K’th Smallest/Largest Element in Unsorted Array

Given an array and a number K where K is smaller than the size of the array. Find the K’th smallest element in the given array. Given that all array elements are distinct.

Examples: 

Input: arr[] = {7, 10, 4, 3, 20, 15}, K = 3 
Output: 7

Input: arr[] = {7, 10, 4, 3, 20, 15}, K = 4 
Output: 10 

We have discussed a similar problem to print k largest elements. 

K’th smallest element in an unsorted array using sorting:

Sort the given array and return the element at index K-1 in the sorted array. 

Follow the given steps to solve the problem:

• Sort the input array in the increasing order
• Return the element at the K-1 index (0 – Based indexing) in the sorted array

Below is the Implementation of the above approach:

C

// C program to find K'th smallest element
#include <stdio.h>
#include <stdlib.h>

// Compare function for qsort
int cmpfunc(const void* a, const void* b)
{
    return (*(int*)a - *(int*)b);
}

// Function to return K'th smallest
// element in a given array
int kthSmallest(int arr[], int N, int K)
{
    // Sort the given array
    qsort(arr, N, sizeof(int), cmpfunc);

    // Return k'th element in the sorted array
    return arr[K - 1];
}

// Driver's code
int main()
{
    int arr[] = { 12, 3, 5, 7, 19 };
    int N = sizeof(arr) / sizeof(arr[0]), K = 2;

    // Function call
    printf("K'th smallest element is %d",
           kthSmallest(arr, N, K));
    return 0;
}

// This code is contributed by Sania Kumari Gupta
// (kriSania804)

C++

// C++ program to find K'th smallest element
#include <bits/stdc++.h>
using namespace std;

// Function to return K'th smallest element in a given array
int kthSmallest(int arr[], int N, int K)
{
    // Sort the given array
    sort(arr, arr + N);

    // Return k'th element in the sorted array
    return arr[K - 1];
}

// Driver's code
int main()
{
    int arr[] = { 12, 3, 5, 7, 19 };
    int N = sizeof(arr) / sizeof(arr[0]), K = 2;

    // Function call
    cout << "K'th smallest element is "
         << kthSmallest(arr, N, K);
    return 0;
}

// This code is contributed by Sania Kumari Gupta
// (kriSania804)

Java

// Java code for Kth smallest element
// in an array
import java.util.Arrays;
import java.util.Collections;

class GFG {
    // Function to return K'th smallest
    // element in a given array
    public static int kthSmallest(Integer[] arr, int K)
    {
        // Sort the given array
        Arrays.sort(arr);

        // Return K'th element in
        // the sorted array
        return arr[K - 1];
    }

    // driver's code
    public static void main(String[] args)
    {
        Integer arr[] = new Integer[] { 12, 3, 5, 7, 19 };
        int K = 2;

        // Function call
        System.out.print("K'th smallest element is "
                         + kthSmallest(arr, K));
    }
}

// This code is contributed by Chhavi

Python3

# Python3 program to find K'th smallest
# element

# Function to return K'th smallest
# element in a given array


def kthSmallest(arr, N, K):

    # Sort the given array
    arr.sort()

    # Return k'th element in the
    # sorted array
    return arr[K-1]


# Driver code
if __name__ == '__main__':
    arr = [12, 3, 5, 7, 19]
    N = len(arr)
    K = 2

    # Function call
    print("K'th smallest element is",
          kthSmallest(arr, N, K))

# This code is contributed by
# Shrikant13

C#

// C# code for Kth smallest element
// in an array
using System;

class GFG {

    // Function to return K'th smallest
    // element in a given array
    public static int kthSmallest(int[] arr, int K)
    {

        // Sort the given array
        Array.Sort(arr);

        // Return k'th element in
        // the sorted array
        return arr[K - 1];
    }

    // driver's program
    public static void Main()
    {
        int[] arr = new int[] { 12, 3, 5, 7, 19 };
        int K = 2;

        // Function call
        Console.Write("K'th smallest element"
                      + " is " + kthSmallest(arr, K));
    }
}

// This code is contributed by nitin mittal.

PHP

<?php
// Simple PHP program to find
// K'th smallest element

// Function to return K'th smallest
// element in a given array
function kthSmallest($arr, $N, $K)
{

    // Sort the given array
    sort($arr);

    // Return k'th element
    // in the sorted array
    return $arr[$K - 1];
}

    // Driver's Code
    $arr = array(12, 3, 5, 7, 19);
    $N =count($arr);
    $K = 2;

    // Function call
    echo "K'th smallest element is ", kthSmallest($arr, $N, $K);

// This code is contributed by anuj_67.
?>

Javascript

// Simple Javascript program to find K'th smallest element

// Function to return K'th smallest element in a given array
function kthSmallest(arr, N, K)
{
    // Sort the given array
    arr.sort((a,b) => a-b);

    // Return k'th element in the sorted array
    return arr[K - 1];
}

// Driver program to test above methods
    let arr = [12, 3, 5, 7, 19];
    let N = arr.length, K = 2;
    document.write("K'th smallest element is " + kthSmallest(arr, N, K));

//This code is contributed by Mayank Tyagi

Output

K'th smallest element is 5

Time Complexity: O(N log N)
Auxiliary Space: O(1) 

K’th smallest element in an unsorted array using set data structure:

 Set data structure can be used to find the kth smallest element as it stores the distinct elements in sorted order. Set can be used because it is mentioned in the question that all the elements in the array are distinct.

Follow the given steps to solve the problem:

• Insert all array elements into the set
• Advance the iterator to the Kth element in the set
• Return the value of the element at which the iterator is pointing

Below is the Implementation of the above approach:

C++

// C++ code for the above approach

#include <bits/stdc++.h>
using namespace std;

int main()
{
    int arr[] = { 12, 3, 5, 7, 19 };
    int N = sizeof(arr) / sizeof(arr[0]);
    int K = 4;

    set<int> s(arr, arr + N);

    // s.begin() returns a pointer to first
    // element in the set
    set<int>::iterator itr = s.begin();

    advance(itr, K - 1); // itr points to kth element in set

    cout << *itr << "\n";

    return 0;
}

Java

// Java code for the above approach

import java.util.*;

class GFG {

    public static void main(String[] args)
    {
        int[] arr = { 12, 3, 5, 7, 19 };
        int N = arr.length;
        int K = 4;

        // since counting starts from 0 so to find kth
        // element we need to reduce K by 1
        K--;

        // for storing elements in sorted form
        // in set we will use TreeSet
        Set<Integer> s = new TreeSet<Integer>();

        // Adding elements to set
        for (int i = 0; i < N; i++)
            s.add(arr[i]);

        // Use iterator method of Iterator
        // for the traversal
        Iterator<Integer> itr = s.iterator();

        while (K > 0) {
            itr.next();
            K--;
        } // itr points to the Kth element in the set

        System.out.println(itr.next());
    }
}

// This code is contributed by Abhijeet Kumar(abhijeet19403)

Python3

# Python3 code for the above approach

if __name__ == '__main__':
    arr = [12, 3, 5, 7, 19]
    N = len(arr)
    K = 4

    s = set(arr)

    for itr in s:
        if K == 1:
            print(itr)  # itr is the Kth element in the set
            break
        K -= 1

# This code is contributed by Abhijeet Kumar(abhijeet19403)

C#

// C# code for the above approach

using System;
using System.Collections.Generic;

class GFG {

    // Driver code
    public static void Main()
    {

        int[] arr = { 12, 3, 5, 7, 19 };
        int N = arr.Length;
        int K = 4;

        SortedSet<int> s = new SortedSet<int>();
        foreach(int i in arr) s.Add(i);

        foreach(int itr in s)
        {
            if (K == 1) {
                Console.WriteLine(itr);
                // itr is the kth element in the set
                break;
            }
            K--;
        }
    }
}

// This code is contributed by Abhijeet Kumar(abhijeet19403)

Output

12

Time Complexity:  O(N*log N)
Auxiliary Space: O(N)

K’th smallest element in an unsorted array using heap data structure:

K’th smallest element in an unsorted array using Min-Heap

Min-Heap can be used to find the kth smallest element, by inserting all the elements into Min-Heap and then and call extractMin() function K times. 

Follow the given steps to solve the problem:

• Insert all the array elements into the Min-Heap
• Call extractMin() function K times
• Return the value obtained at the last call of extractMin() function 

Below is the Implementation of the above approach:

C++

// C++ program to find K'th smallest element using min heap

#include <climits>
#include <iostream>
using namespace std;

// Prototype of a utility function to swap two integers
void swap(int* x, int* y);

// A class for Min Heap
class MinHeap {

    int* harr; // pointer to array of elements in heap
    int capacity; // maximum possible size of min heap
    int heap_size; // Current number of elements in min heap
public:
    MinHeap(int a[], int size); // Constructor

    // To minheapify subtree rooted with index i
    void MinHeapify(int i);
    int parent(int i) { return (i - 1) / 2; }
    int left(int i) { return (2 * i + 1); }
    int right(int i) { return (2 * i + 2); }

    int extractMin(); // extracts root (minimum) element
    int getMin() { return harr[0]; } // Returns minimum
};

MinHeap::MinHeap(int a[], int size)
{
    heap_size = size;
    harr = a; // store address of array
    int i = (heap_size - 1) / 2;
    while (i >= 0) {
        MinHeapify(i);
        i--;
    }
}

// Method to remove minimum element (or root) from min heap
int MinHeap::extractMin()
{
    if (heap_size == 0)
        return INT_MAX;

    // Store the minimum value.
    int root = harr[0];

    // If there are more than 1 items, move the last item to
    // root and call heapify.
    if (heap_size > 1) {
        harr[0] = harr[heap_size - 1];
        MinHeapify(0);
    }
    heap_size--;

    return root;
}

// A recursive method to heapify a subtree with root at
// given index This method assumes that the subtrees are
// already heapified
void MinHeap::MinHeapify(int i)
{
    int l = left(i);
    int r = right(i);
    int smallest = i;

    if (l < heap_size && harr[l] < harr[i])
        smallest = l;

    if (r < heap_size && harr[r] < harr[smallest])
        smallest = r;

    if (smallest != i) {
        swap(&harr[i], &harr[smallest]);
        MinHeapify(smallest);
    }
}

// A utility function to swap two elements
void swap(int* x, int* y)
{
    int temp = *x;
    *x = *y;
    *y = temp;
}

// Function to return k'th smallest element in a given array
int kthSmallest(int arr[], int N, int K)
{
    // Build a heap of n elements: O(n) time
    MinHeap mh(arr, N);

    // Do extract min (K-1) times
    for (int i = 0; i < K - 1; i++)
        mh.extractMin();

    // Return root
    return mh.getMin();
}

// Driver's code
int main()
{
    int arr[] = { 12, 3, 5, 7, 19 };
    int N = sizeof(arr) / sizeof(arr[0]), K = 2;

    // Function call
    cout << "K'th smallest element is "
         << kthSmallest(arr, N, K);
    return 0;
}

Java

// Java program to find K'th smallest element using min heap
import java.util.*;
public class GFG {

    // A class for Max Heap
    class MinHeap {
        int[] harr; // pointer to array of elements in heap
        int capacity; // maximum possible size of min heap
        int heap_size; // Current number of elements in min
                       // heap

        int parent(int i) { return (i - 1) / 2; }
        int left(int i) { return ((2 * i) + 1); }
        int right(int i) { return ((2 * i) + 2); }
        int getMin() { return harr[0]; } // Returns minimum

        // to replace root with new node x and heapify() new
        // root
        void replaceMax(int x)
        {
            this.harr[0] = x;
            minHeapify(0);
        }
        MinHeap(int a[], int size)
        {
            heap_size = size;
            harr = a; // store address of array
            int i = (heap_size - 1) / 2;
            while (i >= 0) {
                minHeapify(i);
                i--;
            }
        }

        // Method to remove maximum element (or root) from
        // min heap
        int extractMin()
        {
            if (heap_size == 0)
                return Integer.MAX_VALUE;

            // Store the maximum value.
            int root = harr[0];

            // If there are more than 1 items, move the last
            // item to root and call heapify.
            if (heap_size > 1) {
                harr[0] = harr[heap_size - 1];
                minHeapify(0);
            }
            heap_size--;
            return root;
        }

        // A recursive method to heapify a subtree with root
        // at given index This method assumes that the
        // subtrees are already heapified
        void minHeapify(int i)
        {
            int l = left(i);
            int r = right(i);
            int smallest = i;
            if (l < heap_size && harr[l] < harr[i])
                smallest = l;
            if (r < heap_size && harr[r] < harr[smallest])
                smallest = r;
            if (smallest != i) {
                int t = harr[i];
                harr[i] = harr[smallest];
                harr[smallest] = t;
                minHeapify(smallest);
            }
        }
    };

    // Function to return k'th largest element in a given
    // array
    int kthSmallest(int arr[], int N, int K)
    {

        // Build a heap of first k elements: O(k) time
        MinHeap mh = new MinHeap(arr, N);

        // Process remaining n-k elements. If current
        // element is smaller than root, replace root with
        // current element
        for (int i = 0; i < K - 1; i++)
            mh.extractMin();

        // Return root
        return mh.getMin();
    }

    // Driver's code
    public static void main(String[] args)
    {
        int arr[] = { 12, 3, 5, 7, 19 };
        int N = arr.length, K = 2;
        GFG gfg = new GFG();

        // Function call
        System.out.print("K'th smallest element is "
                         + gfg.kthSmallest(arr, N, K));
    }
}

// This code is contributed by avanitrachhadiya2155

Python3

# Python3 program to find K'th smallest element
# using min heap

# Class for Min Heap


class MinHeap:

    # Constructor
    def __init__(self, a, size):

        # list of elements in the heap
        self.harr = a

        # maximum possible size of min heap
        self.capacity = None

        # current number of elements in min heap
        self.heap_size = size

        i = int((self.heap_size - 1) / 2)
        while i >= 0:
            self.minHeapify(i)
            i -= 1

    def parent(self, i):
        return (i - 1) / 2

    def left(self, i):
        return 2 * i + 1

    def right(self, i):
        return 2 * i + 2

    # Returns minimum
    def getMin(self):
        return self.harr[0]

    # Method to remove minimum element (or root)
    # from min heap
    def extractMin(self):
        if self.heap_size == 0:
            return float("inf")

        # Store the minimum value
        root = self.harr[0]

        # If there are more than 1 items, move the last item
        # to root and call heapify
        if self.heap_size > 1:
            self.harr[0] = self.harr[self.heap_size - 1]
            self.minHeapify(0)
        self.heap_size -= 1
        return root

    # A recursive method to heapify a subtree with root at
    # given index. This method assumes that the subtrees
    # are already heapified
    def minHeapify(self, i):
        l = self.left(i)
        r = self.right(i)
        smallest = i
        if ((l < self.heap_size) and
                (self.harr[l] < self.harr[i])):
            smallest = l
        if ((r < self.heap_size) and
                (self.harr[r] < self.harr[smallest])):
            smallest = r
        if smallest != i:
            self.harr[i], self.harr[smallest] = (
                self.harr[smallest], self.harr[i])
            self.minHeapify(smallest)

# Function to return k'th smallest element in a given array


def kthSmallest(arr, N, K):

    # Build a heap of n elements in O(n) time
    mh = MinHeap(arr, N)

    # Do extract min (k-1) times
    for i in range(K - 1):
        mh.extractMin()

    # Return root
    return mh.getMin()


# Driver's code
if __name__ == '__main__':
    arr = [12, 3, 5, 7, 19]
    N = len(arr)
    K = 2

    # Function call
    print("K'th smallest element is", kthSmallest(arr, N, K))

# This Code is contributed by Kevin Joshi

C#

using System;
public class GFG {

    public class MinHeap {
        int[] harr; // Pointer to array of elements in heap
        //    int capacity; // maximum possible size of min
        //    heap
        int heap_size; // Current number of elements in min
                       // heap

        int parent(int i) { return (i - 1) / 2; }
        int left(int i) { return ((2 * i) + 1); }
        int right(int i) { return ((2 * i) + 2); }
        public int getMin()
        {
            return harr[0];
        } // Returns minimum

        // To replace root with new node x and heapify() new
        // root
        public void replaceMax(int x)
        {
            this.harr[0] = x;
            minHeapify(0);
        }

        public MinHeap(int[] a, int size)
        {
            heap_size = size;
            harr = a; // store address of array
            int i = (heap_size - 1) / 2;
            while (i >= 0) {
                minHeapify(i);
                i--;
            }
        }

        // Method to remove maximum element (or root) from
        // min heap
        public int extractMin()
        {
            if (heap_size == 0)
                return Int32.MaxValue;

            // Store the maximum value.
            int root = harr[0];

            // If there are more than 1 items, move the last
            // item to root and call heapify.
            if (heap_size > 1) {
                harr[0] = harr[heap_size - 1];
                minHeapify(0);
            }
            heap_size--;
            return root;
        }

        // A recursive method to heapify a subtree with root
        // at given index This method assumes that the
        // subtrees are already heapified
        public void minHeapify(int i)
        {
            int l = left(i);
            int r = right(i);
            int smallest = i;
            if (l < heap_size && harr[l] < harr[i])
                smallest = l;
            if (r < heap_size && harr[r] < harr[smallest])
                smallest = r;
            if (smallest != i) {
                int t = harr[i];
                harr[i] = harr[smallest];
                harr[smallest] = t;
                minHeapify(smallest);
            }
        }
    };

    // Function to return k'th largest element in a given
    // array
    int kthSmallest(int[] arr, int N, int K)
    {

        // Build a heap of first k elements: O(k) time
        MinHeap mh = new MinHeap(arr, N);

        // Process remaining n-k elements. If current
        // element is smaller than root, replace root with
        // current element
        for (int i = 0; i < K - 1; i++)
            mh.extractMin();

        // Return root
        return mh.getMin();
    }

    // Driver's code
    static public void Main()
    {
        int[] arr = { 12, 3, 5, 7, 19 };
        int N = arr.Length, K = 2;
        GFG gfg = new GFG();

        // Function call
        Console.Write("K'th smallest element is "
                      + gfg.kthSmallest(arr, N, K));
    }
}

// This code is contributed by rag2127

Javascript

// Javascript program to find K'th smallest element using min heap

// class for Max Heap
class MinHeap {


    parent(i) {
        return (i - 1) / 2;
    };
    left(i) {
        return ((2 * i) + 1);
    };
    right(i) {
        return ((2 * i) + 2);
    }
    getMin() {
        return this.harr[0];
    } // Returns minimum

    // to replace root with new node x and heapify() new root
    replaceMax(x) {
        this.harr[0] = x;
        minHeapify(0);
    }
    constructor(a, size) {
        this.heap_size = size;
        this.harr = a; // store address of array
        let i = (this.heap_size - 1) / 2;
        while (i >= 0) {
            this.minHeapify(i);
            i--;
        }
    }

    // Method to remove maximum element (or root) from min heap
    extractMin() {
        if (this.heap_size == 0)
            return Number.MAX_SAFE_INTEGER;

        // Store the maximum value.
        let root = this.harr[0];

        // If there are more than 1 items, move the last item to root
        // and call heapify.
        if (this.heap_size > 1) {
            this.harr[0] = this.harr[this.heap_size - 1];
            this.minHeapify(0);
        }
        this.heap_size--;
        return root;
    }

    // A recursive method to heapify a subtree with root at given index
    // This method assumes that the subtrees are already heapified
    minHeapify(i) {
        let l = this.left(i);
        let r = this.right(i);
        let smallest = i;
        if (l < this.heap_size && this.harr[l] < this.harr[i])
            smallest = l;
        if (r < this.heap_size && this.harr[r] < this.harr[smallest])
            smallest = r;
        if (smallest != i) {
            let t = this.harr[i];
            this.harr[i] = this.harr[smallest];
            this.harr[smallest] = t;
            this.minHeapify(smallest);
        }
    }
};

// Function to return k'th largest element in a given array
function kthSmallest(arr, N, K) {

    // Build a heap of first k elements: O(k) time
    let mh = new MinHeap(arr, N);

    // Process remaining N-K elements. If current element is
    // smaller than root, replace root with current element
    for (let i = 0; i < K - 1; i++)
        mh.extractMin();

    // Return root
    return mh.getMin();
}

// Driver program to test above methods
let arr = [12, 3, 5, 7, 19];
let N = arr.length, K = 2;
document.write("K'th smallest element is " + kthSmallest(arr, N, K));

// This code is contributed by gfgking.

Output

K'th smallest element is 5

Time complexity: O(N + K Log N).
Auxiliary Space: O(N)

K’th smallest element in an unsorted array using Max-Heap

Max-Heap can be used to find the kth smallest element, by inserting first K elements into Max-Heap and then compare remaining elements with the root of the Max-Heap and if the element is less than the root then remove the root and insert this element into the heap and finally return root of the Max-Heap 

Follow the given steps to solve the problem:

• Build a Max-Heap MH of the first K elements (arr[0] to arr[K-1]) of the given array. 
• For each element, after the Kth element (arr[K] to arr[n-1]), compare it with the root of MH. 
  • If the element is less than the root then make it the root and call heapify for Max-Heap MH
  • b) Else ignore it. 
• Finally, the root of the MH is the Kth smallest element.

Below is the Implementation of the above approach:

C++

// C++ program to find k'th smallest element using max heap

#include <bits/stdc++.h>
using namespace std;

// Prototype of a utility function to swap two integers
void swap(int* x, int* y);

// A class for Max Heap
class MaxHeap {

    int* harr; // pointer to array of elements in heap
    int capacity; // maximum possible size of max heap
    int heap_size; // Current number of elements in max heap

public:
    MaxHeap(int a[], int size); // Constructor
    void maxHeapify(
        int i); // To maxHeapify subtree rooted with index i
    int parent(int i) { return (i - 1) / 2; }
    int left(int i) { return (2 * i + 1); }
    int right(int i) { return (2 * i + 2); }

    int extractMax(); // extracts root (maximum) element
    int getMax() { return harr[0]; } // Returns maximum

    // to replace root with new node x and heapify() new
    // root
    void replaceMax(int x)
    {
        harr[0] = x;
        maxHeapify(0);
    }
};

MaxHeap::MaxHeap(int a[], int size)
{
    heap_size = size;
    harr = a; // store address of array
    int i = (heap_size - 1) / 2;
    while (i >= 0) {
        maxHeapify(i);
        i--;
    }
}

// Method to remove maximum element (or root) from max heap
int MaxHeap::extractMax()
{
    if (heap_size == 0)
        return INT_MAX;

    // Store the maximum value.
    int root = harr[0];

    // If there are more than 1 items, move the last item to
    // root and call heapify.
    if (heap_size > 1) {
        harr[0] = harr[heap_size - 1];
        maxHeapify(0);
    }
    heap_size--;

    return root;
}

// A recursive method to heapify a subtree with root at
// given index This method assumes that the subtrees are
// already heapified
void MaxHeap::maxHeapify(int i)
{
    int l = left(i);
    int r = right(i);
    int largest = i;

    if (l < heap_size && harr[l] > harr[i])
        largest = l;

    if (r < heap_size && harr[r] > harr[largest])
        largest = r;

    if (largest != i) {
        swap(&harr[i], &harr[largest]);
        maxHeapify(largest);
    }
}

// A utility function to swap two elements
void swap(int* x, int* y)
{
    int temp = *x;
    *x = *y;
    *y = temp;
}

// Function to return k'th largest element in a given array
int kthSmallest(int arr[], int N, int K)
{
    // Build a heap of first k elements: O(k) time
    MaxHeap mh(arr, K);

    // Process remaining n-k elements.  If current element
    // is smaller than root, replace root with current
    // element
    for (int i = K; i < N; i++)
        if (arr[i] < mh.getMax())
            mh.replaceMax(arr[i]);

    // Return root
    return mh.getMax();
}

// Driver's code
int main()
{
    int arr[] = { 12, 3, 5, 7, 19 };
    int N = sizeof(arr) / sizeof(arr[0]), K = 4;

    // Function call
    cout << "K'th smallest element is "
         << kthSmallest(arr, N, K);
    return 0;
}

Java

// A Java program to find k'th smallest element using max
// heap
import java.util.*;
class GFG {

    // A class for Max Heap
    class MaxHeap {
        int[] harr; // pointer to array of elements in heap
        int capacity; // maximum possible size of max heap
        int heap_size; // Current number of elements in max
                       // heap

        int parent(int i) { return (i - 1) / 2; }
        int left(int i) { return (2 * i + 1); }
        int right(int i) { return (2 * i + 2); }
        int getMax() { return harr[0]; } // Returns maximum

        // to replace root with new node x and heapify() new
        // root
        void replaceMax(int x)
        {
            this.harr[0] = x;
            maxHeapify(0);
        }
        MaxHeap(int a[], int size)
        {
            heap_size = size;
            harr = a; // store address of array
            int i = (heap_size - 1) / 2;
            while (i >= 0) {
                maxHeapify(i);
                i--;
            }
        }

        // Method to remove maximum element (or root) from
        // max heap
        int extractMax()
        {
            if (heap_size == 0)
                return Integer.MAX_VALUE;

            // Store the maximum value.
            int root = harr[0];

            // If there are more than 1 items, move the last
            // item to root and call heapify.
            if (heap_size > 1) {
                harr[0] = harr[heap_size - 1];
                maxHeapify(0);
            }
            heap_size--;
            return root;
        }

        // A recursive method to heapify a subtree with root
        // at given index This method assumes that the
        // subtrees are already heapified
        void maxHeapify(int i)
        {
            int l = left(i);
            int r = right(i);
            int largest = i;
            if (l < heap_size && harr[l] > harr[i])
                largest = l;
            if (r < heap_size && harr[r] > harr[largest])
                largest = r;
            if (largest != i) {
                int t = harr[i];
                harr[i] = harr[largest];
                harr[largest] = t;
                maxHeapify(largest);
            }
        }
    };

    // Function to return k'th largest element in a given
    // array
    int kthSmallest(int arr[], int N, int K)
    {

        // Build a heap of first k elements: O(k) time
        MaxHeap mh = new MaxHeap(arr, K);

        // Process remaining n-k elements.  If current
        // element is smaller than root, replace root with
        // current element
        for (int i = K; i < N; i++)
            if (arr[i] < mh.getMax())
                mh.replaceMax(arr[i]);

        // Return root
        return mh.getMax();
    }

    // Driver's code
    public static void main(String[] args)
    {
        int arr[] = { 12, 3, 5, 7, 19 };
        int N = arr.length, K = 4;
        GFG gfg = new GFG();

        // Function call
        System.out.print("K'th smallest element is "
                         + gfg.kthSmallest(arr, N, K));
    }
}

// This code is contributed by Rajput-Ji

Python3

# Python3 program to find K'th smallest element
# using max heap

# Class for Max Heap


class MaxHeap:
    # Constructor
    def __init__(self, a, size):
        # list of elements in the heap
        self.harr = a
        # maximum possible size of max heap
        self.capacity = None
        # current number of elements in max heap
        self.heap_size = size

        i = int((self.heap_size - 1) / 2)
        while i >= 0:
            self.maxHeapify(i)
            i -= 1

    def parent(self, i):
        return (i - 1) / 2

    def left(self, i):
        return 2 * i + 1

    def right(self, i):
        return 2 * i + 2

    # Returns maximum
    def getMax(self):
        return self.harr[0]

    # to replace root with new node x and heapify() new root
    def replaceMax(self, x):
        self.harr[0] = x
        self.maxHeapify(0)

    # Method to remove maximum element (or root)
    # from max heap
    def extractMin(self):
        if self.heap_size == 0:
            return float("inf")

        # Store the maximum value.
        root = self.harr[0]

        # If there are more than 1 items, move the
        # last item to root and call heapify
        if self.heap_size > 1:
            self.harr[0] = self.harr[self.heap_size - 1]
            self.maxHeapify(0)
        self.heap_size -= 1
        return root

    # A recursive method to heapify a subtree with root at
    # given index. This method assumes that the subtrees
    # are already heapified
    def maxHeapify(self, i):
        l = self.left(i)
        r = self.right(i)
        largest = i

        if ((l < self.heap_size) and
                (self.harr[l] > self.harr[i])):
            largest = l

        if ((r < self.heap_size) and
                (self.harr[r] > self.harr[largest])):
            largest = r

        if largest != i:
            self.harr[i], self.harr[largest] = (
                self.harr[largest], self.harr[i])
            self.maxHeapify(largest)


# Function to return k'th smallest element in a given array
def kthSmallest(arr, N, K):
    # Build a heap of first k elements in O(k) time
    mh = MaxHeap(arr, K)

    # Process remaining n-k elements. If current element is
    # smaller than root, replace root with current element
    for i in range(K, N):
        if arr[i] < mh.getMax():
            mh.replaceMax(arr[i])

    # Return root
    return mh.getMax()


# Driver's code
if __name__ == '__main__':
    arr = [12, 3, 5, 7, 19]
    N = len(arr)
    K = 4

    # Function call
    print("K'th smallest element is", kthSmallest(arr, N, K))

# Code contributed by Kevin Joshi

C#

// C# program to find k'th smallest element using max heap

using System;

public class GFG {

    // A class for Max Heap
    public

        class MaxHeap {
        public

            int[] harr; // pointer to array of elements in
                        // heap
        public

            int capacity; // maximum possible size of max
                          // heap
        public

            int heap_size; // Current number of elements in
                           // max heap

        public

            int
            parent(int i)
        {
            return (i - 1) / 2;
        }
        public

            int
            left(int i)
        {
            return (2 * i + 1);
        }
        public

            int
            right(int i)
        {
            return (2 * i + 2);
        }
        public

            int
            getMax()
        {
            return harr[0];
        } // Returns maximum

        // to replace root with new node x and heapify() new
        // root
        public

            void
            replaceMax(int x)
        {
            this.harr[0] = x;
            maxHeapify(0);
        }
        public

            MaxHeap(int[] a, int size)
        {
            heap_size = size;
            harr = a; // store address of array
            int i = (heap_size - 1) / 2;
            while (i >= 0) {
                maxHeapify(i);
                i--;
            }
        }

        // Method to remove maximum element (or root) from
        // max heap
        public

            int
            extractMax()
        {
            if (heap_size == 0)
                return int.MaxValue;

            // Store the maximum value.
            int root = harr[0];

            // If there are more than 1 items, move the last
            // item to root and call heapify.
            if (heap_size > 1) {
                harr[0] = harr[heap_size - 1];
                maxHeapify(0);
            }
            heap_size--;
            return root;
        }

        // A recursive method to heapify a subtree with root
        // at given index This method assumes that the
        // subtrees are already heapified
        public

            void
            maxHeapify(int i)
        {
            int l = left(i);
            int r = right(i);
            int largest = i;

            if (l < heap_size && harr[l] > harr[i])
                largest = l;

            if (r < heap_size && harr[r] > harr[largest])
                largest = r;

            if (largest != i) {
                int t = harr[i];
                harr[i] = harr[largest];
                harr[largest] = t;
                maxHeapify(largest);
            }
        }
    };

    // Function to return k'th largest element in a given
    // array
    int kthSmallest(int[] arr, int N, int K)
    {

        // Build a heap of first k elements: O(k) time
        MaxHeap mh = new MaxHeap(arr, K);

        // Process remaining n-k elements.  If current
        // element is smaller than root, replace root with
        // current element
        for (int i = K; i < N; i++)
            if (arr[i] < mh.getMax())
                mh.replaceMax(arr[i]);

        // Return root
        return mh.getMax();
    }

    // Driver's code
    public static void Main(String[] args)
    {
        int[] arr = { 12, 3, 5, 7, 19 };
        int N = arr.Length, K = 4;
        GFG gfg = new GFG();

        // Function call
        Console.Write("K'th smallest element is "
                      + gfg.kthSmallest(arr, N, K));
    }
}

// This code is contributed by gauravrajput1

Output

K'th smallest element is 12

Time Complexity: O(K + (N-K) * Log K) 
Auxiliary Space: O(K)

K’th smallest element in an unsorted array using QuickSelect:

This is an optimization over method 1, if QuickSort is used as a sorting algorithm in first step. In QuickSort, pick a pivot element, then move the pivot element to its correct position and partition the surrounding array. The idea is, not to do complete quicksort, but stop at the point where pivot itself is k’th smallest element. Also, not to recur for both left and right sides of pivot, but recur for one of them according to the position of pivot. 

Follow the given steps to solve the problem:

• Run quick sort algorithm on the input array
  • In this algorithm pick a pivot element and move it to it’s correct position
  • Now, if index of pivot is equal to K then return the value, else if the index of pivot is greater than K, then recur for the left subarray, else recur for the right subarray 
  • Repeat this process until the element at index K is not found

Below is the Implementation of the above approach:

C

// C code for the above approach

#include <limits.h>
#include <stdio.h>

int partition(int arr[], int l, int r);

// This function returns K'th smallest element in arr[l..r]
// using QuickSort based method. ASSUMPTION: ALL ELEMENTS IN
// ARR[] ARE DISTINCT
int kthSmallest(int arr[], int l, int r, int K)
{
    // If k is smaller than number of elements in array
    if (K > 0 && K <= r - l + 1) {

        // Partition the array around last element and get
        // position of pivot element in sorted array
        int pos = partition(arr, l, r);

        // If position is same as k
        if (pos - l == K - 1)
            return arr[pos];
        if (pos - l > K - 1) // If position is more, recur
                             // for left subarray
            return kthSmallest(arr, l, pos - 1, K);

        // Else recur for right subarray
        return kthSmallest(arr, pos + 1, r,
                           K - pos + l - 1);
    }

    // If k is more than number of elements in array
    return INT_MAX;
}

void swap(int* a, int* b)
{
    int temp = *a;
    *a = *b;
    *b = temp;
}

// Standard partition process of QuickSort(). It considers
// the last element as pivot and moves all smaller element
// to left of it and greater elements to right
int partition(int arr[], int l, int r)
{
    int x = arr[r], i = l;
    for (int j = l; j <= r - 1; j++) {
        if (arr[j] <= x) {
            swap(&arr[i], &arr[j]);
            i++;
        }
    }

    swap(&arr[i], &arr[r]);
    return i;
}

// Driver's code
int main()
{
    int arr[] = { 12, 3, 5, 7, 4, 19, 26 };
    int N = sizeof(arr) / sizeof(arr[0]), K = 3;

    // Function call
    printf("K'th smallest element is %d",
           kthSmallest(arr, 0, N - 1, K));
    return 0;
}

C++

// C++ code for the above approach

#include <bits/stdc++.h>
using namespace std;

int partition(int arr[], int l, int r);

// This function returns K'th smallest element in arr[l..r]
// using QuickSort based method. ASSUMPTION: ALL ELEMENTS IN
// ARR[] ARE DISTINCT
int kthSmallest(int arr[], int l, int r, int K)
{
    // If k is smaller than number of elements in array
    if (K > 0 && K <= r - l + 1) {

        // Partition the array around last element and get
        // position of pivot element in sorted array
        int pos = partition(arr, l, r);

        // If position is same as k
        if (pos - l == K - 1)
            return arr[pos];
        if (pos - l > K - 1) // If position is more, recur
                             // for left subarray
            return kthSmallest(arr, l, pos - 1, K);

        // Else recur for right subarray
        return kthSmallest(arr, pos + 1, r,
                           K - pos + l - 1);
    }

    // If k is more than number of elements in array
    return INT_MAX;
}

void swap(int* a, int* b)
{
    int temp = *a;
    *a = *b;
    *b = temp;
}

// Standard partition process of QuickSort(). It considers
// the last element as pivot and moves all smaller element
// to left of it and greater elements to right
int partition(int arr[], int l, int r)
{
    int x = arr[r], i = l;
    for (int j = l; j <= r - 1; j++) {
        if (arr[j] <= x) {
            swap(&arr[i], &arr[j]);
            i++;
        }
    }

    swap(&arr[i], &arr[r]);
    return i;
}

// Driver's code
int main()
{
    int arr[] = { 12, 3, 5, 7, 4, 19, 26 };
    int N = sizeof(arr) / sizeof(arr[0]), K = 3;

    // Function call
    cout << "K'th smallest element is "
         << kthSmallest(arr, 0, N - 1, K);
    return 0;
}

Java

// Java code for kth smallest element in an array

import java.util.Arrays;
import java.util.Collections;

class GFG {
    // Standard partition process of QuickSort.
    // It considers the last element as pivot
    // and moves all smaller element to left of
    // it and greater elements to right
    public static int partition(Integer[] arr, int l, int r)
    {
        int x = arr[r], i = l;
        for (int j = l; j <= r - 1; j++) {
            if (arr[j] <= x) {

                // Swapping arr[i] and arr[j]
                int temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;

                i++;
            }
        }

        // Swapping arr[i] and arr[r]
        int temp = arr[i];
        arr[i] = arr[r];
        arr[r] = temp;

        return i;
    }

    // This function returns k'th smallest element
    // in arr[l..r] using QuickSort based method.
    // ASSUMPTION: ALL ELEMENTS IN ARR[] ARE DISTINCT
    public static int kthSmallest(Integer[] arr, int l,
                                  int r, int K)
    {
        // If k is smaller than number of elements
        // in array
        if (K > 0 && K <= r - l + 1) {

            // Partition the array around last
            // element and get position of pivot
            // element in sorted array
            int pos = partition(arr, l, r);

            // If position is same as k
            if (pos - l == K - 1)
                return arr[pos];

            // If position is more, recur for
            // left subarray
            if (pos - l > K - 1)
                return kthSmallest(arr, l, pos - 1, K);

            // Else recur for right subarray
            return kthSmallest(arr, pos + 1, r,
                               K - pos + l - 1);
        }

        // If k is more than number of elements
        // in array
        return Integer.MAX_VALUE;
    }

    // Driver's code
    public static void main(String[] args)
    {
        Integer arr[]
            = new Integer[] { 12, 3, 5, 7, 4, 19, 26 };
        int K = 3;

        // Function call
        System.out.print(
            "K'th smallest element is "
            + kthSmallest(arr, 0, arr.length - 1, K));
    }
}

// This code is contributed by Chhavi

Python3

# Python3 code for the above approach

# This function returns k'th smallest element
# in arr[l..r] using QuickSort based method.
# ASSUMPTION: ALL ELEMENTS IN ARR[] ARE DISTINCT
import sys


def kthSmallest(arr, l, r, K):

    # If k is smaller than number of
    # elements in array
    if (K > 0 and K <= r - l + 1):

        # Partition the array around last
        # element and get position of pivot
        # element in sorted array
        pos = partition(arr, l, r)

        # If position is same as k
        if (pos - l == K - 1):
            return arr[pos]
        if (pos - l > K - 1):  # If position is more,
                              # recur for left subarray
            return kthSmallest(arr, l, pos - 1, K)

        # Else recur for right subarray
        return kthSmallest(arr, pos + 1, r,
                           K - pos + l - 1)

    # If k is more than number of
    # elements in array
    return sys.maxsize

# Standard partition process of QuickSort().
# It considers the last element as pivot and
# moves all smaller element to left of it
# and greater elements to right


def partition(arr, l, r):

    x = arr[r]
    i = l
    for j in range(l, r):
        if (arr[j] <= x):
            arr[i], arr[j] = arr[j], arr[i]
            i += 1
    arr[i], arr[r] = arr[r], arr[i]
    return i


# Driver's Code
if __name__ == "__main__":

    arr = [12, 3, 5, 7, 4, 19, 26]
    N = len(arr)
    K = 3
    print("K'th smallest element is",
          kthSmallest(arr, 0, N - 1, K))

# This code is contributed by ita_c

C#

// C# code for kth smallest element
// in an array

using System;

class GFG {

    // Standard partition process of QuickSort.
    // It considers the last element as pivot
    // and moves all smaller element to left of
    // it and greater elements to right
    public static int partition(int[] arr, int l, int r)
    {
        int x = arr[r], i = l;
        int temp = 0;
        for (int j = l; j <= r - 1; j++) {

            if (arr[j] <= x) {
                // Swapping arr[i] and arr[j]
                temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;

                i++;
            }
        }

        // Swapping arr[i] and arr[r]
        temp = arr[i];
        arr[i] = arr[r];
        arr[r] = temp;

        return i;
    }

    // This function returns k'th smallest
    // element in arr[l..r] using QuickSort
    // based method. ASSUMPTION: ALL ELEMENTS
    // IN ARR[] ARE DISTINCT
    public static int kthSmallest(int[] arr, int l, int r,
                                  int K)
    {
        // If k is smaller than number
        // of elements in array
        if (K > 0 && K <= r - l + 1) {
            // Partition the array around last
            // element and get position of pivot
            // element in sorted array
            int pos = partition(arr, l, r);

            // If position is same as k
            if (pos - l == K - 1)
                return arr[pos];

            // If position is more, recur for
            // left subarray
            if (pos - l > K - 1)
                return kthSmallest(arr, l, pos - 1, K);

            // Else recur for right subarray
            return kthSmallest(arr, pos + 1, r,
                               K - pos + l - 1);
        }

        // If k is more than number
        // of elements in array
        return int.MaxValue;
    }

    // Driver's Code
    public static void Main()
    {
        int[] arr = { 12, 3, 5, 7, 4, 19, 26 };
        int K = 3;

        // Function call
        Console.Write(
            "K'th smallest element is "
            + kthSmallest(arr, 0, arr.Length - 1, K));
    }
}

// This code is contributed
// by 29AjayKumar

Javascript

// JavaScript code for kth smallest
// element in an array

    // Standard partition process of QuickSort.
    // It considers the last element as pivot
    // and moves all smaller element to left of
    // it and greater elements to right
    function partition( arr , l , r)
    {
        var x = arr[r], i = l;
        for (j = l; j <= r - 1; j++) {
            if (arr[j] <= x) {
                // Swapping arr[i] and arr[j]
                var temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;

                i++;
            }
        }

        // Swapping arr[i] and arr[r]
        var temp = arr[i];
        arr[i] = arr[r];
        arr[r] = temp;

        return i;
    }

    // This function returns k'th smallest element
    // in arr[l..r] using QuickSort based method.
    // ASSUMPTION: ALL ELEMENTS IN ARR ARE DISTINCT
    function kthSmallest( arr , l , r , k) {
        // If k is smaller than number of elements
        // in array
        if (k > 0 && k <= r - l + 1) {
            // Partition the array around last
            // element and get position of pivot
            // element in sorted array
            var pos = partition(arr, l, r);

            // If position is same as k
            if (pos - l == k - 1)
                return arr[pos];

            // If position is more, recur for
            // left subarray
            if (pos - l > k - 1)
                return kthSmallest(arr, l, pos - 1, k);

            // Else recur for right subarray
            return kthSmallest(arr, pos + 1, r,
            k - pos + l - 1);
        }

        // If k is more than number of elements
        // in array
        return Number.MAX_VALUE;
    }

    // Driver program to test above methods

        var arr = [ 12, 3, 5, 7, 4, 19, 26 ];
        var k = 3;
        document.write("K'th smallest element is " +
        kthSmallest(arr, 0, arr.length - 1, k));

// This code contributed by Rajput-Ji

Output

K'th smallest element is 5

Time Complexity: O(N²) in worst case and O(N) on average 
Auxiliary Space: O(1)

K’th smallest element in an unsorted array using Map:

This approach is very much similar to the QuickSelect and counting sort algorithm but much easier to implement. Use a map and then map each element with its frequency. And as an ordered map would store the data in a sorted manner, so keep on adding the frequency of each element till it does not become greater than or equal to k so that the k’th element from the start can be reached i.e. the k’th smallest element.

Example: A[] = {7, 0, 25, 6, 16, 17, 0}, K = 3

Follow the given steps to solve the problem:

• Store frequency of every element in a Map mp
• Now traverse over sorted elements in the Map mp and add their frequencies in a variable freq
• If at any point the value of freq is greater than or equal to K, then return the value of iterator of Map mp

Below is the Implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

int Kth_smallest(map<int, int> mp, int K)
{
    int freq = 0;
    for (auto it = mp.begin(); it != mp.end(); it++) {
        freq += (it->second); // adding the frequencies of
                              // each element

        if (freq >= K) // if at any point frequency becomes
                       // greater than or equal to k then
                       // return that element
        {
            return it->first;
        }
    }

    return -1; // returning -1 if k>size of the array which
               // is an impossible scenario
}

// Driver's code
int main()
{
    int N = 5;
    int K = 2;
    vector<int> arr = { 12, 3, 5, 7, 19 };

    map<int, int> mp;
    for (int i = 0; i < N; i++) {
        mp[arr[i]] += 1; // mapping every element with it's
                         // frequency
    }

    // Function call
    int ans = Kth_smallest(mp, K);
    cout << "The " << K << "th smallest element is " << ans
         << endl;

    return 0;
}

Java

// Java program for the above approach

import java.util.*;

class GFG {
    static int Kth_smallest(TreeMap<Integer, Integer> mp,
                            int K)
    {
        int freq = 0;
        for (Map.Entry it : mp.entrySet()) {

            // adding the frequencies of each element
            freq += (int)it.getValue();

            // if at any point frequency becomes
            // greater than or equal to k then
            // return that element
            if (freq >= K) {
                return (int)it.getKey();
            }
        }

        return -1; // returning -1 if k>size of the array
                   // which is an impossible scenario
    }

    // Driver's code
    public static void main(String[] args)
    {
        int N = 5;
        int K = 2;
        int[] arr = { 12, 3, 5, 7, 19 };
        TreeMap<Integer, Integer> mp = new TreeMap<>();

        for (int i = 0; i < N; i++) {

            // mapping every element with
            // it's
            // frequency
            mp.put(arr[i], mp.getOrDefault(arr[i], 0) + 1);
        }

        // Function call
        int ans = Kth_smallest(mp, K);

        System.out.println(
            "The " + K + "th smallest element is " + ans);
    }
}

// This code is contributed by harshit17.

Python3

# Python3 program for the above approach


def Kth_smallest(mp, K):

    freq = 0
    for it in sorted(mp.keys()):
        freq += mp[it]  # adding the frequencies of
        # each element
        if freq >= K:  # if at any point frequency becomes
            return it   # greater than or equal to k then
            # return that element
    return -1  # returning -1 if k>size of the array which
    # is an impossible scenario


# driver's code
if __name__ == "__main__":
    N = 5
    K = 2
    arr = [12, 3, 5, 7, 19]
    mp = {}
    for i in range(N):
        if arr[i] in mp:    # mapping every element with it's
            mp[arr[i]] = mp[arr[i]] + 1  # frequency
        else:
            mp[arr[i]] = 1

    # Function call
    ans = Kth_smallest(mp, K)
    print("The ", K, "th smallest element is ", ans)

# This code is contributed by Abhijeet Kumar(abhijeet19403)

C#

// C# program for the above approach

using System;
using System.Collections;
using System.Collections.Generic;

public class GFG {
    static int Kth_smallest(SortedDictionary<int, int> mp,
                            int K)
    {
        int freq = 0;
        foreach(var it in mp)
        {

            // Adding the frequencies of each element
            freq += (int)it.Value;

            // If at any point frequency becomes
            // greater than or equal to k then
            // return that element
            if (freq >= K) {
                return (int)it.Key;
            }
        }

        return -1; // returning -1 if K > size of the array
                   // which is an impossible scenario
    }

    // Driver's code
    public static void Main(String[] args)
    {
        int N = 5;
        int K = 2;
        int[] arr = { 12, 3, 5, 7, 19 };

        SortedDictionary<int, int> mp
            = new SortedDictionary<int, int>();
        for (int i = 0; i < N; i++) {

            // mapping every element with
            // it's frequency
            mp.Add(arr[i], mp.ContainsKey(arr[i])
                               ? mp[arr[i]] + 1
                               : 1);
        }

        // Function call
        int ans = Kth_smallest(mp, K);

        Console.WriteLine(
            "The " + K + "th smallest element is " + ans);
    }
}

// This code is contributed by Abhijeet Kumar(abhijeet19403)

Javascript

// Javascript program to implement the approach
      //Function for creating Map
      function crateMap(arr, N) {
        var brr = arr.sort(function (a, b) {
          return a - b;
        });

        let mp = {};
        for (var i = 0; i < N; i++) {
          mp[brr[i]] = 0;
        }

        for (var i = 0; i < N; i++) {
          mp[brr[i]] += 1;
        }
        return mp;
      }

      //Function for finding kth Smallest
      function Kth_smallest(mp, K) {
        var freq = 0;
        for (const key in mp) {
          freq += mp[key]; // adding the frequencies of each element

          if (freq >= K) {
            // if at any point frequency becomes
            // greater than or equal to k then
            // return that element
            return key;
          }
        }

        return -1; // returning -1 if k>size of the array which
        // is an impossible scenario
      }

      var N = 5;
      var K = 2;
      var arr = [12, 3, 5, 7, 19];
      let mpp = crateMap(arr, N);

      // Function call
      var ans = Kth_smallest(mpp, K);
      console.log("The " + K + "th smallest element is " + ans);

Output

The 2th smallest element is 5

Time Complexity: O(N log N)
Auxiliary Space: O(N)

K’th smallest element in an unsorted array using Priority Queue:

To find the Kth minimum element in an array, insert the elements into the priority queue until the size of it is less than K, and then compare remaining elements with the root of the priority queue and if the element is less than the root then remove the root and insert this element into the priority queue and finally return root of the priority queue

Follow the given steps to solve the problem:

• Build a priority queue of the first K elements (arr[0] to arr[K-1]) of the given array. 
• For each element, after the Kth element (arr[K] to arr[n-1]), compare it with the root of priority queue. 
  • If the element is less than the root then remove the root and insert this element into the priority queue
  • b) Else ignore it. 
• Finally, the root of the priority queue is the Kth smallest element.

Below is the Implementation of the above approach:

C++

// C++ code to implement the approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the kth smallest array element
int kthSmallest(int arr[], int N, int K)
{

    // For finding min element we need (Max heap)priority
    // queue
    priority_queue<int> pq;

    for (int i = 0; i < K; i++) {
        // First push first K elements into heap
        pq.push(arr[i]);
    }
    // Now check from k to last element
    for (int i = K; i < N; i++) {

        // If current element is < top that means
        // there are  other k-1 lesser elements
        // are present at bottom thus, pop that element
        // and add kth largest element into the heap till
        // curr at last all the greater element than kth
        // element will get pop off and at the top of heap
        // there will be kth smallest element
        if (arr[i] < pq.top()) {
            pq.pop();
            // Push curr element
            pq.push(arr[i]);
        }
    }

    // Return top of element
    return pq.top();
}

// Driver's code:
int main()
{
    int N = 10;
    int arr[N] = { 10, 5, 4, 3, 48, 6, 2, 33, 53, 10 };
    int K = 4;

    // Function call
    cout << "Kth Smallest Element is: "
         << kthSmallest(arr, N, K);
}

Java

// Java code to implement the approach

import java.util.*;

// Custom comparator class to form the Max heap
class MinHeapComparator implements Comparator<Integer> {

    @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 int kthSmallest(int[] v, int N, int K)
    {
        // For finding min element we need (Max
        // heap)priority queue
        PriorityQueue<Integer> heap1
            = new PriorityQueue<Integer>(
                new MinHeapComparator());

        for (int i = 0; i < N; ++i) {

            // Insert elements into
            // the priority queue
            heap1.add(v[i]);

            // If current element is less than top, that
            // means there are other k-1 lesser elements are
            // present at bottom
            // thus pop that element and add kth largest
            // element into the heap till curr at last all
            // the greater element than kth element will get
            // pop off and at the top of heap there will be
            // kth smallest element
            if (heap1.size() > K) {
                heap1.remove();
            }
        }

        // Return the top of the heap as kth smallest
        // element
        return heap1.peek();
    }

    // Driver's code
    public static void main(String[] args)
    {
        // Given array
        int[] vec
            = { 10, 5, 4, 3, 48, 15, 6, 2, 33, 53, 10 };

        // Size of array
        int N = vec.length;

        // Given K
        int K = 4;

        // Function Call
        System.out.println("Kth Smallest Element: "
                           + kthSmallest(vec, N, K));
    }
}

Python3

# Python3 code to implement the approach
import heapq

# Function to find the kth smallest array element


def kthSmallest(arr, N, K):

    # For finding min element we need (Max heap)priority queue
    pq = []
    for i in range(K):

        # First push first K elements into heap
        heapq.heappush(pq, arr[i])
        heapq._heapify_max(pq)

    # Now check from k to last element
    for i in range(K, N):

        # If current element is < first that means
        # there are  other k-1 lesser elements
        # are present at bottom thus, pop that element
        # and add kth largest element into the heap till curr
        # at last all the greater element than kth element will get pop off
        # and at the top of heap there will be kth smallest element
        if arr[i] < pq[0]:
            heapq.heappop(pq)

            # Push curr element
            heapq.heappush(pq, arr[i])
            heapq._heapify_max(pq)
    # Return first of element
    return pq[0]


# Driver's code:
if __name__ == "__main__":
    N = 10
    arr = [10, 5, 4, 3, 48, 6, 2, 33, 53, 10]
    K = 4

    # Function call
    print("Kth Smallest Element is:", kthSmallest(arr, N, K))


# This code is contributed by Tapesh(tapeshdua420)

C#

// C# program to implement
// the above approach

using System;
using System.Collections.Generic;

class GFG {

    // Function to find the kth smallest array element
    static int kthSmallest(int[] arr, int N, int K)
    {

        // For finding min element we need (Max
        // heap)priority queue
        List<int> pq = new List<int>();

        for (int i = 0; i < K; i++) {

            // First push first K elements into heap
            pq.Add(arr[i]);
        }
        // Now check from k to last element
        for (int i = K; i < N; i++) {

            // If current element is < top that means
            // there are  other k-1 lesser elements
            // are present at bottom thus, pop that element
            // and add kth largest element into the heap
            // till curr at last all the greater element
            // than kth element will get pop off and at the
            // top of heap there will be kth smallest
            // element
            if (arr[i] < pq[0]) {
                pq.Sort();
                pq.Reverse();

                pq.RemoveAt(0);
                // Push curr element
                pq.Add(arr[i]);
            }
        }

        // Return top of element
        return pq[0];
    }

    // Driver's Code
    public static void Main()
    {
        // Given array
        int[] vec
            = { 10, 5, 4, 3, 48, 15, 6, 2, 33, 53, 10 };

        // Size of array
        int N = vec.Length;

        // Given K
        int K = 4;

        // Function Call
        Console.WriteLine("Kth Smallest Element: "
                          + kthSmallest(vec, N, K));
    }
}

// This code is contributed by sanjoy_62.

Output

Kth Smallest Element is: 5

Time complexity: O(K log K +  (N – K) log K)
Auxiliary Space: O(K)

K’th smallest element in an unsorted array using Binary Search:

The idea to solve this problem is that the Kth smallest element would be the element at the kth position if the array was sorted in increasing order. Using this logic, binary search can be used to predict the index of an element as if the array was sorted but without actually sorting the array. 

Follow the given steps to solve the problem:

• Find low and high that is the range where our answer can lie. 
• Apply Binary Search on this range. 
• If the selected element which would be mid has less than K elements lesser to it then increase the number that is low = mid + 1.
• Otherwise, Decrement the high pointer, i.e high = mid
• The Binary Search will end when only one element remains in the answer space which would be the answer.

Below is the implementation of the above approach:

C++

// C++ code for the above approach

#include <bits/stdc++.h>
#include <iostream>

using namespace std;

int count(vector<int>& nums, int& mid)
{
    // function to calculate number of elements less than
    // equal to mid
    int cnt = 0;

    for (int i = 0; i < nums.size(); i++)
        if (nums[i] <= mid)
            cnt++;

    return cnt;
}

int kthSmallest(vector<int> nums, int& k)
{
    int low = INT_MAX;
    int high = INT_MIN;
    // calculate minimum and maximum the array.
    for (int i = 0; i < nums.size(); i++) {
        low = min(low, nums[i]);
        high = max(high, nums[i]);
    }
    // Our answer range lies between minimum and maximum
    // element of the array on which Binary Search is
    // Applied
    while (low < high) {
        int mid = low + (high - low) / 2;
        /*if the count of number of elements in the array
          less than equal to mid is less than k then
          increase the number. Otherwise decrement the
          number and try to find a better answer.
        */
        if (count(nums, mid) < k)
            low = mid + 1;

        else
            high = mid;
    }

    return low;
}

// Driver's code
int main()
{

    vector<int> nums{ 1, 4, 5, 3, 19, 3 };
    int k = 3;

    // Function call
    cout << "K'th smallest element is "
         << kthSmallest(nums, k);
    return 0;
}

// This code is contributed by garvjuneja98

Java

// Java code for kth smallest element in an array

import java.util.Arrays;
import java.util.Collections;

class GFG {
    static int count(int[] nums, int mid)
    {
        // function to calculate number of elements less
        // than equal to mid
        int cnt = 0;

        for (int i = 0; i < nums.length; i++)
            if (nums[i] <= mid)
                cnt++;

        return cnt;
    }

    static int kthSmallest(int[] nums, int k)
    {
        int low = Integer.MAX_VALUE;
        int high = Integer.MIN_VALUE;
        // calculate minimum and maximum the array.
        for (int i = 0; i < nums.length; i++) {
            low = Math.min(low, nums[i]);
            high = Math.max(high, nums[i]);
        }
        // Our answer range lies between minimum and maximum
        // element of the array on which Binary Search is
        // Applied
        while (low < high) {
            int mid = low + (high - low) / 2;
            /*if the count of number of elements in the
              array less than equal to mid is less than k
              then increase the number. Otherwise decrement
              the number and try to find a better answer.
            */
            if (count(nums, mid) < k)
                low = mid + 1;

            else
                high = mid;
        }

        return low;
    }

    // Driver's code
    public static void main(String[] args)
    {
        int arr[] = { 1, 4, 5, 3, 19, 3 };
        int k = 3;

        // Function call
        System.out.print("Kth smallest element is "
                         + kthSmallest(arr, k));
    }
}

// This code is contributed by CodeWithMini

Python3

# Python3 code for kth smallest element in an array

import sys

# function to calculate number of elements
# less than equal to mid


def count(nums, mid):
    cnt = 0
    for i in range(len(nums)):
        if nums[i] <= mid:
            cnt += 1
    return cnt


def kthSmallest(nums, k):
    low = sys.maxsize
    high = -sys.maxsize - 1

    # calculate minimum and maximum the array.
    for i in range(len(nums)):
        low = min(low, nums[i])
        high = max(high, nums[i])

        # Our answer range lies between minimum and maximum element
        # of the array on which Binary Search is Applied
    while low < high:
        mid = low + (high - low) // 2
        # if the count of number of elements in the array less than equal
        # to mid is less than k then increase the number. Otherwise decrement
        # the number and try to find a better answer.
        if count(nums, mid) < k:
            low = mid + 1
        else:
            high = mid
    return low


# Driver's code
if __name__ == "__main__":
    nums = [1, 4, 5, 3, 19, 3]
    k = 3

    # Function call
    print("K'th smallest element is", kthSmallest(nums, k))

# This code is contributed by Tapesh(tapeshdua420)

C#

// C# program to implement
// the above approach

using System;
using System.Collections.Generic;

class GFG {
    static int count(int[] nums, int mid)
    {
        // function to calculate number of elements less
        // than equal to mid
        int cnt = 0;

        for (int i = 0; i < nums.Length; i++)
            if (nums[i] <= mid)
                cnt++;

        return cnt;
    }

    static int kthSmallest(int[] nums, int k)
    {
        int low = Int32.MaxValue;
        int high = Int32.MinValue;

        // calculate minimum and maximum the array.
        for (int i = 0; i < nums.Length; i++) {
            low = Math.Min(low, nums[i]);
            high = Math.Max(high, nums[i]);
        }

        // Our answer range lies between minimum
        // and maximum element of the array on which Binary
        // Search is Applied
        while (low < high) {
            int mid = low + (high - low) / 2;

            /*if the count of number of elements in the
                     array less than equal to mid is less
               than k then increase the number. Otherwise
                       decrement the number and try to find
               a better answer.
                     */
            if (count(nums, mid) < k)
                low = mid + 1;

            else
                high = mid;
        }

        return low;
    }

    // Driver's Code
    public static void Main()
    {

        // Given array
        int[] vec = { 1, 4, 5, 3, 19, 3 };

        // Given K
        int K = 3;

        // Function Call
        Console.WriteLine("Kth Smallest Element: "
                          + kthSmallest(vec, K));
    }
}

// This code is contributed by CodeWithMini

Javascript

// Javascript program to find the K’th
    // Smallest/Largest Element in Unsorted Array
    function count(nums, mid)
    {
    // function to calculate number of elements less than equal to mid
            var cnt = 0;

            for(var i = 0; i < nums.length; i++)
               if(nums[i] <= mid)
                  cnt++;

            return cnt;
    }

    function  kthSmallest(nums,k){
        var low = Number. MAX_VALUE;
        var high = Number. MIN_VALUE;
        // calculate minimum and maximum the array.
        for(var i = 0; i < nums.length; i++)
        {
            low = Math.min(low, nums[i]);
            high = Math.max(high, nums[i]);
        }
        // Our answer range lies between minimum and
        // maximum element of the array on which Binary Search is Applied
        while(low < high)
        {
            var mid = Math.floor(low + ((high - low) / 2));
           /*if the count of number of elements in the array
           less than equal to mid is less than k
             then increase the number. Otherwise
             decrement the number and try to find a better answer.
           */
            if(count(nums, mid) < k)
               low = mid + 1;

            else
                high = mid;
        }

        return low;
    }

    var k = 3;
    var nums = [1, 4, 5, 3, 19, 3];
    document.write("K'th smallest element is " + kthSmallest(nums, k));

    // This code is contributed by shruti456rawal

Output

K'th smallest element is 3

Time complexity: O(n * log (mx-mn)), where mn be minimum and mx be maximum.
Auxiliary Space: O(1)

Next:

• K’th Smallest/Largest Element in Unsorted Array | Set 2 (Expected Linear Time)
• K’th Smallest/Largest Element in Unsorted Array | Set 3 (Worst-Case Linear Time)