# Insertion Sort

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

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]

Example: Another Example:
12, 11, 13, 5, 6

Let us loop for i = 1 (second element of the array) to 4 (last element of the array)

i = 1. Since 11 is smaller than 12, move 12 and insert 11 before 12
11, 12, 13, 5, 6

i = 2. 13 will remain at its position as all elements in A[0..I-1] are smaller than 13
11, 12, 13, 5, 6

i = 3. 5 will move to the beginning and all other elements from 11 to 13 will move one position ahead of their current position.
5, 11, 12, 13, 6

i = 4. 6 will move to position after 5, and elements from 11 to 13 will move one position ahead of their current position.
5, 6, 11, 12, 13

## C/C++

 `// C program for insertion sort ` `#include ` `#include ` ` `  `/* Function to sort an array using insertion sort*/` `void` `insertionSort(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `i, key, j; ` `    ``for` `(i = 1; i < n; i++) { ` `        ``key = arr[i]; ` `        ``j = i - 1; ` ` `  `        ``/* 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] > key) { ` `            ``arr[j + 1] = arr[j]; ` `            ``j = j - 1; ` `        ``} ` `        ``arr[j + 1] = key; ` `    ``} ` `} ` ` `  `// A utility function to print an array of size n ` `void` `printArray(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `i; ` `    ``for` `(i = 0; i < n; i++) ` `        ``printf``(``"%d "``, arr[i]); ` `    ``printf``(````" "````); ` `} ` ` `  `/* Driver program to test insertion sort */` `int` `main() ` `{ ` `    ``int` `arr[] = { 12, 11, 13, 5, 6 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``insertionSort(arr, n); ` `    ``printArray(arr, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program for implementation of Insertion Sort ` `class` `InsertionSort { ` `    ``/*Function to sort array using insertion sort*/` `    ``void` `sort(``int` `arr[]) ` `    ``{ ` `        ``int` `n = arr.length; ` `        ``for` `(``int` `i = ``1``; i < n; ++i) { ` `            ``int` `key = arr[i]; ` `            ``int` `j = i - ``1``; ` ` `  `            ``/* 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] > key) { ` `                ``arr[j + ``1``] = arr[j]; ` `                ``j = j - ``1``; ` `            ``} ` `            ``arr[j + ``1``] = key; ` `        ``} ` `    ``} ` ` `  `    ``/* A utility function to print array of size n*/` `    ``static` `void` `printArray(``int` `arr[]) ` `    ``{ ` `        ``int` `n = arr.length; ` `        ``for` `(``int` `i = ``0``; i < n; ++i) ` `            ``System.out.print(arr[i] + ``" "``); ` ` `  `        ``System.out.println(); ` `    ``} ` ` `  `    ``// Driver method ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `arr[] = { ``12``, ``11``, ``13``, ``5``, ``6` `}; ` ` `  `        ``InsertionSort ob = ``new` `InsertionSort(); ` `        ``ob.sort(arr); ` ` `  `        ``printArray(arr); ` `    ``} ` `} ``/* This code is contributed by Rajat Mishra. */`

## Python

 `# Python program for implementation of Insertion Sort ` ` `  `# Function to do insertion sort ` `def` `insertionSort(arr): ` ` `  `    ``# Traverse through 1 to len(arr) ` `    ``for` `i ``in` `range``(``1``, ``len``(arr)): ` ` `  `        ``key ``=` `arr[i] ` ` `  `        ``# Move elements of arr[0..i-1], that are ` `        ``# greater than key, to one position ahead ` `        ``# of their current position ` `        ``j ``=` `i``-``1` `        ``while` `j >``=` `0` `and` `key < arr[j] : ` `                ``arr[j ``+` `1``] ``=` `arr[j] ` `                ``j ``-``=` `1` `        ``arr[j ``+` `1``] ``=` `key ` ` `  ` `  `# Driver code to test above ` `arr ``=` `[``12``, ``11``, ``13``, ``5``, ``6``] ` `insertionSort(arr) ` `for` `i ``in` `range``(``len``(arr)): ` `    ``print` `(``"% d"` `%` `arr[i]) ` ` `  `# This code is contributed by Mohit Kumra `

## C#

 `// C# program for implementation of Insertion Sort ` `using` `System; ` ` `  `class` `InsertionSort { ` ` `  `    ``// Function to sort array ` `    ``// using insertion sort ` `    ``void` `sort(``int``[] arr) ` `    ``{ ` `        ``int` `n = arr.Length; ` `        ``for` `(``int` `i = 1; i < n; ++i) { ` `            ``int` `key = arr[i]; ` `            ``int` `j = i - 1; ` ` `  `            ``// 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] > key) { ` `                ``arr[j + 1] = arr[j]; ` `                ``j = j - 1; ` `            ``} ` `            ``arr[j + 1] = key; ` `        ``} ` `    ``} ` ` `  `    ``// A utility function to print ` `    ``// array of size n ` `    ``static` `void` `printArray(``int``[] arr) ` `    ``{ ` `        ``int` `n = arr.Length; ` `        ``for` `(``int` `i = 0; i < n; ++i) ` `            ``Console.Write(arr[i] + ``" "``); ` ` `  `        ``Console.Write(````" "````); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int``[] arr = { 12, 11, 13, 5, 6 }; ` `        ``InsertionSort ob = ``new` `InsertionSort(); ` `        ``ob.sort(arr); ` `        ``printArray(arr); ` `    ``} ` `} ` ` `  `// This code is contributed by ChitraNayal. `

## PHP

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

Output:

`5 6 11 12 13`

Time Complexity: O(n*2)

Auxiliary Space: O(1)

Boundary Cases: Insertion sort takes maximum time to sort if elements are sorted in reverse order. And it takes minimum time (Order of n) when elements are already sorted.

Sorting In Place: Yes

Stable: Yes

Online: Yes

Uses: Insertion sort is used when number of elements is small. It can also be useful when input array is almost sorted, only few elements are misplaced in complete big array.

What is Binary Insertion Sort?
We can use binary search to reduce the number of comparisons in normal insertion sort. Binary Insertion Sort uses binary search to find the proper location to insert the selected item at each iteration. In normal insertion, sorting takes O(i) (at ith iteration) in worst case. We can reduce it to O(logi) by using binary search. The algorithm, as a whole, still has a running worst case running time of O(n2) because of the series of swaps required for each insertion. Refer this for implementation.

How to implement Insertion Sort for Linked List?
Below is simple insertion sort algorithm for linked list.

```1) Create an empty sorted (or result) list
2) Traverse the given list, do following for every node.
......a) Insert current node in sorted way in sorted or result list.

Refer this for implementation.