearance of each character
		// and store it in a map
		Map<Character, Integer> freq = new HashMap<>();
		for (int i = 0 ; i < text.length(); i++) {
			if (!freq.containsKey(text.charAt(i))) {
				freq.put(text.charAt(i), 0);
			}
			freq.put(text.charAt(i), freq.get(text.charAt(i)) + 1);
		}

		// Create a priority queue to store live nodes of Huffman tree
		// Notice that highest priority item has lowest frequency
		PriorityQueue<Node> pq = new PriorityQueue<>(
										(l, r) -> l.freq - r.freq);

		// Create a leaf node for each character and add it
		// to the priority queue.
		for (Map.Entry<Character, Integer> entry : freq.entrySet()) {
			pq.add(new Node(entry.getKey(), entry.getValue()));
		}

		// do till there is more than one node in the queue
		while (pq.size() != 1)
		{
			// Remove the two nodes of highest priority
			// (lowest frequency) from the queue
			Node left = pq.poll();
			Node right = pq.poll();

			// Create a new internal node with these two nodes as children 
			// and with frequency equal to the sum of the two nodes
			// frequencies. Add the new node to the priority queue.
			int sum = left.freq + right.freq;
			pq.add(new Node('\0', sum, left, right));
		}

		// root stores pointer to root of Huffman Tree
		Node root = pq.peek();

		// traverse the Huffman tree and store the Huffman codes in a map
		Map<Character, String> huffmanCode = new HashMap<>();
		encode(root, "", huffmanCode);

		// print the Huffman codes
		System.out.println("Huffman Codes are :\n");
		for (Map.Entry<Character, String> entry : huffmanCode.entrySet()) {
			System.out.println(entry.getKey() + " " + entry.getValue());
		}

		System.out.println("\nOriginal string was :\n" + text);

		// print encoded string
		StringBuilder sb = new StringBuilder();
		for (int i = 0 ; i < text.length(); i++) {
			sb.append(huffmanCode.get(text.charAt(i)));
		}

		System.out.println("\nEncoded string is :\n" + sb);

		// traverse the Huffman Tree again and this time
		// decode the encoded string
		int index = -1;
		System.out.println("\nDecoded string is: \n");
		while (index < sb.length() - 2) {
			index = decode(root, index, sb);
		}
	}

	public static void main(String[] args)
	{
		String text = "Huffman coding is a data compression algorithm.";

		buildHuffmanTree(text);
	}
}

Sources: