Example of Huffman algorithm by using heap.

NOTIFICATION: These examples are provided for educational purposes. Using this code is under your own responsibility and risk. The code is given ‘as is’. I do not take responsibilities of how they are used.


 * Program: Huffman using heap
 * Author: Alejandro G. Carlstein

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>

#define MAX_CODE 1000000
#define MAX_LETTERS 4
#define MAX_HEAP 10
#define LEFT(i) ((i << 1) + 1)
#define RIGHT(i) ((i << 1) + 2)
#define PARENT(i) (((i + 1) >> 1) - 1)
#define DIV_BY_2(i) (i >> 1)
#define DBG_LV0 1
#define DBG_LV1 1
#define DBG_LV2 1
#define DBG_LV3 0
#define LETTER_A 65
#define DIR_LEFT '0'
#define DIR_RIGHT '1'

#define ROOT_INDEX 0

struct Data{
  int letter;
  int frequency;
  int left;
  int right;
  int parent;

struct Data data[MAX_LETTERS];
int heap[MAX_HEAP];

void readInputLetters(void);
void readInputCode(void);
void printCodes(int *codes, int numCodes);
void printStructArray(struct Data array[], int length);
int huffman(void);
void buildMinHeap(int array[], int heapSize);
void minHeapify(int array[], int index, int heapSize);
int heapMin(int array[]);
int heapExtractMin(int array[], int *length);
void insertMinHeap(int array[], int value, int *length);
void exchange(int *a, int *b);
void printArray(int array[], int length);
int isLeft(struct Data array[], int indexLeft, int indexRight);
void test1();
void test2();

int num_letters;
int numCodes = 0;

int main(int argc, char* argv[]){



	if (DBG_LV3) printStructArray(data, num_letters);

	int i;
	for (i = 0; i < num_letters; ++i)
		heap[i] = i;

  printf('ROOT(huffman): %d \n', huffman());

	if (DBG_LV1) printStructArray(data, num_letters);

  //decodeMessage(data, num_letters, &code[0][0], numCodes);

	if (DBG_LV2) printf('\n');

	return 0;


void readInputLetters(void){
	if (DBG_LV0) printf('\nreadInputLetters()\n');

  for (num_letters = 0; num_letters < MAX_LETTERS; ++num_letters){       
    scanf('%d', &data[num_letters].frequency);
    data[num_letters].letter = LETTER_A + num_letters;
    data[num_letters].left = -1;
    data[num_letters].right = -1;
		data[num_letters].parent = -1;

    heap[num_letters] = -1;


void readInputCode(void){
	if (DBG_LV0) printf('\nreadInputCode()\n');

	int c;
  int indexCode = 0;

  numCodes = 0;

  while ((c = getchar()) != EOF){

    if (c != ' ' && c != '\n'){
      if (DBG_LV3) printf('[%d][%d]%c{%d}\n', numCodes, indexCode, c, c);
      code[numCodes][indexCode] = (int)c;

    if (c == '\n'){
      code[numCodes][indexCode] = -1;
      if (DBG_LV3) printf('{{%d}}\n', code[numCodes][indexCode]);
      indexCode = 0;


	if (DBG_LV3){
	  printf('CODES: \n');
	  printCodes(&code[0][0], numCodes);



void printCodes(int *codes, int numCodes){
  if (DBG_LV2) printf('printCodes(numCodes: %d)\n', numCodes);

  int indexCode, index;
	int indexArray;

  for (indexCode = 0; indexCode < numCodes; ++indexCode){

		indexArray = indexCode * sizeof(int);

    for (index = 0; codes[indexArray + index] > -1 ; ++index){

      printf('[%d][%d]: %c(%d) \n', 
             indexArray, index, 
             codes[indexArray + index], codes[indexArray + index]);    





void printStructArray(struct Data array[], int length){
  if (DBG_LV0) printf('printStructArray()\n');

  int i;
  for (i = 0; i < length; ++i)
	  printf('[%d]%c - %d (L:%d, R:%d, P:%d) \n',
	         i, data[i].letter, data[i].frequency, data[i].left, data[i].right, data[i].parent);

int huffman(void){
	if (DBG_LV0) printf('\nHUFFMAN()\n');

	int length = num_letters;
	int i;
	int left;
	int right;
	int parent;
	int n = length;


	printf('length: %d\n\n', length);

	if (DBG_LV1) printArray(heap, num_letters);

	for (i = 0; i < n - 1; ++i){

		left = heapExtractMin(heap, &length);

		printf('length: %d\n\n', length);

		right = heapExtractMin(heap, &length);

		parent = left + right;

		data[left].parent = parent;
		data[right].parent = parent;

		printf('length: %d\n\n', length);

		if (DBG_LV2){
			printf('left: %d, ', left);				
			printf('right: %d, ', right);
			printf('parent: %d\n', parent);
			printArray(heap, length);		

		insertMinHeap(heap, parent, &length);

		printf('length: %d\n\n', length);


	if (DBG_LV1) printArray(heap, num_letters);

	return heapExtractMin(heap, &length);

void buildMinHeap(int array[], int heapSize){

	int index;

	for (index = DIV_BY_2(heapSize); index >= ROOT_INDEX; --index){

		minHeapify(array, index, heapSize);



void minHeapify(int array[], int index, int heapSize){

	int left, right, smallest;

	smallest = index;
	left = LEFT(index);
	right = RIGHT(index);	

	// Find smallest value
	if (left < heapSize && array[left] < array[index])
		smallest = left;	

	if (right < heapSize && array[right] < array[smallest]) 
		smallest = right;

	if (smallest != index){

		// Exchange 
		exchange(&array[index], &array[smallest]);

		// Rebuild heap region		
		minHeapify(array, smallest, heapSize);	



int heapMin(int array[]){
	return array[ROOT_INDEX];

int heapExtractMin(int array[], int *length){
	if (DBG_LV0) printf('heapExtractMin()\n');

	if (length < 0){
		printf('[X] Error: heap overflow!\n');
		return -1;


	int heapSize = *length;

	int min = array[ROOT_INDEX];


	printf('exchange: array[%d]: %d, array[%d]:%d \n',
				 heapSize, array[heapSize]);

	exchange(&array[ROOT_INDEX], &array[heapSize]);


	minHeapify(array, ROOT_INDEX, heapSize);

	return min;

void insertMinHeap(int array[], int value, int *length){

	if (DBG_LV0) printf('insertMinHeap(value: %d, length: %d)\n',
											value, *length);

	int heapSize = *length;


	array[heapSize] = INT_MAX;

	if (value > array[heapSize]){
		printf('[X] Error: new value is bigger than biggest element!\n');

		array[heapSize] = value;

		if (DBG_LV2) printArray(array, *length);

		while (heapSize > ROOT_INDEX && 
					 array[PARENT(heapSize)] > array[heapSize]){

			exchange(&array[heapSize], &array[PARENT(heapSize)]);

			heapSize = PARENT(heapSize);




void exchange(int *a, int *b){
		if (DBG_LV3) printf('exchange()\n');

		int temp;
		temp = *a;
		*a = *b;
		*b = temp;

void printArray(int array[], int length){
	if (DBG_LV0) printf('printArray()\n');

	int i;

	for (i = 0; i < length; ++i)
		printf('[%d]', i);


	for (i = 0; i < length; ++i)
		printf(' %d ', array[i]);

	if (DBG_LV1) printf('\n\n');

int isLeft(struct Data array[], int indexLeft, int indexRight){
	if (DBG_LV0) printf('isLeft()\n');

	if (array[indexLeft].frequency == array[indexRight].frequency){

		 	if (array[indexLeft].letter < array[indexRight].letter){
		 		return DIR_LEFT;
		 		return DIR_RIGHT;

	}else if (array[indexLeft].frequency < array[indexRight].frequency){
		return DIR_LEFT;	 	
		return DIR_RIGHT;


void test1(){
	if (DBG_LV1) printf('test1()\n');

	int i, length = 5;

	if(DBG_LV1)	printf('BUILD HEAP ARRAY:\n');
	for(i = 0; i < length; ++i){
		heap[i] = i * 2;
		printf('heap[%d]: %d \n', i, heap[i]);
	heap[4] = 1;

	buildMinHeap(heap, length);

	printArray(heap, length);

	insertMinHeap(heap, 3, &length);

	printArray(heap, length);

void test2(){

	int heapLen = num_letters;

	printf('heapLen: %d\n', heapLen);

	printArray(heap, heapLen);

	int result1, result2;

	result1 = heapExtractMin(heap, &heapLen);
  printf('result1: %d\n', result1);
	printArray(heap, heapLen);

	printf('heapLen: %d\n', heapLen);

	result2 = heapExtractMin(heap, &heapLen);
  printf('result2: %d\n', result2);
	printArray(heap, heapLen);

	printf('heapLen: %d\n', heapLen);



1 0 0 
1 0 1 
1 1 

If you encounter any problems or errors, please let me know by providing an example of the code, input, output, and an explanation. Thanks.

© 2010, Alejandro G. Carlstein Ramos Mejia. All rights reserved.


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