La codificación Huffman es un algoritmo de compresión de datos sin pérdidas. La idea es asignar códigos de longitud variable a los caracteres de entrada, las longitudes de los códigos asignados se basan en las frecuencias de los caracteres correspondientes. El carácter más frecuente obtiene el código más pequeño y el carácter menos frecuente obtiene el código más grande.
Los códigos de longitud variable asignados a los caracteres de entrada son códigos de prefijo , lo que significa que los códigos (secuencias de bits) se asignan de tal manera que el código asignado a un carácter no es el prefijo del código asignado a ningún otro carácter. Así es como Huffman Coding se asegura de que no haya ambigüedad al decodificar el flujo de bits generado.
Entendamos los códigos de prefijo con un contraejemplo. Sean cuatro caracteres a, b, c y d, y sus correspondientes códigos de longitud variable sean 00, 01, 0 y 1. Esta codificación genera ambigüedad porque el código asignado a c es el prefijo de los códigos asignados a ay b. Si el flujo de bits comprimido es 0001, la salida descomprimida puede ser «cccd» o «ccb» o «acd» o «ab».
Ver esto para aplicaciones de Huffman Coding.
Hay principalmente dos partes principales en Huffman Coding
- Cree un árbol de Huffman a partir de los caracteres de entrada.
- Atraviesa el árbol de Huffman y asigna códigos a los personajes.
Pasos para construir el árbol de Huffman
La entrada es una array de caracteres únicos junto con su frecuencia de aparición y la salida es el árbol de Huffman.
C
// C program for Huffman Coding
#include <stdio.h>
#include <stdlib.h>
// This constant can be avoided by explicitly
// calculating height of Huffman Tree
#define MAX_TREE_HT 100
// A Huffman tree node
struct MinHeapNode {
// One of the input characters
char data;
// Frequency of the character
unsigned freq;
// Left and right child of this node
struct MinHeapNode *left, *right;
};
// A Min Heap: Collection of
// min-heap (or Huffman tree) nodes
struct MinHeap {
// Current size of min heap
unsigned size;
// capacity of min heap
unsigned capacity;
// Array of minheap node pointers
struct MinHeapNode** array;
};
// A utility function allocate a new
// min heap node with given character
// and frequency of the character
struct MinHeapNode* newNode(char data, unsigned freq)
{
struct MinHeapNode* temp = (struct MinHeapNode*)malloc(
sizeof(struct MinHeapNode));
temp->left = temp->right = NULL;
temp->data = data;
temp->freq = freq;
return temp;
}
// A utility function to create
// a min heap of given capacity
struct MinHeap* createMinHeap(unsigned capacity)
{
struct MinHeap* minHeap
= (struct MinHeap*)malloc(sizeof(struct MinHeap));
// current size is 0
minHeap->size = 0;
minHeap->capacity = capacity;
minHeap->array = (struct MinHeapNode**)malloc(
minHeap->capacity * sizeof(struct MinHeapNode*));
return minHeap;
}
// A utility function to
// swap two min heap nodes
void swapMinHeapNode(struct MinHeapNode** a,
struct MinHeapNode** b)
{
struct MinHeapNode* t = *a;
*a = *b;
*b = t;
}
// The standard minHeapify function.
void minHeapify(struct MinHeap* minHeap, int idx)
{
int smallest = idx;
int left = 2 * idx + 1;
int right = 2 * idx + 2;
if (left < minHeap->size
&& minHeap->array[left]->freq
< minHeap->array[smallest]->freq)
smallest = left;
if (right < minHeap->size
&& minHeap->array[right]->freq
< minHeap->array[smallest]->freq)
smallest = right;
if (smallest != idx) {
swapMinHeapNode(&minHeap->array[smallest],
&minHeap->array[idx]);
minHeapify(minHeap, smallest);
}
}
// A utility function to check
// if size of heap is 1 or not
int isSizeOne(struct MinHeap* minHeap)
{
return (minHeap->size == 1);
}
// A standard function to extract
// minimum value node from heap
struct MinHeapNode* extractMin(struct MinHeap* minHeap)
{
struct MinHeapNode* temp = minHeap->array[0];
minHeap->array[0] = minHeap->array[minHeap->size - 1];
--minHeap->size;
minHeapify(minHeap, 0);
return temp;
}
// A utility function to insert
// a new node to Min Heap
void insertMinHeap(struct MinHeap* minHeap,
struct MinHeapNode* minHeapNode)
{
++minHeap->size;
int i = minHeap->size - 1;
while (i
&& minHeapNode->freq
< minHeap->array[(i - 1) / 2]->freq) {
minHeap->array[i] = minHeap->array[(i - 1) / 2];
i = (i - 1) / 2;
}
minHeap->array[i] = minHeapNode;
}
// A standard function to build min heap
void buildMinHeap(struct MinHeap* minHeap)
{
int n = minHeap->size - 1;
int i;
for (i = (n - 1) / 2; i >= 0; --i)
minHeapify(minHeap, i);
}
// A utility function to print an array of size n
void printArr(int arr[], int n)
{
int i;
for (i = 0; i < n; ++i)
printf("%d", arr[i]);
printf("\n");
}
// Utility function to check if this node is leaf
int isLeaf(struct MinHeapNode* root)
{
return !(root->left) && !(root->right);
}
// Creates a min heap of capacity
// equal to size and inserts all character of
// data[] in min heap. Initially size of
// min heap is equal to capacity
struct MinHeap* createAndBuildMinHeap(char data[],
int freq[], int size)
{
struct MinHeap* minHeap = createMinHeap(size);
for (int i = 0; i < size; ++i)
minHeap->array[i] = newNode(data[i], freq[i]);
minHeap->size = size;
buildMinHeap(minHeap);
return minHeap;
}
// The main function that builds Huffman tree
struct MinHeapNode* buildHuffmanTree(char data[],
int freq[], int size)
{
struct MinHeapNode *left, *right, *top;
// Step 1: Create a min heap of capacity
// equal to size. Initially, there are
// modes equal to size.
struct MinHeap* minHeap
= createAndBuildMinHeap(data, freq, size);
// Iterate while size of heap doesn't become 1
while (!isSizeOne(minHeap)) {
// Step 2: Extract the two minimum
// freq items from min heap
left = extractMin(minHeap);
right = extractMin(minHeap);
// Step 3: Create a new internal
// node with frequency equal to the
// sum of the two nodes frequencies.
// Make the two extracted node as
// left and right children of this new node.
// Add this node to the min heap
// '$' is a special value for internal nodes, not
// used
top = newNode('$', left->freq + right->freq);
top->left = left;
top->right = right;
insertMinHeap(minHeap, top);
}
// Step 4: The remaining node is the
// root node and the tree is complete.
return extractMin(minHeap);
}
// Prints huffman codes from the root of Huffman Tree.
// It uses arr[] to store codes
void printCodes(struct MinHeapNode* root, int arr[],
int top)
{
// Assign 0 to left edge and recur
if (root->left) {
arr[top] = 0;
printCodes(root->left, arr, top + 1);
}
// Assign 1 to right edge and recur
if (root->right) {
arr[top] = 1;
printCodes(root->right, arr, top + 1);
}
// If this is a leaf node, then
// it contains one of the input
// characters, print the character
// and its code from arr[]
if (isLeaf(root)) {
printf("%c: ", root->data);
printArr(arr, top);
}
}
// The main function that builds a
// Huffman Tree and print codes by traversing
// the built Huffman Tree
void HuffmanCodes(char data[], int freq[], int size)
{
// Construct Huffman Tree
struct MinHeapNode* root
= buildHuffmanTree(data, freq, size);
// Print Huffman codes using
// the Huffman tree built above
int arr[MAX_TREE_HT], top = 0;
printCodes(root, arr, top);
}
// Driver code
int main()
{
char arr[] = { 'a', 'b', 'c', 'd', 'e', 'f' };
int freq[] = { 5, 9, 12, 13, 16, 45 };
int size = sizeof(arr) / sizeof(arr[0]);
HuffmanCodes(arr, freq, size);
return 0;
}
C++
// C++ program for Huffman Coding
#include <iostream>
#include <cstdlib>
using namespace std;
// This constant can be avoided by explicitly
// calculating height of Huffman Tree
#define MAX_TREE_HT 100
// A Huffman tree node
struct MinHeapNode {
// One of the input characters
char data;
// Frequency of the character
unsigned freq;
// Left and right child of this node
struct MinHeapNode *left, *right;
};
// A Min Heap: Collection of
// min-heap (or Huffman tree) nodes
struct MinHeap {
// Current size of min heap
unsigned size;
// capacity of min heap
unsigned capacity;
// Array of minheap node pointers
struct MinHeapNode** array;
};
// A utility function allocate a new
// min heap node with given character
// and frequency of the character
struct MinHeapNode* newNode(char data, unsigned freq)
{
struct MinHeapNode* temp
= (struct MinHeapNode*)malloc
(sizeof(struct MinHeapNode));
temp->left = temp->right = NULL;
temp->data = data;
temp->freq = freq;
return temp;
}
// A utility function to create
// a min heap of given capacity
struct MinHeap* createMinHeap(unsigned capacity)
{
struct MinHeap* minHeap
= (struct MinHeap*)malloc(sizeof(struct MinHeap));
// current size is 0
minHeap->size = 0;
minHeap->capacity = capacity;
minHeap->array
= (struct MinHeapNode**)malloc(minHeap->
capacity * sizeof(struct MinHeapNode*));
return minHeap;
}
// A utility function to
// swap two min heap nodes
void swapMinHeapNode(struct MinHeapNode** a,
struct MinHeapNode** b)
{
struct MinHeapNode* t = *a;
*a = *b;
*b = t;
}
// The standard minHeapify function.
void minHeapify(struct MinHeap* minHeap, int idx)
{
int smallest = idx;
int left = 2 * idx + 1;
int right = 2 * idx + 2;
if (left < minHeap->size && minHeap->array[left]->
freq < minHeap->array[smallest]->freq)
smallest = left;
if (right < minHeap->size && minHeap->array[right]->
freq < minHeap->array[smallest]->freq)
smallest = right;
if (smallest != idx) {
swapMinHeapNode(&minHeap->array[smallest],
&minHeap->array[idx]);
minHeapify(minHeap, smallest);
}
}
// A utility function to check
// if size of heap is 1 or not
int isSizeOne(struct MinHeap* minHeap)
{
return (minHeap->size == 1);
}
// A standard function to extract
// minimum value node from heap
struct MinHeapNode* extractMin(struct MinHeap* minHeap)
{
struct MinHeapNode* temp = minHeap->array[0];
minHeap->array[0]
= minHeap->array[minHeap->size - 1];
--minHeap->size;
minHeapify(minHeap, 0);
return temp;
}
// A utility function to insert
// a new node to Min Heap
void insertMinHeap(struct MinHeap* minHeap,
struct MinHeapNode* minHeapNode)
{
++minHeap->size;
int i = minHeap->size - 1;
while (i && minHeapNode->freq < minHeap->array[(i - 1) / 2]->freq) {
minHeap->array[i] = minHeap->array[(i - 1) / 2];
i = (i - 1) / 2;
}
minHeap->array[i] = minHeapNode;
}
// A standard function to build min heap
void buildMinHeap(struct MinHeap* minHeap)
{
int n = minHeap->size - 1;
int i;
for (i = (n - 1) / 2; i >= 0; --i)
minHeapify(minHeap, i);
}
// A utility function to print an array of size n
void printArr(int arr[], int n)
{
int i;
for (i = 0; i < n; ++i)
cout<< arr[i];
cout<<"\n";
}
// Utility function to check if this node is leaf
int isLeaf(struct MinHeapNode* root)
{
return !(root->left) && !(root->right);
}
// Creates a min heap of capacity
// equal to size and inserts all character of
// data[] in min heap. Initially size of
// min heap is equal to capacity
struct MinHeap* createAndBuildMinHeap(char data[], int freq[], int size)
{
struct MinHeap* minHeap = createMinHeap(size);
for (int i = 0; i < size; ++i)
minHeap->array[i] = newNode(data[i], freq[i]);
minHeap->size = size;
buildMinHeap(minHeap);
return minHeap;
}
// The main function that builds Huffman tree
struct MinHeapNode* buildHuffmanTree(char data[], int freq[], int size)
{
struct MinHeapNode *left, *right, *top;
// Step 1: Create a min heap of capacity
// equal to size. Initially, there are
// modes equal to size.
struct MinHeap* minHeap = createAndBuildMinHeap(data, freq, size);
// Iterate while size of heap doesn't become 1
while (!isSizeOne(minHeap)) {
// Step 2: Extract the two minimum
// freq items from min heap
left = extractMin(minHeap);
right = extractMin(minHeap);
// Step 3: Create a new internal
// node with frequency equal to the
// sum of the two nodes frequencies.
// Make the two extracted node as
// left and right children of this new node.
// Add this node to the min heap
// '$' is a special value for internal nodes, not used
top = newNode('$', left->freq + right->freq);
top->left = left;
top->right = right;
insertMinHeap(minHeap, top);
}
// Step 4: The remaining node is the
// root node and the tree is complete.
return extractMin(minHeap);
}
// Prints huffman codes from the root of Huffman Tree.
// It uses arr[] to store codes
void printCodes(struct MinHeapNode* root, int arr[], int top)
{
// Assign 0 to left edge and recur
if (root->left) {
arr[top] = 0;
printCodes(root->left, arr, top + 1);
}
// Assign 1 to right edge and recur
if (root->right) {
arr[top] = 1;
printCodes(root->right, arr, top + 1);
}
// If this is a leaf node, then
// it contains one of the input
// characters, print the character
// and its code from arr[]
if (isLeaf(root)) {
cout<< root->data <<": ";
printArr(arr, top);
}
}
// The main function that builds a
// Huffman Tree and print codes by traversing
// the built Huffman Tree
void HuffmanCodes(char data[], int freq[], int size)
{
// Construct Huffman Tree
struct MinHeapNode* root
= buildHuffmanTree(data, freq, size);
// Print Huffman codes using
// the Huffman tree built above
int arr[MAX_TREE_HT], top = 0;
printCodes(root, arr, top);
}
// Driver code
int main()
{
char arr[] = { 'a', 'b', 'c', 'd', 'e', 'f' };
int freq[] = { 5, 9, 12, 13, 16, 45 };
int size = sizeof(arr) / sizeof(arr[0]);
HuffmanCodes(arr, freq, size);
return 0;
}
C++
// C++(STL) program for Huffman Coding with STL
#include <bits/stdc++.h>
using namespace std;
// A Huffman tree node
struct MinHeapNode {
// One of the input characters
char data;
// Frequency of the character
unsigned freq;
// Left and right child
MinHeapNode *left, *right;
MinHeapNode(char data, unsigned freq)
{
left = right = NULL;
this->data = data;
this->freq = freq;
}
};
// For comparison of
// two heap nodes (needed in min heap)
struct compare {
bool operator()(MinHeapNode* l, MinHeapNode* r)
{
return (l->freq > r->freq);
}
};
// Prints huffman codes from
// the root of Huffman Tree.
void printCodes(struct MinHeapNode* root, string str)
{
if (!root)
return;
if (root->data != '$')
cout << root->data << ": " << str << "\n";
printCodes(root->left, str + "0");
printCodes(root->right, str + "1");
}
// The main function that builds a Huffman Tree and
// print codes by traversing the built Huffman Tree
void HuffmanCodes(char data[], int freq[], int size)
{
struct MinHeapNode *left, *right, *top;
// Create a min heap & inserts all characters of data[]
priority_queue<MinHeapNode*, vector<MinHeapNode*>, compare> minHeap;
for (int i = 0; i < size; ++i)
minHeap.push(new MinHeapNode(data[i], freq[i]));
// Iterate while size of heap doesn't become 1
while (minHeap.size() != 1) {
// Extract the two minimum
// freq items from min heap
left = minHeap.top();
minHeap.pop();
right = minHeap.top();
minHeap.pop();
// Create a new internal node with
// frequency equal to the sum of the
// two nodes frequencies. Make the
// two extracted node as left and right children
// of this new node. Add this node
// to the min heap '$' is a special value
// for internal nodes, not used
top = new MinHeapNode('$', left->freq + right->freq);
top->left = left;
top->right = right;
minHeap.push(top);
}
// Print Huffman codes using
// the Huffman tree built above
printCodes(minHeap.top(), "");
}
// Driver Code
int main()
{
char arr[] = { 'a', 'b', 'c', 'd', 'e', 'f' };
int freq[] = { 5, 9, 12, 13, 16, 45 };
int size = sizeof(arr) / sizeof(arr[0]);
HuffmanCodes(arr, freq, size);
return 0;
}
// This code is contributed by Aditya Goel
Java
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Comparator;
// node class is the basic structure
// of each node present in the Huffman - tree.
class HuffmanNode {
int data;
char c;
HuffmanNode left;
HuffmanNode right;
}
// comparator class helps to compare the node
// on the basis of one of its attribute.
// Here we will be compared
// on the basis of data values of the nodes.
class MyComparator implements Comparator<HuffmanNode> {
public int compare(HuffmanNode x, HuffmanNode y)
{
return x.data - y.data;
}
}
public class Huffman {
// recursive function to print the
// huffman-code through the tree traversal.
// Here s is the huffman - code generated.
public static void printCode(HuffmanNode root, String s)
{
// base case; if the left and right are null
// then its a leaf node and we print
// the code s generated by traversing the tree.
if (root.left
== null
&& root.right
== null
&& Character.isLetter(root.c)) {
// c is the character in the node
System.out.println(root.c + ":" + s);
return;
}
// if we go to left then add "0" to the code.
// if we go to the right add"1" to the code.
// recursive calls for left and
// right sub-tree of the generated tree.
printCode(root.left, s + "0");
printCode(root.right, s + "1");
}
// main function
public static void main(String[] args)
{
Scanner s = new Scanner(System.in);
// number of characters.
int n = 6;
char[] charArray = { 'a', 'b', 'c', 'd', 'e', 'f' };
int[] charfreq = { 5, 9, 12, 13, 16, 45 };
// creating a priority queue q.
// makes a min-priority queue(min-heap).
PriorityQueue<HuffmanNode> q
= new PriorityQueue<HuffmanNode>(n, new MyComparator());
for (int i = 0; i < n; i++) {
// creating a Huffman node object
// and add it to the priority queue.
HuffmanNode hn = new HuffmanNode();
hn.c = charArray[i];
hn.data = charfreq[i];
hn.left = null;
hn.right = null;
// add functions adds
// the huffman node to the queue.
q.add(hn);
}
// create a root node
HuffmanNode root = null;
// Here we will extract the two minimum value
// from the heap each time until
// its size reduces to 1, extract until
// all the nodes are extracted.
while (q.size() > 1) {
// first min extract.
HuffmanNode x = q.peek();
q.poll();
// second min extract.
HuffmanNode y = q.peek();
q.poll();
// new node f which is equal
HuffmanNode f = new HuffmanNode();
// to the sum of the frequency of the two nodes
// assigning values to the f node.
f.data = x.data + y.data;
f.c = '-';
// first extracted node as left child.
f.left = x;
// second extracted node as the right child.
f.right = y;
// marking the f node as the root node.
root = f;
// add this node to the priority-queue.
q.add(f);
}
// print the codes by traversing the tree
printCode(root, "");
}
}
// This code is contributed by Kunwar Desh Deepak Singh
Python3
# A Huffman Tree Node
class node:
def __init__(self, freq, symbol, left=None, right=None):
# frequency of symbol
self.freq = freq
# symbol name (character)
self.symbol = symbol
# node left of current node
self.left = left
# node right of current node
self.right = right
# tree direction (0/1)
self.huff = ''
# utility function to print huffman
# codes for all symbols in the newly
# created Huffman tree
def printNodes(node, val=''):
# huffman code for current node
newVal = val + str(node.huff)
# if node is not an edge node
# then traverse inside it
if(node.left):
printNodes(node.left, newVal)
if(node.right):
printNodes(node.right, newVal)
# if node is edge node then
# display its huffman code
if(not node.left and not node.right):
print(f"{node.symbol} -> {newVal}")
# characters for huffman tree
chars = ['a', 'b', 'c', 'd', 'e', 'f']
# frequency of characters
freq = [ 5, 9, 12, 13, 16, 45]
# list containing unused nodes
nodes = []
# converting characters and frequencies
# into huffman tree nodes
for x in range(len(chars)):
nodes.append(node(freq[x], chars[x]))
while len(nodes) > 1:
# sort all the nodes in ascending order
# based on their frequency
nodes = sorted(nodes, key=lambda x: x.freq)
# pick 2 smallest nodes
left = nodes[0]
right = nodes[1]
# assign directional value to these nodes
left.huff = 0
right.huff = 1
# combine the 2 smallest nodes to create
# new node as their parent
newNode = node(left.freq+right.freq, left.symbol+right.symbol, left, right)
# remove the 2 nodes and add their
# parent as new node among others
nodes.remove(left)
nodes.remove(right)
nodes.append(newNode)
# Huffman Tree is ready!
printNodes(nodes[0])
Javascript
<script>
// node class is the basic structure
// of each node present in the Huffman - tree.
class HuffmanNode
{
constructor()
{
this.data = 0;
this.c = '';
this.left = this.right = null;
}
}
// recursive function to print the
// huffman-code through the tree traversal.
// Here s is the huffman - code generated.
function printCode(root,s)
{
// base case; if the left and right are null
// then its a leaf node and we print
// the code s generated by traversing the tree.
if (root.left == null
&& root.right == null
&& (root.c).toLowerCase() != (root.c).toUpperCase()) {
// c is the character in the node
document.write(root.c + ":" + s+"<br>");
return;
}
// if we go to left then add "0" to the code.
// if we go to the right add"1" to the code.
// recursive calls for left and
// right sub-tree of the generated tree.
printCode(root.left, s + "0");
printCode(root.right, s + "1");
}
// main function
// number of characters.
let n = 6;
let charArray = [ 'a', 'b', 'c', 'd', 'e', 'f' ];
let charfreq = [ 5, 9, 12, 13, 16, 45 ];
// creating a priority queue q.
// makes a min-priority queue(min-heap).
let q = [];
for (let i = 0; i < n; i++) {
// creating a Huffman node object
// and add it to the priority queue.
let hn = new HuffmanNode();
hn.c = charArray[i];
hn.data = charfreq[i];
hn.left = null;
hn.right = null;
// add functions adds
// the huffman node to the queue.
q.push(hn);
}
// create a root node
let root = null;
q.sort(function(a,b){return a.data-b.data;});
// Here we will extract the two minimum value
// from the heap each time until
// its size reduces to 1, extract until
// all the nodes are extracted.
while (q.length > 1) {
// first min extract.
let x = q[0];
q.shift();
// second min extract.
let y = q[0];
q.shift();
// new node f which is equal
let f = new HuffmanNode();
// to the sum of the frequency of the two nodes
// assigning values to the f node.
f.data = x.data + y.data;
f.c = '-';
// first extracted node as left child.
f.left = x;
// second extracted node as the right child.
f.right = y;
// marking the f node as the root node.
root = f;
// add this node to the priority-queue.
q.push(f);
q.sort(function(a,b){return a.data-b.data;});
}
// print the codes by traversing the tree
printCode(root, "");
// This code is contributed by avanitrachhadiya2155
</script>
Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA