Insertion Sort Algorithm in DSA Javascript

Mental Model

Insertion sort builds a sorted list one item at a time by placing each new item into its correct position.

Analogy: Imagine sorting playing cards in your hand by picking one card at a time and inserting it into the right spot among the cards you already sorted.

Unsorted array:
[5, 3, 8, 4, 2]

Sorted portion ↑
[5, 3, 8, 4, 2]
 ↑

Dry Run Walkthrough

Input: array: [5, 3, 8, 4, 2]

Goal: Sort the array in ascending order using insertion sort

Step 1: Take element 3 and compare with 5, shift 5 right

[5, 5, 8, 4, 2] ↑ (insertion point found)

Why: We move 5 to the right to make space for 3 in the sorted part

Step 2: Insert 3 at position 0

[3, 5, 8, 4, 2] ↑

Why: 3 is smaller than 5, so it goes before 5

Step 3: Take element 8, no shift needed as 8 > 5

[3, 5, 8, 4, 2] ↑

Why: 8 is already in correct position

Step 4: Take element 4, shift 8 and 5 right to insert 4

[3, 5, 8, 8, 2] ↑

Why: We move 8 right to make space for 4

Step 5: Shift 5 right to continue making space for 4

[3, 5, 5, 8, 2] ↑

Why: 5 is greater than 4, so it moves right

Step 6: Insert 4 at position 1

[3, 4, 5, 8, 2] ↑

Why: 4 fits between 3 and 5

Step 7: Take element 2, shift 8, 5, 4, 3 right to insert 2

[3, 4, 5, 8, 8] ↑

Why: Shift 8 right to make space for 2

Step 8: Shift 5 right

[3, 4, 5, 5, 8] ↑

Why: Shift 5 right to continue making space

Step 9: Shift 4 right

[3, 4, 4, 5, 8] ↑

Why: Shift 4 right to continue making space

Step 10: Shift 3 right

[3, 3, 4, 5, 8] ↑

Why: Shift 3 right to continue making space

Step 11: Insert 2 at position 0

[2, 3, 4, 5, 8] ↑

Why: 2 is smallest, goes at start

Result:

[2, 3, 4, 5, 8]

Annotated Code

DSA Javascript

class InsertionSort {
  static sort(arr) {
    for (let i = 1; i < arr.length; i++) {
      let key = arr[i];
      let j = i - 1;
      // Move elements greater than key one position ahead
      while (j >= 0 && arr[j] > key) {
        arr[j + 1] = arr[j];
        j--;
      }
      arr[j + 1] = key;
    }
    return arr;
  }
}

// Driver code
const array = [5, 3, 8, 4, 2];
const sortedArray = InsertionSort.sort(array);
console.log(sortedArray.join(", ") + "\n");

for (let i = 1; i < arr.length; i++) {

iterate over each element starting from second to insert it correctly

let key = arr[i];

store current element to insert

while (j >= 0 && arr[j] > key) {

shift elements greater than key to the right

arr[j + 1] = arr[j];

move element one position right to make space

j--;

move left to compare next element

arr[j + 1] = key;

insert key at correct sorted position

Output

2, 3, 4, 5, 8

Complexity Analysis

Time: O(n^2) because in worst case each element is compared and shifted with all previous elements

Space: O(1) because sorting is done in place without extra storage

vs Alternative: Compared to bubble sort, insertion sort is often faster on nearly sorted data because it stops shifting early

Edge Cases

empty array

returns empty array immediately without errors

DSA Javascript

for (let i = 1; i < arr.length; i++) {

array with one element

returns the same single-element array as sorted

DSA Javascript

for (let i = 1; i < arr.length; i++) {

array with all elements equal

no shifts occur, returns the same array

DSA Javascript

while (j >= 0 && arr[j] > key) {

When to Use This Pattern

When you need to sort a small or nearly sorted list by inserting elements one by one, reach for insertion sort because it builds the sorted list gradually and efficiently.

Common Mistakes

Mistake: Not shifting elements to the right before inserting the key, causing overwriting values
Fix: Use a while loop to shift all elements greater than key one position right before inserting key

Mistake: Starting the outer loop from index 0 instead of 1
Fix: Start from index 1 because the first element is trivially sorted

Summary

Insertion sort builds a sorted array by inserting each element into its correct position.

Use it for small or nearly sorted arrays where simple insertion is efficient.

The key insight is shifting larger elements right to make space for the current element.