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

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+1));`   `    ``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);` `}`   `// 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 at any time holds at max k elements.

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