kth smallest/largest in a small range unsorted array

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Find kth smallest or largest element in an unsorted array, where k<=size of array. It is given that elements of array are in small range.

Examples:

Input : arr[] = {3, 2, 9, 5, 7, 11, 13}
        k = 5
Output: 9

Input : arr[] = {16, 8, 9, 21, 43}
        k = 3
Output: 16

Input : arr[] = {50, 50, 40}
        k = 2
Output: 50

As the given array elements are in a small range, we can direct the index table to do something similar to counting sort. We store counts of elements, then we traverse the count array and print k-th element.

Implementation: Following is the implementation of the above algorithm

C++

// C++ program of kth smallest/largest in 
// a small range unsorted array
#include <bits/stdc++.h>
using namespace std;
#define maxs 1000001
 
int kthSmallestLargest(int* arr, int n, int k)
{
    int max_val = *max_element(arr, arr+n);
    int hash[max_val+1] = { 0 };
 
    // Storing counts of elements
    for (int i = 0; i < n; i++) 
        hash[arr[i]]++;    
     
    // Traverse hash array build above until
    // we reach k-th smallest element.
    int count = 0;
    for (int i=0; i <= max_val; i++)
    {
        while (hash[i] > 0)
        {
           count++;
           if (count == k)
              return i;
           hash[i]--;
        }
    }
     
    return -1;
}
 
int main()
{
    int arr[] = { 11, 6, 2, 9, 4, 3, 16 };
    int n = sizeof(arr) / sizeof(arr[0]), k = 3;
    cout << "kth smallest number is: "
         << kthSmallestLargest(arr, n, k) << endl;
    return 0;
}

Java

// Java program of kth smallest/largest in 
// a small range unsorted array 
import java.util.Arrays;
 
class GFG 
{
 
    static int maxs = 1000001;
 
    static int kthSmallestLargest(int[] arr, int n, int k) 
    {
        int max_val = Arrays.stream(arr).max().getAsInt();
        int hash[] = new int[max_val + 1];
 
        // Storing counts of elements
        for (int i = 0; i < n; i++) 
        {
            hash[arr[i]]++;
        }
 
        // Traverse hash array build above until
        // we reach k-th smallest element.
        int count = 0;
        for (int i = 0; i <= max_val; i++)
        {
            while (hash[i] > 0) 
            {
                count++;
                if (count == k) 
                {
                    return i;
                }
                hash[i]--;
            }
        }
 
        return -1;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int arr[] = {11, 6, 2, 9, 4, 3, 16};
        int n = arr.length, k = 3;
        System.out.println("kth smallest number is: "
                + kthSmallestLargest(arr, n, k));
    }
}
 
// This code has been contributed by 29AjayKumar

Python3

# Python 3 program of kth smallest/largest 
# in a small range unsorted array
 
def kthSmallestLargest(arr, n, k):
    max_val = arr[0]
    for i in range(len(arr)):
        if (arr[i] > max_val):
            max_val = arr[i]
    hash = [0 for i in range(max_val + 1)] 
 
    # Storing counts of elements
    for i in range(n):
        hash[arr[i]] += 1
     
    # Traverse hash array build above until
    # we reach k-th smallest element.
    count = 0
    for i in range(max_val + 1):
        while (hash[i] > 0):
            count += 1
            if (count == k):
                return i
            hash[i] -= 1
         
    return -1
 
# Driver Code
if __name__ == '__main__':
    arr = [11, 6, 2, 9, 4, 3, 16]
    n = len(arr)
    k = 3
    print("kth smallest number is:",
           kthSmallestLargest(arr, n, k))
     
# This code is contributed by
# Surendra_Gangwar

C#

// C# program of kth smallest/largest in 
// a small range unsorted array 
using System;
using System.Linq;
 
class GFG 
{ 
 
    static int maxs = 1000001; 
 
    static int kthSmallestLargest(int[] arr, int n, int k) 
    { 
        int max_val = arr.Max(); 
        int []hash = new int[max_val + 1]; 
 
        // Storing counts of elements 
        for (int i = 0; i < n; i++) 
        { 
            hash[arr[i]]++; 
        } 
 
        // Traverse hash array build above until 
        // we reach k-th smallest element. 
        int count = 0; 
        for (int i = 0; i <= max_val; i++) 
        { 
            while (hash[i] > 0) 
            { 
                count++; 
                if (count == k) 
                { 
                    return i; 
                } 
                hash[i]--; 
            } 
        } 
        return -1; 
    } 
 
    // Driver code 
    public static void Main() 
    { 
        int []arr = {11, 6, 2, 9, 4, 3, 16}; 
        int n = arr.Length, k = 3; 
        Console.WriteLine("kth smallest number is: "
                + kthSmallestLargest(arr, n, k)); 
    } 
} 
 
/* This code contributed by PrinciRaj1992 */

PHP

<?php
// PHP program of kth smallest/largest in 
// a small range unsorted array
$maxs = 1000001;
  
function kthSmallestLargest(&$arr, $n, $k)
{
    global $maxs;
    $max_val = max($arr);
    $hash = array_fill(0,$max_val+1, NULL);
  
    // Storing counts of elements
    for ($i = 0; $i < $n; $i++) 
        $hash[$arr[$i]]++;    
      
    // Traverse hash array build above until
    // we reach k-th smallest element.
    $count = 0;
    for ($i=0; $i <= $max_val; $i++)
    {
        while ($hash[$i] > 0)
        {
           $count++;
           if ($count == $k)
              return $i;
           $hash[$i]--;
        }
    }
      
    return -1;
}
  
 
    $arr = array ( 11, 6, 2, 9, 4, 3, 16 );
    $n = sizeof($arr) / sizeof($arr[0]);
    $k = 3;
    echo "kth smallest number is: "
         . kthSmallestLargest($arr, $n, $k)."\n";
    return 0;
?>

Javascript

<script>
// Javascript program of kth smallest/largest in 
// a small range unsorted array 
     
    let maxs = 1000001;
    function kthSmallestLargest(arr,n,k)
    {
        let max_val = Math.max(...arr);
        let hash = new Array(max_val + 1);
        for(let i=0;i<hash.length;i++)
        {
            hash[i]=0;
        }
   
        // Storing counts of elements
        for (let i = 0; i < n; i++) 
        {
            hash[arr[i]]++;
        }
   
        // Traverse hash array build above until
        // we reach k-th smallest element.
        let count = 0;
        for (let i = 0; i <= max_val; i++)
        {
            while (hash[i] > 0) 
            {
                count++;
                if (count == k) 
                {
                    return i;
                }
                hash[i]--;
            }
        }
   
        return -1;
    }
     
    // Driver code
    let arr=[11, 6, 2, 9, 4, 3, 16];
    let n = arr.length, k = 3;
    document.write("kth smallest number is: "
                + kthSmallestLargest(arr, n, k));
     
 
// This code is contributed by avanitrachhadiya2155
</script>

Output

kth smallest number is: 4

Complexity Analysis:

Time Complexity: O(n + max_val)
Auxiliary Space: O(n) for hash array.

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