8.HeapSort.cpp

#include <iostream>
#include <algorithm>
#include <string>
#include <cmath>
#include <iomanip>
#include <limits>
#include <vector>
#include <set>
#include <map>
using namespace std;
typedef unsigned long long ull;

void heapify(int arr[], int n, int i) //  O(lgn)
{
    int largest = i;  // Initialize largest as root
    int l = 2*i + 1;  // left = 2*i + 1
    int r = 2*i + 2;  // right = 2*i + 2

    // If left child is larger than root
    if (l < n && arr[l] > arr[largest])
        largest = l;

    // If right child is larger than largest so far
    if (r < n && arr[r] > arr[largest])
        largest = r;

    // If largest is not root
    if (largest != i)
    {
        swap(arr[i], arr[largest]);

        // Recursively heapify the affected sub-tree
        heapify(arr, n, largest);
    }
}

void heap_sort(int arr[], int n) // O(nlgn) tighter bound
{
    // Build heap (rearrange array)
    for (int i = n / 2 - 1; i >= 0; i--)
        heapify(arr, n, i);

    // One by one extract an element from heap
    for (int i=n-1; i>=0; i--)
    {
        // Move current root to end
        swap(arr[0], arr[i]);

        // call max heapify on the reduced heap
        heapify(arr, i, 0);
    }
}

int main()
{

    int a[] = {10, 7, 8, 9, 1, 5, 96, 12, 6, 13};

    heap_sort(a,10); //sorting
    for(int i=0;i<10; i++)
        cout << a[i] << " ";
}