# Recursive Insertion Sort

Insertion sort is a simple sorting algorithm that works the way we sort playing cards in our hands.

Below is an iterative algorithm for insertion sort

Algorithm

```// Sort an arr[] of size n
insertionSort(arr, n)
Loop from i = 1 to n-1.
a) Pick element arr[i] and insert
it into sorted sequence arr[0..i-1] ```

Refer Insertion Sort for more details.

How to implement it recursively?
Recursive Insertion Sort has no performance/implementation advantages, but can be a good question to check one’s understanding of Insertion Sort and recursion.

If we take a closer look at Insertion Sort algorithm, we keep processed elements sorted and insert new elements one by one in the inserted array.

Recursion Idea.

1. Base Case: If array size is 1 or smaller, return.
2. Recursively sort first n-1 elements.
3. Insert last element at its correct position in sorted array.

Below is implementation of above idea.

## C/C++

 `// Recursive C++ program for insertion sort ` `#include ` `using` `namespace` `std; ` ` `  `// Recursive function to sort an array using ` `// insertion sort ` `void` `insertionSortRecursive(``int` `arr[], ``int` `n) ` `{ ` `    ``// Base case ` `    ``if` `(n <= 1) ` `        ``return``; ` ` `  `    ``// Sort first n-1 elements ` `    ``insertionSortRecursive( arr, n-1 ); ` ` `  `    ``// Insert last element at its correct position ` `    ``// in sorted array. ` `    ``int` `last = arr[n-1]; ` `    ``int` `j = n-2; ` ` `  `    ``/* Move elements of arr[0..i-1], that are ` `      ``greater than key, to one position ahead ` `      ``of their current position */` `    ``while` `(j >= 0 && arr[j] > last) ` `    ``{ ` `        ``arr[j+1] = arr[j]; ` `        ``j--; ` `    ``} ` `    ``arr[j+1] = last; ` `} ` ` `  `// A utility function to print an array of size n ` `void` `printArray(``int` `arr[], ``int` `n) ` `{ ` `    ``for` `(``int` `i=0; i < n; i++) ` `        ``cout << arr[i] <<``" "``; ` `} ` ` `  `/* Driver program to test insertion sort */` `int` `main() ` `{ ` `    ``int` `arr[] = {12, 11, 13, 5, 6}; ` `    ``int` `n = ``sizeof``(arr)/``sizeof``(arr); ` ` `  `    ``insertionSortRecursive(arr, n); ` `    ``printArray(arr, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Recursive Java program for insertion sort ` ` `  `import` `java.util.Arrays; ` ` `  `public` `class` `GFG  ` `{ ` `    ``// Recursive function to sort an array using ` `    ``// insertion sort ` `    ``static` `void` `insertionSortRecursive(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``// Base case ` `        ``if` `(n <= ``1``) ` `            ``return``; ` `      `  `        ``// Sort first n-1 elements ` `        ``insertionSortRecursive( arr, n-``1` `); ` `      `  `        ``// Insert last element at its correct position ` `        ``// in sorted array. ` `        ``int` `last = arr[n-``1``]; ` `        ``int` `j = n-``2``; ` `      `  `        ``/* Move elements of arr[0..i-1], that are ` `          ``greater than key, to one position ahead ` `          ``of their current position */` `        ``while` `(j >= ``0` `&& arr[j] > last) ` `        ``{ ` `            ``arr[j+``1``] = arr[j]; ` `            ``j--; ` `        ``} ` `        ``arr[j+``1``] = last; ` `    ``} ` `     `  `    ``// Driver Method ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = {``12``, ``11``, ``13``, ``5``, ``6``}; ` `      `  `        ``insertionSortRecursive(arr, arr.length); ` `         `  `        ``System.out.println(Arrays.toString(arr)); ` `    ``} ` `} `

## Python

 `# Recursive Python program for insertion sort ` `# Recursive function to sort an array using insertion sort ` ` `  `def` `insertionSortRecursive(arr,n): ` `    ``# base case ` `    ``if` `n<``=``1``: ` `        ``return` `     `  `    ``# Sort first n-1 elements ` `    ``insertionSortRecursive(arr,n``-``1``) ` `    ``'''Insert last element at its correct position ` `        ``in sorted array.'''` `    ``last ``=` `arr[n``-``1``] ` `    ``j ``=` `n``-``2` `     `  `      ``# Move elements of arr[0..i-1], that are ` `      ``# greater than key, to one position ahead ` `      ``# of their current position  ` `    ``while` `(j>``=``0` `and` `arr[j]>last): ` `        ``arr[j``+``1``] ``=` `arr[j] ` `        ``j ``=` `j``-``1` ` `  `    ``arr[j``+``1``]``=``last ` `     `  `# A utility function to print an array of size n ` `def` `printArray(arr,n): ` `    ``for` `i ``in` `range``(n): ` `        ``print` `arr[i], ` ` `  `# Driver program to test insertion sort  ` `arr ``=` `[``12``,``11``,``13``,``5``,``6``] ` `n ``=` `len``(arr) ` `insertionSortRecursive(arr, n) ` `printArray(arr, n) ` ` `  `# Contributed by Harsh Valecha `

## C#

 `// Recursive C# program  ` `// for insertion sort ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `    ``// Recursive function to sort  ` `    ``// an array using insertion sort ` `    ``static` `void` `insertionSortRecursive(``int` `[]arr,  ` `                                       ``int` `n) ` `    ``{ ` `        ``// Base case ` `        ``if` `(n <= 1) ` `            ``return``; ` `     `  `        ``// Sort first n-1 elements ` `        ``insertionSortRecursive(arr, n - 1); ` `     `  `        ``// Insert last element at  ` `        ``// its correct position ` `        ``// in sorted array. ` `        ``int` `last = arr[n - 1]; ` `        ``int` `j = n - 2; ` `     `  `        ``/* Move elements of arr[0..i-1],  ` `        ``that are greater than key, to  ` `        ``one position ahead of their ` `        ``current position */` `        ``while` `(j >= 0 && arr[j] > last) ` `        ``{ ` `            ``arr[j + 1] = arr[j]; ` `            ``j--; ` `        ``} ` `        ``arr[j + 1] = last; ` `    ``} ` `     `  `    ``//Driver Code ` `    ``static` `void` `Main() ` `    ``{ ` `        ``int` `[]arr = {12, 11, 13, 5, 6}; ` `     `  `        ``insertionSortRecursive(arr, arr.Length); ` `         `  `        ``for``(``int` `i = 0; i < arr.Length; i++) ` `        ``Console.Write(arr[i] + ``" "``); ` `    ``} ` `} ` ` `  `// This code is contributed by Sam007 `

## PHP

 `= 0 && ``\$arr``[``\$j``] > ``\$last``) ` `        ``{ ` `            ``\$arr``[``\$j` `+ 1] = ``\$arr``[``\$j``]; ` `            ``\$j``--; ` `        ``} ` `        ``\$arr``[``\$j` `+ 1] = ``\$last``; ` `    ``} ` `     `  `    ``// A utility function to  ` `    ``// print an array of size n ` `    ``function` `printArray(&``\$arr``, ``\$n``) ` `    ``{ ` `        ``for` `(``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++) ` `            ``echo` `\$arr``[``\$i``].``" "``; ` `    ``} ` ` `  `// Driver Code ` `\$arr` `= ``array``(12, 11, 13, 5, 6); ` `\$n` `= sizeof(``\$arr``); ` ` `  `insertionSortRecursive(``\$arr``, ``\$n``); ` `printArray(``\$arr``, ``\$n``); ` ` `  `// This code is contributed by ChitraNayal. ` `?> `

Output :

`5 6 11 12 13 `

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Improved By : Sam007, chitranayal

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