[DATA STRUCTURE] HEAP

What is Binary Heap?
Let us first define a Complete Binary Tree. A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible (Source Wikipedia)

A Binary Heap is a Complete Binary Tree where items are stored in a special order such that value in a parent node is greater(or smaller) than the values in its two children nodes. The former is called as max heap and the latter is called min heap. The heap can be represented by binary tree or array.

Why array based representation for Binary Heap?
Since a Binary Heap is a Complete Binary Tree, it can be easily represented as array and array based representation is space efficient. If the parent node is stored at index I, the left child can be calculated by 2 * I + 1 and right child by 2 * I + 2 (assuming the indexing starts at 0).

public class HeapSort {

    void sort(int[] arr) {

        int n = arr.length;

        for (int i = n / 2 - 1; i >= 0; i--) {

            System.out.println(i);

            maxHeapify(arr, n, i);

        }

        // One by one extract an element from heap

        for (int i = n - 1; i > 0; i--) {

            // Move current root to end

            int temp = arr[0];

            arr[0] = arr[i];

            arr[i] = temp;

            // call max heapify on the reduced heap

            maxHeapify(arr, i, 0);

        }

    }

    private void maxHeapify(int[] arr, int n, int i) {

        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;

        }

        if (largest != i) {

            int swap = arr[i];

            arr[i] = arr[largest];

            arr[largest] = swap;

            maxHeapify(arr, n, largest);

        }

    }

    private void smallHeapify(int[] arr, int n, int i) {

        int smallest = i;

        int left = 2 * i + 1;

        int right = 2 * i + 2;

        if (left < n && arr[left] < arr[smallest]) {

            smallest = left;

        }

        if (right < n && arr[right] < arr[smallest]) {

            smallest = right;

        }

        if (smallest != i) {

            int swap = arr[i];

            arr[i] = arr[smallest];

            arr[smallest] = swap;

            smallHeapify(arr, n, smallest);

        }

    }

    static void printArray(int arr[]) {

        int n = arr.length;

        for (int i = 0; i < n; i++) {

            System.out.println(arr[i] + " ");

            System.out.println();

        }

    }

    public static void main(String[] args) {

        int arr[] = { 12, 11, 13, 5, 6, 7 };

        int n = arr.length;

        HeapSort h = new HeapSort();

        h.sort(arr);

        System.out.println("Sorted array is");

        printArray(arr);

    }

}

REFERENCE

https://www.geeksforgeeks.org/heap-sort/