Recursive Selection Sort

The Selection Sort algorithm sorts maintain two parts. 

1. The first part that is already sorted
2. The second part is yet to be sorted.

The algorithm works by repeatedly finding the minimum element (considering ascending order) from the unsorted part and putting it at the end of the sorted part. 

arr[] = 64 25 12 22 11

// Find the minimum element in arr[0...4]
// and place it at beginning
11 25 12 22 64

// Find the minimum element in arr[1...4]
// and place it at beginning of arr[1...4]
11 12 25 22 64

// Find the minimum element in arr[2...4]
// and place it at beginning of arr[2...4]
11 12 22 25 64

// Find the minimum element in arr[3...4]
// and place it at beginning of arr[3...4]
11 12 22 25 64 

We have already discussed Iterative Selection Sort. In this article recursive approach is discussed. The idea of a recursive solution is to one by one increment sorted part and recursively call for the remaining (yet to be sorted) part.

C++

// Recursive C++ program to sort an array
// using selection sort
#include <iostream>
using namespace std;

// Return minimum index
int minIndex(int a[], int i, int j)
{
    if (i == j)
        return i;

    // Find minimum of remaining elements
    int k = minIndex(a, i + 1, j);

    // Return minimum of current and remaining.
    return (a[i] < a[k])? i : k;
}

// Recursive selection sort. n is size of a[] and index
// is index of starting element.
void recurSelectionSort(int a[], int n, int index = 0)
{
    // Return when starting and size are same
    if (index == n)
       return;

    // calling minimum index function for minimum index
    int k = minIndex(a, index, n-1);

    // Swapping when index and minimum index are not same
    if (k != index)
       swap(a[k], a[index]);

    // Recursively calling selection sort function
    recurSelectionSort(a, n, index + 1);
}

// Driver code
int main()
{
    int arr[] = {3, 1, 5, 2, 7, 0};
    int n = sizeof(arr)/sizeof(arr[0]);

    // Calling function
    recurSelectionSort(arr, n);

    //printing sorted array
    for (int i = 0; i<n ; i++)
        cout << arr[i] << " ";
    cout << endl;
    return 0;
}

Java

// Recursive Java program to sort an array
// using selection sort

class Test
{
    // Return minimum index
    static int minIndex(int a[], int i, int j)
    {
        if (i == j)
            return i;

        // Find minimum of remaining elements
        int k = minIndex(a, i + 1, j);

        // Return minimum of current and remaining.
        return (a[i] < a[k])? i : k;
    }

    // Recursive selection sort. n is size of a[] and index
    // is index of starting element.
    static void recurSelectionSort(int a[], int n, int index)
    {

        // Return when starting and size are same
        if (index == n)
           return;

        // calling minimum index function for minimum index
        int k = minIndex(a, index, n-1);

        // Swapping when index and minimum index are not same
        if (k != index){
           // swap
           int temp = a[k];
           a[k] = a[index];
           a[index] = temp;
        }
        // Recursively calling selection sort function
        recurSelectionSort(a, n, index + 1);
    }


    // Driver method
    public static void main(String args[])
    {
        int arr[] = {3, 1, 5, 2, 7, 0};

        // Calling function
        recurSelectionSort(arr, arr.length, 0);

        //printing sorted array
        for (int i = 0; i< arr.length; i++)
            System.out.print(arr[i] + " ");
    }
}

Python3

# Recursive Python3 code to sort
# an array using selection sort

# Return minimum index
def minIndex( a , i , j ):
    if i == j:
        return i

    # Find minimum of remaining elements
    k = minIndex(a, i + 1, j)

    # Return minimum of current
    # and remaining.
    return (i if a[i] < a[k] else k)

# Recursive selection sort. n is
# size of a[] and index is index of
# starting element.
def recurSelectionSort(a, n, index = 0):

    # Return when starting and
    # size are same
    if index == n:
        return -1

    # calling minimum index function
    # for minimum index
    k = minIndex(a, index, n-1)

    # Swapping when index and minimum
    # index are not same
    if k != index:
        a[k], a[index] = a[index], a[k]

    # Recursively calling selection
    # sort function
    recurSelectionSort(a, n, index + 1)

# Driver code
arr = [3, 1, 5, 2, 7, 0]
n = len(arr)

# Calling function
recurSelectionSort(arr, n)

# printing sorted array
for i in arr:
    print(i, end = ' ')

# This code is contributed by "Sharad_Bhardwaj".

C#

// Recursive C# program to sort an array
// using selection sort
using System;

class GFG
{
    // Return minimum index
    static int minIndex(int []a, int i, int j)
    {
        if (i == j)
            return i;

        // Find minimum of remaining elements
        int k = minIndex(a, i + 1, j);

        // Return minimum of current and remaining.
        return (a[i] < a[k])? i : k;
    }

    // Recursive selection sort. n is size of
    // a[] and index is index of starting element.
    static void recurSelectionSort(int []a, int n,
                                   int index)
    {

        // Return when starting and size are same
        if (index == n)
        return;

        // calling minimum index function
        // for minimum index
        int k = minIndex(a, index, n - 1);

        // Swapping when index and minimum index
        // are not same
        if (k != index)
        {
            // swap
            int temp = a[k];
            a[k] = a[index];
            a[index] = temp;
        }

        // Recursively calling selection sort function
        recurSelectionSort(a, n, index + 1);
    }

    // Driver Code
    public static void Main(String []args)
    {
        int []arr = {3, 1, 5, 2, 7, 0};

        // Calling function
        recurSelectionSort(arr, arr.Length, 0);

        //printing sorted array
        for (int i = 0; i< arr.Length; i++)
            Console.Write(arr[i] + " ");
    }
}

// This code is contributed by Princi Singh

Javascript

// Recursive JavaScript program to sort an array
// using selection sort

// Return minimum index
function minIndex(a, i, j) {
    if (i == j)
        return i;

    // Find minimum of remaining elements
    var k = minIndex(a, i + 1, j);

    // Return minimum of current and remaining.
    return (a[i] < a[k])? i : k;
}

// Recursive selection sort. n is size of a[] and index
// is index of starting element.
function recurSelectionSort(a, n, index = 0) {
    // Return when starting and size are same
    if (index == n)
        return;

    // calling minimum index function for minimum index
    var k = minIndex(a, index, n-1);

    // Swapping when index and minimum index are not same
    if (k != index)
        [a[k], a[index]] = [a[index], a[k]];

    // Recursively calling selection sort function
    recurSelectionSort(a, n, index + 1);
}

// Driver code
var arr = [3, 1, 5, 2, 7, 0];
var n = arr.length;

// Calling function
recurSelectionSort(arr, n);

//printing sorted array
console.log(arr.join(' '));

Output:

0 1 2 3 5 7 

Time Complexity: O(n²)
Auxiliary Space: O(n)

This article is contributed by Sahil Rajput. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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