Data Structure - Heap

---

Overview

Heap represents a special tree based data structure used to represent priority queue or for heap sort. We'll going to discuss binary heap tree specifically.

Binary heap tree can be classified as a binary tree with two constraints:

• Completeness - Binary heap tree is a complete binary tree except the last level which may not have all elements but elements from left to right should be filled in.

• Heapness - All parent nodes should be greater or smaller to their children. If parent node is to be greater than its child then it is called Max heap otherwise it is called Min heap. Max heap is used for heap sort and Min heap is used for priority queue. We're considering Min Heap and will use array implementation for the same.

Basic Operations

Following are basic primary operations of a Min heap which are following.

• Insert - insert an element in a heap.

• Get Minimum - get minimum element from the heap.

• Remove Minimum - remove the minimum element from the heap

Insert Operation

• Whenever an element is to be inserted. Insert element at the end of the array. Increase the size of heap by 1.

• Heap up the element while heap property is broken. Compare element with parent's value and swap them if required.

void insert(int value) {            
   size++;
   intArray[size - 1] = value;
   heapUp(size - 1);
}

void heapUp(int nodeIndex){
   int parentIndex, tmp;
   if (nodeIndex != 0) {
      parentIndex = getParentIndex(nodeIndex);
      if (intArray[parentIndex] > intArray[nodeIndex]) {
         tmp = intArray[parentIndex];
         intArray[parentIndex] = intArray[nodeIndex];
         intArray[nodeIndex] = tmp;
         heapUp(parentIndex);
      }
   }
}

Get Minimum

Get the first element of the array implementing the heap being root.

int getMinimum(){
   return intArray[0];
}

Remove Minimum

• Whenever an element is to be removed. Get the last element of the array and reduce size of heap by 1.

• Heap down the element while heap property is broken. Compare element with children's value and swap them if required.

void removeMin() {
   intArray[0] = intArray[size - 1];
   size--;
   if (size > 0)
      heapDown(0);
}

void heapDown(int nodeIndex){
   int leftChildIndex, rightChildIndex, minIndex, tmp;
   leftChildIndex = getLeftChildIndex(nodeIndex);
   rightChildIndex = getRightChildIndex(nodeIndex);
   if (rightChildIndex >= size) {
      if (leftChildIndex >= size)
         return;
      else
         minIndex = leftChildIndex;
   } else {
      if (intArray[leftChildIndex] <= intArray[rightChildIndex])
         minIndex = leftChildIndex;
      else
         minIndex = rightChildIndex;
   }
   if (intArray[nodeIndex] > intArray[minIndex]) {
      tmp = intArray[minIndex];
      intArray[minIndex] = intArray[nodeIndex];
      intArray[nodeIndex] = tmp;
      heapDown(minIndex);
   }
}

Demo Program

HeapDemo.c

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdbool.h>

int intArray[10];
int size;

bool isEmpty(){
   return size == 0;
}

int getMinimum(){
   return intArray[0];
}

int getLeftChildIndex(int nodeIndex){
   return 2*nodeIndex +1;
}

int getRightChildIndex(int nodeIndex){
   return 2*nodeIndex +2;
}

int getParentIndex(int nodeIndex){
   return (nodeIndex -1)/2;
}

bool isFull(){
   return size == 10;
}

/**
* Heap up the new element,until heap property is broken. 
* Steps:
* 1. Compare node's value with parent's value. 
* 2. Swap them, If they are in wrong order.
* */
void heapUp(int nodeIndex){
   int parentIndex, tmp;
   if (nodeIndex != 0) {
      parentIndex = getParentIndex(nodeIndex);
      if (intArray[parentIndex] > intArray[nodeIndex]) {
         tmp = intArray[parentIndex];
         intArray[parentIndex] = intArray[nodeIndex];
         intArray[nodeIndex] = tmp;
         heapUp(parentIndex);
      }
   }
}

/**
* Heap down the root element being least in value,until heap property is broken. 
* Steps:
* 1.If current node has no children, done.  
* 2.If current node has one children and heap property is broken, 
* 3.Swap the current node and child node and heap down.
* 4.If current node has one children and heap property is broken, find smaller one  
* 5.Swap the current node and child node and heap down.
* */
void heapDown(int nodeIndex){
   int leftChildIndex, rightChildIndex, minIndex, tmp;
   leftChildIndex = getLeftChildIndex(nodeIndex);
   rightChildIndex = getRightChildIndex(nodeIndex);
   if (rightChildIndex >= size) {
      if (leftChildIndex >= size)
         return;
      else
         minIndex = leftChildIndex;
   } else {
      if (intArray[leftChildIndex] <= intArray[rightChildIndex])
         minIndex = leftChildIndex;
      else
         minIndex = rightChildIndex;
   }
   if (intArray[nodeIndex] > intArray[minIndex]) {
      tmp = intArray[minIndex];
      intArray[minIndex] = intArray[nodeIndex];
      intArray[nodeIndex] = tmp;
      heapDown(minIndex);
   }
}

void insert(int value) {            
   size++;
   intArray[size - 1] = value;
   heapUp(size - 1);
}

void removeMin() {
   intArray[0] = intArray[size - 1];
   size--;
   if (size > 0)
      heapDown(0);
}

void main() {
   /*                     5                //Level 0
   * 
   */
   insert(5);
   /*                     1                //Level 0
   *                     |
   *                 5---|                //Level 1
   */   
   insert(1);
   /*                     1                //Level 0
   *                     |
   *                 5---|---3            //Level 1
   */
   insert(3);
   /*                     1                //Level 0
   *                     |
   *                 5---|---3            //Level 1
   *                 |
   *              8--|                    //Level 2
   */
   insert(8);
   /*                     1                //Level 0
   *                     |
   *                 5---|---3            //Level 1
   *                 |
   *              8--|--9                 //Level 2
   */
   insert(9);
   /*                     1                 //Level 0
   *                     |
   *                 5---|---3             //Level 1
   *                 |       |
   *              8--|--9 6--|             //Level 2
   */
   insert(6);
   /*                     1                 //Level 0
   *                     |
   *                 5---|---2             //Level 1
   *                 |       |
   *              8--|--9 6--|--3          //Level 2
   */
   insert(2);

   printf("%d", getMinimum());

   removeMin();
   /*                     2                 //Level 0
   *                     |
   *                 5---|---3             //Level 1
   *                 |       |
   *              8--|--9 6--|             //Level 2
   */
   printf("\n%d", getMinimum());   
}

If we compile and run the above program then it would produce following result −

1
2