Sorting all array elements except one

Given an array, a positive integer, sort the array in ascending order such that the element at index K in the unsorted array stays unmoved and all other elements are sorted. 

Examples:

Input : arr[] = {10, 4, 11, 7, 6, 20}
            k = 2;
Output : arr[] = {4, 6, 11, 7, 10, 20}

Input : arr[] = {30, 20, 10}
         k = 0
Output : arr[] = {30, 10, 20} 

A simple solution is to copy all elements except k-th of a given array to another array. Then sort the other array using a sorting algorithm. Finally, again copy the sorted array to the original array. While copying, skip k-th element.

Below is an efficient solution.  

1. Swap k-th element with the last element.
2. Sort all elements except the last.
3. For every element from (k+1)-th to last, move them one position ahead.1
4. Copy k-th element back to position k. 

C++

// CPP program to sort all elements except
// element at index k.
#include <bits/stdc++.h>
using namespace std;

int sortExceptK(int arr[], int k, int n)
{
    // Move k-th element to end
    swap(arr[k], arr[n-1]);

    // Sort all elements except last
    sort(arr, arr + n - 1);

    // Store last element (originally k-th)
    int last = arr[n-1];

    // Move all elements from k-th to one
    // position ahead.
    for (int i=n-1; i>k; i--)
       arr[i] = arr[i-1];

    // Restore k-th element
    arr[k] = last;
}

// Driver code
int main()
{
    int a[] = {10, 4, 11, 7, 6, 20 };
    int k = 2;
    int n = sizeof(a) / sizeof(a[0]);
    sortExceptK(a, k, n);
    for (int i = 0; i < n; i++)
        cout << a[i] << " ";
}

Java

// Java program to sort all elements except
// element at index k.
import java.util.Arrays;

class GFG {

    static int sortExceptK(int arr[], int k, int n)
    {

        // Move k-th element to end
        int temp = arr[k];
        arr[k] = arr[n-1];
        arr[n-1] = temp;

        // Sort all elements except last
        Arrays.sort(arr, 0, n-1);

        // Store last element (originally k-th)
        int last = arr[n-1];

        // Move all elements from k-th to one
        // position ahead.
        for (int i = n-1; i > k; i--)
        arr[i] = arr[i-1];

        // Restore k-th element
        arr[k] = last;
        return 0;
    }

    //Driver code
    public static void main (String[] args)
    {
        int a[] = {10, 4, 11, 7, 6, 20 };
        int k = 2;
        int n = a.length;

        sortExceptK(a, k, n);

        for (int i = 0; i < n; i++)
            System.out.print(a[i] + " ");
    }
}

//This code is contributed by Anant Agarwal.

Python3

# Python3 program to sort all elements except
# element at index k.
def sortExcept(arr, k, n):

    # Move k-th element to end
    arr[k], arr[-1] = arr[-1], arr[k]

    # Sort all elements except last
    arr = sorted(arr, key = lambda i: (i is arr[-1], i))

    # Store last element (originally k-th)
    last = arr[-1]

    # Move all elements from k-th to one
    # position ahead.
    i = n - 1
    while i > k:
        arr[i] = arr[i - 1]
        i -= 1

    # Restore k-th element
    arr[k] = last
    return arr

# Driver code
if __name__ == '__main__':
    a = [10, 4, 11, 7, 6, 20]
    k = 2
    n = len(a)
    a = sortExcept(a, k, n)
    print(" ".join(list(map(str, a))))

# This code is contributed by Shivam Singh.

C#

// C# program to sort all elements except
// element at index k.
using System;

public class GFG {

    static int sortExceptK(int[] arr, int k, int n)
    {
        // Move k-th element to end
        int temp = arr[k];
        arr[k] = arr[n - 1];
        arr[n - 1] = temp;

        // Sort all elements except last
        Array.Sort(arr, 0, n - 1);

        // Store last element (originally k-th)
        int last = arr[n - 1];

        // Move all elements from k-th to one
        // position ahead.
        for (int i = n - 1; i > k; i--)
            arr[i] = arr[i - 1];

        // Restore k-th element
        arr[k] = last;

        return 0;
    }

    // Driver code
    public static void Main()
    {
        int[] a = { 10, 4, 11, 7, 6, 20 };
        int k = 2;
        int n = a.Length;

        sortExceptK(a, k, n);

        for (int i = 0; i < n; i++)
        Console.Write(a[i] + " ");
    }
}

// This article is contributed by shiv_bhakt

PHP

<?php
// PHP program to sort all
// elements except element
// at index k.
function sortExceptK(&$arr, $k, $n)
{
    // Move k-th element to end
    $t = $arr[$k];
    $arr[$k] = $arr[$n - 1];
    $arr[$n - 1] = $t;

    // Sort all elements
    // except last
    $t = $arr[count($arr) - 1];
    $arr = array_slice($arr, 0, -1);
    sort($arr);
    array_push($arr, $t);

    // Store last element
    // (originally k-th)
    $last = $arr[$n - 1];

    // Move all elements from
    // k-th to one position ahead.
    for ($i = $n - 1; $i > $k; $i--)
    $arr[$i] = $arr[$i - 1];

    // Restore k-th element
    $arr[$k] = $last;
}

// Driver code
$a = array(10, 4, 11,
            7, 6, 20 );
$k = 2;
$n = count($a);
sortExceptK($a, $k, $n);

for ($i = 0; $i < $n; $i++)
    echo ($a[$i]." ");

// This code is contributed by
// Manish Shaw(manishshaw1)
?>

Javascript

<script>
    // Javascript program to sort all elements except
    // element at index k.

    function sortExceptK(arr, k, n)
    {

        // Move k-th element to end
        let temp = arr[k];
        arr[k] = arr[n-1];
        arr[n-1] = temp;

        // Sort all elements except last
        arr.sort(function(a, b){
            return a - b});

        // Store last element (originally k-th)
        let last = arr[n-1];

        // Move all elements from k-th to one
        // position ahead.
        for (let i = n-1; i > k; i--)
            arr[i] = arr[i-1];

        // Restore k-th element
        arr[k] = last;

        // Move k-th element to end
        temp = arr[k];
        arr[k] = arr[n-1];
        arr[n-1] = temp;

        return 0;
    }

    let a = [10, 4, 11, 7, 6, 20 ];
    let k = 2;
    let n = a.length;

    sortExceptK(a, k, n);

    for(let i = 0; i < n; i++)
      document.write(a[i] + " ");

</script>

Output:

4 6 11 7 10 20 

Time Complexity: O(n*log(n)) where n is the number of elements.
Auxiliary Space: O(1)