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Insertion Sort Algorithm - GeeksforGeeks

Insertion Sort Algorithm

Last Updated : 23 Jul, 2025

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Insertion sort is a simple sorting algorithm that works by iteratively inserting each element of an unsorted list into its correct position in a sorted portion of the list. It is like sorting playing cards in your hands. You split the cards into two groups: the sorted cards and the unsorted cards. Then, you pick a card from the unsorted group and put it in the right place in the sorted group.

We start with the second element of the array as the first element is assumed to be sorted.
Compare the second element with the first element if the second element is smaller then swap them.
Move to the third element, compare it with the first two elements, and put it in its correct position
Repeat until the entire array is sorted.

C++


 // C++ program for implementation of Insertion Sort
#include <iostream>
using namespace std;

/* Function to sort array using insertion sort */
void insertionSort(int arr[], int n)
{
    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 */
void printArray(int arr[], int n)
{
    for (int i = 0; i < n; ++i)
        cout << arr[i] << " ";
    cout << endl;
}

// Driver method
int main()
{
    int arr[] = { 12, 11, 13, 5, 6 };
    int n = sizeof(arr) / sizeof(arr[0]);

    insertionSort(arr, n);
    printArray(arr, n);

    return 0;
}

/* This code is contributed by Hritik Shah. */


 // C program for implementation of Insertion Sort
#include <stdio.h>

/* Function to sort array using insertion sort */
void insertionSort(int arr[], int n)
{
    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 */
void printArray(int arr[], int n)
{
    for (int i = 0; i < n; ++i)
        printf("%d ", arr[i]);
    printf("\n");
}

// Driver method
int main()
{
    int arr[] = { 12, 11, 13, 5, 6 };
    int n = sizeof(arr) / sizeof(arr[0]);

    insertionSort(arr, n);
    printArray(arr, n);

    return 0;
}

/* This code is contributed by Hritik Shah. */

Java


 // Java program for implementation of Insertion Sort
public 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 Hritik Shah. */

Python


 # Python program for implementation of Insertion Sort

# Function to sort array using insertion sort
def insertionSort(arr):
    for i in range(1, len(arr)):
        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 and key < arr[j]:
            arr[j + 1] = arr[j]
            j -= 1
        arr[j + 1] = key

# A utility function to print array of size n
def printArray(arr):
    for i in range(len(arr)):
        print(arr[i], end=" ")
    print()

# Driver method
if __name__ == "__main__":
    arr = [12, 11, 13, 5, 6]
    insertionSort(arr)
    printArray(arr)

    # This code is contributed by Hritik Shah.


 // 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.WriteLine();
    }

    // Driver method
    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 Hritik Shah. */

JavaScript


 // Javascript program for insertion sort 

// Function to sort array using insertion sort
function insertionSort(arr) {
    for (let i = 1; i < arr.length; i++) {
        let key = arr[i];
        let 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
function printArray(arr) {
    console.log(arr.join(" "));
}

// Driver method
let arr = [12, 11, 13, 5, 6];

insertionSort(arr);
printArray(arr);

// This code is contributed by Hritik Shah.

PHP


 <?php 
// PHP program for insertion sort

// Function to sort an array using insertion sort
function insertionSort(&$arr, $n)
{
    for ($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
function printArray(&$arr, $n)
{
    for ($i = 0; $i < $n; $i++)
        echo $arr[$i] . " ";
    echo "\n";
}

// Driver Code
$arr = array(12, 11, 13, 5, 6);
$n = sizeof($arr);
insertionSort($arr, $n);
printArray($arr, $n);

// This code is contributed by Hritik Shah.
?>

Illustration

arr = {23, 1, 10, 5, 2}

Initial:

Current element is 23

The first element in the array is assumed to be sorted.

The sorted part until 0th index is : [23]

First Pass:

Compare 1 with 23 (current element with the sorted part).

Since 1 is smaller, insert 1 before 23 .

The sorted part until 1st index is: [1, 23]

Second Pass:

Compare 10 with 1 and 23 (current element with the sorted part).

Since 10 is greater than 1 and smaller than 23 , insert 10 between 1 and 23 .

The sorted part until 2nd index is: [1, 10, 23]

Third Pass:

Compare 5 with 1 , 10 , and 23 (current element with the sorted part).

Since 5 is greater than 1 and smaller than 10 , insert 5 between 1 and 10

The sorted part until 3rd index is : [1, 5, 10, 23]

Fourth Pass:

Compare 2 with 1, 5, 10 , and 23 (current element with the sorted part).

Since 2 is greater than 1 and smaller than 5 insert 2 between 1 and 5 .

The sorted part until 4th index is: [1, 2, 5, 10, 23]

Final Array:

The sorted array is: [1, 2, 5, 10, 23]

Complexity Analysis of Insertion Sort

Time Complexity

Best case: O(n), If the list is already sorted, where n is the number of elements in the list.
Average case: O(n²), If the list is randomly ordered
Worst case: O(n²), If the list is in reverse order

Space Complexity

Auxiliary Space: O(1), Insertion sort requires O(1) additional space, making it a space-efficient sorting algorithm.

Please refer Complexity Analysis of Insertion Sort for details.

Advantages and Disadvantages of Insertion Sort

Advantages

Simple and easy to implement.
Stable sorting algorithm.
Efficient for small lists and nearly sorted lists.
Space-efficient as it is an in-place algorithm.
Adoptive. the number of inversions is directly proportional to number of swaps. For example, no swapping happens for a sorted array and it takes O(n) time only.

Disadvantages

Inefficient for large lists.
Not as efficient as other sorting algorithms (e.g., merge sort, quick sort) for most cases.

Applications of Insertion Sort

Insertion sort is commonly used in situations where:

The list is small or nearly sorted.
Simplicity and stability are important.
Used as a subroutine in Bucket Sort
Can be useful when array is already almost sorted (very few inversions)
Since Insertion sort is suitable for small sized arrays, it is used in Hybrid Sorting algorithms along with other efficient algorithms like Quick Sort and Merge Sort. When the subarray size becomes small, we switch to insertion sort in these recursive algorithms. For example IntroSort and TimSort use insertions sort.

What are the Boundary Cases of the Insertion Sort algorithm?

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

What is the Algorithmic Paradigm of the Insertion Sort algorithm?

The Insertion Sort algorithm follows an incremental approach.

Is Insertion Sort an in-place sorting algorithm?

Yes, insertion sort is an in-place sorting algorithm.

Is Insertion Sort a stable algorithm?

Yes, insertion sort is a stable sorting algorithm.

When is the Insertion Sort algorithm used?

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

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