# Recursive Selection Sort

• Difficulty Level : Medium
• Last Updated : 13 Jun, 2022

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 ``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);` `    ``// Calling function``    ``recurSelectionSort(arr, n);` `    ``//printing sorted array``    ``for` `(``int` `i = 0; i

## 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 nd 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`

Output:

`0 1 2 3 5 7 `

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

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