Question

Suppose that you are given an array of N elements. Develop an optimum algorithm that finds the minimum k elements of this array in at most nlogn time. Try your algorithm on an example N-sized array and some value of k.

Answer 1

Below is the implementation in C++.

CODE

#include <iostream>
#include <vector>
#include <queue>
using namespace std;

// Function to find the K'th smallest element in the
// array using max-heap
int findKthSmallest(vector<int> const &v, int k)
{
   // create an max-heap using std::priority_queue and
   // insert first k elements of the array into the heap
   priority_queue<int, vector<int>> pq(v.begin(), v.begin() + k);

   // do for remaining array elements
   for (int i = k; i < v.size(); i++)
   {
       // if current element is less than the root of the heap
       if (v[i] < pq.top())
       {
           // replace root with the current element
           pq.pop();
           pq.push(v[i]);
       }
   }

   // return the root of max-heap
   return pq.top();
}

// Find K'th smallest element in an array
int main()
{
   vector<int> vec = { 7, 4, 6, 3, 9, 1 };
   const size_t k = 3;

   cout << "K'th smallest element in the array is " <<
           findKthSmallest(vec, k);

   return 0;
}