huffman.cpp

// 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; 

	// Attay 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 capacity given
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 program to test above functions 
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; 
}