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# K-th Smallest Element in an Unsorted Array using Priority Queue

• Last Updated : 22 Jul, 2021

Given an array arr[] consisting of N integers and an integer K, the task is to find the Kth smallest element in the array using Priority Queue.

Examples:

Input: arr[] = {5, 20, 10, 7, 1}, N = 5, K = 2
Output: 5
Explanation: In the given array, the 2nd smallest element is 5. Therefore, the required output is 5.

Input: arr[] = {5, 20, 10, 7, 1}, N = 5, K = 5
Output: 20
Explanation: In the given array, the 5th smallest element is 20. Therefore, the required output is 20.

Approach: The idea is to use PriorityQueue Collection in Java or priority_queue STL library to implement Max_Heap to find the Kth smallest array element. Follow the steps below to solve the problem:

1. Implement Max Heap using a priority_queue.
2. Push first K array elements into the priority_queue.
3. From there on, after every insertion of an array element, pop the element at the top of the priority_queue.
4. After complete traversal of the array, print the element at the top of the priority queue as the required answer.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Function to find kth smallest array element``void` `kthSmallest(vector<``int``>& v, ``int` `N, ``int` `K)``{``    ``// Implement Max Heap using``    ``// a Priority Queue``    ``priority_queue<``int``> heap1;` `    ``for` `(``int` `i = 0; i < N; ++i) {` `        ``// Insert elements into``        ``// the priority queue``        ``heap1.push(v[i]);` `        ``// If size of the priority``        ``// queue exceeds k``        ``if` `(heap1.size() > K) {``            ``heap1.pop();``        ``}``    ``}` `    ``// Print the k-th smallest element``    ``cout << heap1.top() << endl;``}` `// Driver code``int` `main()``{``    ``// Given array``    ``vector<``int``> vec = { 5, 20, 10, 7, 1 };` `    ``// Size of array``    ``int` `N = vec.size();` `    ``// Given K``    ``int` `K = 2;` `    ``// Function Call``    ``kthSmallest(vec, N, K % N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;``class` `CustomComparator ``implements` `Comparator {` `    ``@Override``    ``public` `int` `compare(Integer number1, Integer number2) {``        ``int` `value =  number1.compareTo(number2);``      ` `        ``// elements are sorted in reverse order``        ``if` `(value > ``0``) {``            ``return` `-``1``;``        ``}``        ``else` `if` `(value < ``0``) {``            ``return` `1``;``        ``}``        ``else` `{``            ``return` `0``;``        ``}``    ``}``}``class` `GFG{` `// Function to find kth smallest array element``static` `void` `kthSmallest(``int` `[]v, ``int` `N, ``int` `K)``{``    ``// Implement Max Heap using``    ``// a Priority Queue``    ``PriorityQueue heap1 = ``new` `PriorityQueue(``new` `CustomComparator());` `    ``for` `(``int` `i = ``0``; i < N; ++i) {` `        ``// Insert elements into``        ``// the priority queue``        ``heap1.add(v[i]);` `        ``// If size of the priority``        ``// queue exceeds k``        ``if` `(heap1.size() > K) {``            ``heap1.remove();``        ``}``    ``}` `    ``// Print the k-th smallest element``    ``System.out.print(heap1.peek() +``"\n"``);``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``// Given array``    ``int` `[]vec = { ``5``, ``20``, ``10``, ``7``, ``1` `};` `    ``// Size of array``    ``int` `N = vec.length;` `    ``// Given K``    ``int` `K = ``2``;` `    ``// Function Call``    ``kthSmallest(vec, N, K % N);``}``}` `// This code is contributed by Amit Katiyar`

## Python3

 `# Python3 program for the above approach` `# Function to find kth smallest array element``def` `kthSmallest(v, N, K):``    ` `    ``# Implement Max Heap using``    ``# a Priority Queue``    ``heap1 ``=` `[]`` ` `    ``for` `i ``in` `range``(N):``        ` `        ``# Insert elements into``        ``# the priority queue``        ``heap1.append(v[i])`` ` `        ``# If size of the priority``        ``# queue exceeds k``        ``if` `(``len``(heap1) > K):``            ``heap1.sort()``            ``heap1.reverse()``            ``del` `heap1[``0``]`` ` `    ``# Print the k-th smallest element``    ``heap1.sort()``    ``heap1.reverse()``    ``print``(heap1[``0``])` `# Driver code` `# Given array``vec ``=` `[ ``5``, ``20``, ``10``, ``7``, ``1` `]` `# Size of array``N ``=` `len``(vec)` `# Given K``K ``=` `2` `# Function Call``kthSmallest(vec, N, K ``%` `N)` `# This code is contributed by divyeshrabadiya07`

## C#

 `// C# program for the above approach``using` `System;``using` `System.Collections.Generic;``class` `GFG``{` `// Function to find kth smallest array element``static` `void` `kthSmallest(``int` `[]v, ``int` `N, ``int` `K)``{``  ` `    ``// Implement Max Heap using``    ``// a Priority Queue``    ``List<``int``> heap1 = ``new` `List<``int``>();``    ``for` `(``int` `i = 0; i < N; ++i) {` `        ``// Insert elements into``        ``// the priority queue``        ``heap1.Add(v[i]);` `        ``// If size of the priority``        ``// queue exceeds k``        ``if` `(heap1.Count > K) {``            ``heap1.Sort();``            ``heap1.Reverse();``            ``heap1.RemoveAt(0);``        ``}``    ``}``    ``heap1.Sort();``            ``heap1.Reverse();` `    ``// Print the k-th smallest element``    ``Console.WriteLine(heap1[0]);``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``  ` `    ``// Given array``    ``int` `[]vec = { 5, 20, 10, 7, 1 };` `    ``// Size of array``    ``int` `N = vec.Length;` `    ``// Given K``    ``int` `K = 2;` `    ``// Function Call``    ``kthSmallest(vec, N, K % N);``}``}` `// This code is contributed by gauravrajput1`

## Javascript

 ``
Output:
`5`

Time Complexity: O(N LogK)
Auxiliary Space: O(K), since the priority queue ay any time holds at max k elements.

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