K’th Smallest/Largest Element in Unsorted Array | Set 1

Difficulty Level : Medium
Last Updated : 03 Jul, 2021

Given an array and a number k where k is smaller than the size of the array, we need to find the k’th smallest element in the given array. It is 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.

Method 1 (Simple Solution)
A simple solution is to sort the given array using a O(N log N) sorting algorithm like Merge Sort, Heap Sort, etc, and return the element at index k-1 in the sorted array.
Time Complexity of this solution is O(N Log N)

C++

// Simple C++ program to find k'th smallest element
#include <algorithm>
#include <iostream>
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 program to test above methods
int main()
{
    int arr[] = { 12, 3, 5, 7, 19 };
    int n = sizeof(arr) / sizeof(arr[0]), k = 2;
    cout << "K'th smallest element is " << kthSmallest(arr, n, k);
    return 0;
}

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 program
    public static void main(String[] args)
    {
        Integer arr[] = new Integer[] { 12, 3, 5, 7, 19 };
        int k = 2;
        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
    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 program
    public static void Main()
    {
        int[] arr = new int[] { 12, 3, 5,
                                7, 19 };
        int k = 2;
        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 Code
    $arr = array(12, 3, 5, 7, 19);
    $n =count($arr);
    $k = 2;
    echo "K'th smallest element is ", kthSmallest($arr, $n, $k);
 
// This code is contributed by anuj_67.
?>

Javascript

<script>
 
// 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
</script>

Output

K'th smallest element is 5

Method 2 (using set from C++ STL)

we can find the kth smallest element in time complexity better than O(N log N). we know the Set in C++ STL is implemented using Binary Search Tree and we also know that the time compexity of all cases(searching , inserting, deleting ) in BST is log (n) in average case and O(n) in worst case . we are using set because it is mentioned in the question that all the elements in array re distinct.

The following is C++ implementation of above method.

C++

/* the following code demonstrates how to find kth smallest
element using set from C++ STL */
 
#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);
    set<int>::iterator itr
        = s.begin(); // s.begin() returns a pointer to first
                     // element in the set
    advance(itr, k - 1); // itr points to kth element in set
 
    cout << *itr << "\n";
 
    return 0;
}

Output

Time Complexity: O( log N) in Average Case and O(N) in Worst Case
Auxiliary Space: O(N)

Method 3 (Using Min Heap – HeapSelect)
We can find k’th smallest element in time complexity better than O(N Log N). A simple optimization is to create a Min Heap of the given n elements and call extractMin() k times.

The following is C++ implementation of above method.

C++

// A 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
    void MinHeapify(int i); // To minheapify 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 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 vakue.
    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 program to test above methods
int main()
{
    int arr[] = { 12, 3, 5, 7, 19 };
    int n = sizeof(arr) / sizeof(arr[0]), k = 2;
    cout << "K'th smallest element is " << kthSmallest(arr, n, k);
    return 0;
}

Java

// A Java program to find k'th smallest element using min heap
import java.util.*;
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 vakue.
      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 program to test above methods
  public static void main(String[] args)
  {
    int arr[] = { 12, 3, 5, 7, 19 };
    int n = arr.length, k = 2;
    GFG gfg = new GFG();
    System.out.print("K'th smallest element is " +
                     gfg.kthSmallest(arr, n, k));
  }
}
 
// This code is contributed by avanitrachhadiya2155

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 vakue.
      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 program to test above methods
  static public void Main (){
    int[] arr = { 12, 3, 5, 7, 19 };
    int n = arr.Length, k = 2;
    GFG gfg = new GFG();
    Console.Write("K'th smallest element is " +
                  gfg.kthSmallest(arr, n, k));
  }
}
 
// This code is contributed by rag2127

Output

K'th smallest element is 5

Time complexity of this solution is O(n + kLogn).

Method 4 (Using Max-Heap)
We can also use Max Heap for finding the k’th smallest element. Following is an algorithm.
1) Build a Max-Heap MH of the first k elements (arr[0] to arr[k-1]) of the given array. O(k)
2) For each element, after the k’th element (arr[k] to arr[n-1]), compare it with root of MH.
……a) If the element is less than the root then make it root and call heapify for MH
……b) Else ignore it.
// The step 2 is O((n-k)*logk)
3) Finally, the root of the MH is the kth smallest element.
Time complexity of this solution is O(k + (n-k)*Logk)

The following is C++ implementation of the above algorithm

C++

// A C++ program to find k'th smallest element using max 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 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 vakue.
    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 program to test above methods
int main()
{
    int arr[] = { 12, 3, 5, 7, 19 };
    int n = sizeof(arr) / sizeof(arr[0]), k = 4;
    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 vakue.
      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 program to test above methods
  public static void main(String[] args)
  {
    int arr[] = { 12, 3, 5, 7, 19 };
    int n = arr.length, k = 4;
    GFG gfg = new GFG();
    System.out.print("K'th smallest element is " + 
                     gfg.kthSmallest(arr, n, k));
  }
}
 
// This code is contributed by Rajput-Ji

C#

// A 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 vakue.
            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 code
    public static void Main(String[] args)
    {
        int[] arr = { 12, 3, 5, 7, 19 };
        int n = arr.Length, k = 4;
        GFG gfg = new GFG();
        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

Method 5 (QuickSelect)
This is an optimization over method 1 if QuickSort is used as a sorting algorithm in first step. In QuickSort, we 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. The worst case time complexity of this method is O(n²), but it works in O(n) on average.

C++

#include <climits>
#include <iostream>
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 program to test above methods
int main()
{
    int arr[] = { 12, 3, 5, 7, 4, 19, 26 };
    int n = sizeof(arr) / sizeof(arr[0]), k = 3;
    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 program to test above methods
    public static void main(String[] args)
    {
        Integer arr[] = new Integer[] { 12, 3, 5, 7, 4, 19, 26 };
        int k = 3;
        System.out.print("K'th smallest element is " + kthSmallest(arr, 0, arr.length - 1, k));
    }
}
 
// This code is contributed by Chhavi

Python3

# 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 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 Code
    public static void Main()
    {
        int[] arr = { 12, 3, 5, 7, 4, 19, 26 };
        int k = 3;
        Console.Write("K'th smallest element is " + kthSmallest(arr, 0, arr.Length - 1, k));
    }
}
 
// This code is contributed
// by 29AjayKumar

Javascript

<script>
 
// 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
 
</script>

Output

K'th smallest element is 5

Method 6 (Map STL)

A map based STL approach is although very much similar to the quickselect and counting sort algorithm but much easier to implement. We can use an ordered map and map each element with it’s frequency. And as we know that an ordered map would store the data in an sorted manner, we keep on adding the frequency of each element till it does not become greater than or equal to k so that we reach the k’th element from the start i.e. the k’th smallest element.

Eg –

Array={7,0,25,6,16,17,0}

k=3

Now in order to get the k’th largest element, we need to add the frequencies till it becomes greater than or equal to 3. It is clear from the above that the frequency of 0 + frequency of 6 will become equal to 3 so the third smallest number in the array will be 6.

We can achieve the above using an iterator to traverse the map.

C++

#include <bits/stdc++.h>
using namespace std;
int Kth_smallest(map<int, int> m, int k)
{
    int freq = 0;
    for (auto it = m.begin(); it != m.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
}
int main()
{
    int n = 5;
    int k = 2;
    vector<int> arr = { 12, 3, 5, 7, 19 };
    map<int, int> m;
    for (int i = 0; i < n; i++) {
        m[arr[i]] += 1; // mapping every element with it's
                        // frequency
    }
    int ans = Kth_smallest(m, k);
    cout << "The " << k << "rd smallest element is " << ans
         << endl;
    return 0;
}

Output

The 2rd smallest element is 5

There are two more solutions which are better than above discussed ones: One solution is to do randomized version of quickSelect() and other solution is the worst case linear time algorithm (see the following posts).
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)

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