kth smallest/largest in a small range unsorted array

Last Updated : 07 Sep, 2022

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# 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.

K’th Smallest Element in Unsorted Array

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