C++ Program to Find kth Largest Element in a Sequence

In this program, we need to extract the Kth largest element from a sequence. the time complexity of this technique can be improved by approaching the problem using max-heap. The time complexity of this program is O(n + k*log(n)).

Algorithm

Begin
   Send the max of the heap to the end of the sequence.
   Heapify the remaining sequence.
   Repeat the process for ‘k’ times.
   Print the final state of the array.
   Print the max from the heap extracted from kth iteration as a result.
End.

Example Code

#include <iostream>
using namespace std;
void MaxHeapify(int a[], int i, int n) {
   int j, t;
   t = a[i];
   j = 2*i;
   while (j <= n) {
      if (j < n && a[j+1] > a[j])
      j = j+1;
      if (t > a[j])
      break;
      else if (t <= a[j]) {
         a[j/2] = a[j];
         j = 2*j;
      }
   }
   a[j/2] = t;
   return;
}
void Build_MaxHeapify(int a[], int n) {
   int i;
   for(i = n/2; i >= 1; i--)
   MaxHeapify(a, i, n);
}
int main() {
   int n, i, temp, k;
      cout<<"\nEnter the number of data element to be sorted: ";
      cin>>n;
      n++;
      int arr[n];
      for(i = 1; i < n; i++) {
         cout<<"Enter element "<<i<<": ";
         cin>>arr[i];
      }
     cout<<"\nEnter the k value: ";
     cin>>k;
     Build_MaxHeapify(arr, n-1);
     for(i = n-1; i >= n-k; i--) {
        temp = arr[i];
        arr[i] = arr[1];
        arr[1] = temp;
        MaxHeapify(arr, 1, i - 1);
    }
    cout<<"\nAfter max-heapify the given array "<<k<<" times the array state is: ";
    for(i = 1; i < n; i++)
      cout<<"->"<<arr[i];
    cout<<"\n\nThe "<<k<<"th largest element is: "<<arr[n-k];
    return 0;
}

Output

Enter the number of data element to be sorted: 5
Enter element 1: 20
Enter element 2: 10
Enter element 3: 30
Enter element 4: 70
Enter element 5: 60
Enter the k value: 2
After max-heapify the given array 2 times the array state is: ->30->20->10->60->70
The 2th largest element is: 60