# 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& v, int N, int K) {     // Implement Max Heap using     // a Priority Queue     priority_queue 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 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 heap1 = new List();     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 at any time holds at max k elements.

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