Finding the $k^{th}$ smallest element of an array efficiently may seem a little tricky at first. However, it can be found easily using a [min-heap](https://www.educative.io/shoteditor/5170884784422912/preview) or [by sorting the array](https://www.educative.io/shoteditor/5300590148059136/preview).

# Algorithm

The following steps are involved in finding the $k^{th}$ smallest element using a min-heap.

1. Create a min-heap using the given array.

2. Remove the element at the root of the heap $k-1$ times.

3. The element on the root of the heap is the $k^{th}$ smallest element.

The illustration below further explains this concept.​

# Implementation

The following code snippet implements the above algorithm in C++.

#include <bits/stdc++.h> 
using namespace std; 
  
int main () 
{ 
  // Creating a min-heap. 
  priority_queue <int, vector<int>, greater<int> > minheap; 
  minheap.push(10); 
  minheap.push(1); 
  minheap.push(0); 
  minheap.push(8); 
  minheap.push(7); 
  minheap.push(2);
  // Removing the element at the root of the min-heap k-1 times.
  for(int i = 0; i < 2; i++){ 
      minheap.pop(); 
  } 
  // Displaying the element at the root of the min-heap.
  cout<<"The third smallest element in the given array is: "
  <<minheap.top() << endl; 
  return 0; 
} 

Find the kth smallest element from an array using a min-heap

Use a min-heap to find the kth smallest element by removing the root k-1 times.