Example 1: Heap sort in c++
#include <iostream>
using namespace std;
void heapify(int arr[], int n, int i)
{
int largest = i;
int l = 2 * i + 1;
int r = 2 * i + 2;
if (l < n && arr[l] > arr[largest])
largest = l;
if (r < n && arr[r] > arr[largest])
largest = r;
if (largest != i) {
swap(arr[i], arr[largest]);
heapify(arr, n, largest);
}
}
void heapSort(int arr[], int n)
{
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
for (int i = n - 1; i > 0; i--) {
swap(arr[0], arr[i]);
heapify(arr, i, 0);
}
}
void printArray(int arr[], int n)
{
for (int i = 0; i < n; ++i)
cout << arr[i] << " ";
cout << "\n";
}
int main()
{
int arr[] = { 12, 11, 13, 5, 6, 7 };
int n = sizeof(arr) / sizeof(arr[0]);
heapSort(arr, n);
cout << "Sorted array is \n";
printArray(arr, n);
}
Example 2: heap in java
In Java PriorityQueue can be used as a Heap.
Min Heap
PriorityQueue<Integer> minHeap = new PriorityQueue<>();
Max Heap:
PriorityQueue<Integer> maxHeap = new PriorityQueue<>(Comparator.reverseOrder());
Example 3: heaps in java
public class BinaryHeap {
private static final int d= 2;
private int[] heap;
private int heapSize;
/**
* This will initialize our heap with default size.
*/
public BinaryHeap(int capacity){
heapSize = 0;
heap = new int[ capacity+1];
Arrays.fill(heap, -1);
}
/**
* This will check if the heap is empty or not
* Complexity: O(1)
*/
public boolean isEmpty(){
return heapSize==0;
}
/**
* This will check if the heap is full or not
* Complexity: O(1)
*/
public boolean isFull(){
return heapSize == heap.length;
}
private int parent(int i){
return (i-1)/d;
}
private int kthChild(int i,int k){
return d*i +k;
}
/**
* This will insert new element in to heap
* Complexity: O(log N)
* As worst case scenario, we need to traverse till the root
*/
public void insert(int x){
if(isFull())
throw new NoSuchElementException("Heap is full, No space to insert new element");
heap[heapSize++] = x;
heapifyUp(heapSize-1);
}
/**
* This will delete element at index x
* Complexity: O(log N)
*
*/
public int delete(int x){
if(isEmpty())
throw new NoSuchElementException("Heap is empty, No element to delete");
int key = heap[x];
heap[x] = heap[heapSize -1];
heapSize--;
heapifyDown(x);
return key;
}
/**
* This method used to maintain the heap property while inserting an element.
*
*/
private void heapifyUp(int i) {
int temp = heap[i];
while(i>0 && temp > heap[parent(i)]){
heap[i] = heap[parent(i)];
i = parent(i);
}
heap[i] = temp;
}
/**
* This method used to maintain the heap property while deleting an element.
*
*/
private void heapifyDown(int i){
int child;
int temp = heap[i];
while(kthChild(i, 1) < heapSize){
child = maxChild(i);
if(temp < heap[child]){ heap[i] = heap[child]; }else break; i = child; } heap[i] = temp; } private int maxChild(int i) { int leftChild = kthChild(i, 1); int rightChild = kthChild(i, 2); return heap[leftChild]>heap[rightChild]?leftChild:rightChild;
}
/**
* This method used to print all element of the heap
*
*/
public void printHeap()
{
System.out.print("nHeap = ");
for (int i = 0; i < heapSize; i++)
System.out.print(heap[i] +" ");
System.out.println();
}
/**
* This method returns the max element of the heap.
* complexity: O(1)
*/
public int findMax(){
if(isEmpty())
throw new NoSuchElementException("Heap is empty.");
return heap[0];
}
public static void main(String[] args){
BinaryHeap maxHeap = new BinaryHeap(10);
maxHeap.insert(10);
maxHeap.insert(4);
maxHeap.insert(9);
maxHeap.insert(1);
maxHeap.insert(7);
maxHeap.insert(5);
maxHeap.insert(3);
maxHeap.printHeap();
maxHeap.delete(5);
maxHeap.printHeap();
}
}
Example 4: heap sort
// Heap Sort in C
#include <stdio.h>
// Function to swap the the position of two elements
void swap(int *a, int *b) {
int temp = *a;
*a = *b;
*b = temp;
}
void heapify(int arr[], int n, int i) {
// Find largest among root, left child and right child
int largest = i;
int left = 2 * i + 1;
int right = 2 * i + 2;
if (left < n && arr[left] > arr[largest])
largest = left;
if (right < n && arr[right] > arr[largest])
largest = right;
// Swap and continue heapifying if root is not largest
if (largest != i) {
swap(&arr[i], &arr[largest]);
heapify(arr, n, largest);
}
}
// Main function to do heap sort
void heapSort(int arr[], int n) {
// Build max heap
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
// Heap sort
for (int i = n - 1; i >= 0; i--) {
swap(&arr[0], &arr[i]);
// Heapify root element to get highest element at root again
heapify(arr, i, 0);
}
}
// Print an array
void printArray(int arr[], int n) {
for (int i = 0; i < n; ++i)
printf("%d ", arr[i]);
printf("\n");
}
// Driver code
int main() {
int arr[] = {1, 12, 9, 5, 6, 10};
int n = sizeof(arr) / sizeof(arr[0]);
heapSort(arr, n);
printf("Sorted array is \n");
printArray(arr, n);
}
Example 5: heap sort
// @see https://www.youtube.com/watch?v=H5kAcmGOn4Q
function heapify(list, size, index) {
let largest = index;
let left = index * 2 + 1;
let right = left + 1;
if (left < size && list[left] > list[largest]) {
largest = left;
}
if (right < size && list[right] > list[largest]) {
largest = right;
}
if (largest !== index) {
[list[index], list[largest]] = [list[largest], list[index]];
heapify(list, size, largest);
}
return list;
}
function heapsort(list) {
const size = list.length;
let index = ~~(size / 2 - 1);
let last = size - 1;
while (index >= 0) {
heapify(list, size, --index);
}
while (last >= 0) {
[list[0], list[last]] = [list[last], list[0]];
heapify(list, --last, 0);
}
return list;
}
heapsort([4, 7, 2, 6, 4, 1, 8, 3]);
Example 6: heap sort heapify and max heap in binary tree
Implementation of heap sort in C:
#include <stdio.h>
int main()
{
int heap[10], array_size, i, j, c, root, temporary;
printf("\n Enter size of array to be sorted :");
scanf("%d", &array_size);
printf("\n Enter the elements of array : ");
for (i = 0; i < array_size; i++)
scanf("%d", &heap[i]);
for (i = 1; i < array_size; i++)
{
c = i;
do
{
root = (c - 1) / 2;
if (heap[root] < heap[c]) /* to create MAX heap array */
{ // if child is greater than parent swap them
temporary = heap[root]; // as structure is of complete binary tree
heap[root] = heap[c]; // it took logn steps to reach from root to leaf
heap[c] = temporary;
}
c = root;
} while (c != 0);
}
printf("Heap array : ");
for (i = 0; i < array_size; i++)
printf("%d\t ", heap[i]); //printing the heap array
for (j = array_size - 1; j >= 0; j--)
{
temporary = heap[0];
heap[0] = heap[j] ; /* swap max element with rightmost leaf element */
heap[j] = temporary;
root = 0;
do
{
c = 2 * root + 1; /* left node of root element */
if ((heap[c] < heap[c + 1]) && c < j-1)
c++;
if (heap[root]<heap[c] && c<j) /* again rearrange to max heap array */
{
temporary = heap[root];
heap[root] = heap[c];
heap[c] = temporary;
}
root = c;
} while (c < j);
}
printf("\n The sorted array is : ");
for (i = 0; i < array_size; i++)
printf("\t %d", heap[i]);
}