Kth smallest element after every insertion

Given an infinite stream of integers, find the k’th largest element at any point of time. It may be assumed that 1 <= k <= n.

Input:
stream[] = {10, 20, 11, 70, 50, 40, 100, 5, ...}
k = 3
Output:    {_,   _, 10, 11, 20, 40, 50,  50, ...}

Extra space allowed is O(k).



The idea is to use min heap.
1) Store first k elements in min heap.
2) For every element from (k+1)-th to n-th, do following.
……a) Print root of heap.
……b) If current element is more than root of heap, pop root and insert

// CPP program to find k-th largest element in a 
// stream after every insertion.
#include <bits/stdc++.h>
using namespace std;

int kthLargest(int stream[], int n, int k)
{
   // Create a min heap and store first k-1 elements
   // of stream into 
   priority_queue<int, vector<int>, greater<int> > pq;

   // Push first k elements and print "_" (k-1) times
   for (int i=0; i<k-1; i++)
   {
      pq.push(stream[i]);
      cout << "_ ";
   }
   pq.push(stream[k-1]);

   for (int i=k; i<n; i++)
   {
       // We must insert last element before we
       // decide last k-th largest output.
       if (i < n-1)
          cout << pq.top() << " ";

       if (stream[i] > pq.top())
       {
           pq.pop();
           pq.push(stream[i]);
       }  
   }  

   // Print last k-th largest element (after
   // (inserting last element)
   cout << pq.top();
}

// Driver code
int main()
{
   int arr[] = {10, 20, 11, 70, 50, 40, 100, 55};
   int k = 3;
   int n = sizeof(arr)/sizeof(arr[0]);
   kthLargest(arr, n, k);
   return 0;
}
Output:

_ _ 10 11 20 40 55

If stream contains elements of non-primitive types, we may define our own compactor function and create a priority_queue accordingly.



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