Insertion Sort Algorithm in DSA Javascript - Build from Scratch

Insertion Sort Algorithm

📖 Scenario: You have a list of numbers that you want to arrange in order from smallest to largest, just like organizing books by height on a shelf.

🎯 Goal: Build a program that sorts a list of numbers using the insertion sort method, which places each number in its correct spot one by one.

📋 What You'll Learn

Create an array called numbers with the exact values [8, 3, 5, 4, 6].

Create a variable called n that stores the length of the numbers array.

Use a for loop with the variable i starting from 1 up to n to iterate through the array.

Inside the loop, create a variable called key to hold the current number at index i.

Use a while loop with variable j to move elements greater than key one position ahead.

Place the key in its correct sorted position.

Print the sorted numbers array.

💡 Why This Matters

🌍 Real World

Sorting is used everywhere, like arranging books, organizing files, or displaying search results in order.

💼 Career

Understanding sorting algorithms helps in software development, data analysis, and optimizing performance in many tech jobs.

1

Create the initial array

Create an array called numbers with these exact values: [8, 3, 5, 4, 6].

DSA Javascript

// Create the array called numbers with the values [8, 3, 5, 4, 6]
// Your code here

Hint

Use const numbers = [8, 3, 5, 4, 6]; to create the array.

2

Set up the length variable

Create a variable called n that stores the length of the numbers array.

DSA Javascript

const numbers = [8, 3, 5, 4, 6];
// Create a variable n to store the length of numbers
// Your code here

Hint

Use const n = numbers.length; to get the array length.

3

Implement the insertion sort logic

Use a for loop with variable i from 1 to n. Inside it, create a variable key to hold numbers[i]. Use a while loop with variable j to move elements greater than key one position ahead. Finally, place key in its correct position.

DSA Javascript

const numbers = [8, 3, 5, 4, 6];
const n = numbers.length;
// Write the insertion sort algorithm below
// Your code here

Hint

Use a for loop starting at 1, a while loop to shift larger numbers, and place the key correctly.

4

Print the sorted array

Write a console.log statement to print the sorted numbers array.

DSA Javascript

const numbers = [8, 3, 5, 4, 6];
const n = numbers.length;

for (let i = 1; i = 0 && numbers[j] > key) {
        numbers[j + 1] = numbers[j];
        j = j - 1;
    }
    numbers[j + 1] = key;
}
// Print the sorted numbers array
// Your code here

Hint

Use console.log(numbers); to show the sorted array.

Practice

1. What is the main idea behind the Insertion Sort algorithm?

easy

A. Build the sorted array one element at a time by inserting elements in the correct position

B. Divide the array into halves and sort each half separately

C. Swap adjacent elements if they are in the wrong order repeatedly

D. Select the smallest element and swap it with the first unsorted element

Solution

1. Step 1: Understand insertion sort process

   Insertion sort builds the sorted list by taking one element at a time and placing it in the correct position among the already sorted elements.

2. Step 2: Compare with other sorting methods

   Other options describe different algorithms: dividing (merge sort), swapping adjacent (bubble sort), selecting smallest (selection sort).

3. Final Answer:

   Build the sorted array one element at a time by inserting elements in the correct position -> Option A

4. Quick Check:

   Insertion sort = Insert elements step-by-step [OK]

Hint: Insertion sort inserts elements one by one in order [OK]

Common Mistakes:

• Confusing insertion sort with bubble sort
• Thinking it divides the array like merge sort
• Mixing it up with selection sort

2. Which of the following is the correct syntax to start the outer loop for insertion sort in JavaScript for an array arr?

easy

A. for(let i = 0; i < arr.length; i++)

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

C. for(let i = arr.length - 1; i >= 0; i--)

D. for(let i = 0; i <= arr.length; i++)

Solution

1. Step 1: Identify starting index for insertion sort

   Insertion sort starts from the second element (index 1) because the first element is considered sorted.

2. Step 2: Check loop condition correctness

   The loop runs while i < arr.length to cover all elements. Starting at 0 or going beyond length is incorrect.

3. Final Answer:

   for(let i = 1; i < arr.length; i++) -> Option B

4. Quick Check:

   Start loop at 1 for insertion sort [OK]

Hint: Start outer loop at 1, not 0, in insertion sort [OK]

Common Mistakes:

• Starting loop at 0 instead of 1
• Using <= instead of < in loop condition
• Looping backwards incorrectly

3. What will be the output of the following JavaScript code?

function insertionSort(arr) {
  for(let i = 1; i < arr.length; i++) {
    let key = arr[i];
    let j = i - 1;
    while(j >= 0 && arr[j] > key) {
      arr[j + 1] = arr[j];
      j--;
    }
    arr[j + 1] = key;
  }
  return arr;
}

console.log(insertionSort([4, 2, 7, 1]));

medium

A. [2, 1, 4, 7]

B. [4, 2, 7, 1]

C. [1, 4, 2, 7]

D. [1, 2, 4, 7]

Solution

1. Step 1: Trace first iteration (i=1)

   key=2, compare with 4, shift 4 right, insert 2 at index 0 -> [2,4,7,1]

2. Step 2: Trace remaining iterations

   i=2: key=7, no shift -> [2,4,7,1]; i=3: key=1, shift 7,4,2 right, insert 1 at index 0 -> [1,2,4,7]

3. Final Answer:

   [1, 2, 4, 7] -> Option D

4. Quick Check:

   Sorted array = [1, 2, 4, 7] [OK]

Hint: Insertion sort outputs sorted array in ascending order [OK]

Common Mistakes:

• Not shifting elements correctly
• Returning original array without sorting
• Confusing key placement index

4. Find the error in this insertion sort code snippet:

function insertionSort(arr) {
  for(let i = 1; i <= arr.length; i++) {
    let key = arr[i];
    let j = i - 1;
    while(j >= 0 && arr[j] > key) {
      arr[j + 1] = arr[j];
      j--;
    }
    arr[j + 1] = key;
  }
  return arr;
}

medium

A. The outer loop condition should be i < arr.length instead of <=.

B. The inner while loop condition should be arr[j] < key.

C. The key should be assigned after the while loop, not before.

D. The variable j should start at i, not i - 1.

Solution

1. Step 1: Check outer loop boundary

   The loop runs from 1 to arr.length inclusive, but array indices go from 0 to arr.length - 1, so i < arr.length is correct.

2. Step 2: Verify other parts

   Inner loop condition and key assignment are correct; j starts at i - 1 to compare with previous elements.

3. Final Answer:

   The outer loop condition should be i < arr.length instead of <=. -> Option A

4. Quick Check:

   Loop must not exceed array length [OK]

Hint: Use i < arr.length to avoid out-of-bounds [OK]

Common Mistakes:

• Using <= causes index out of range error
• Changing inner loop condition incorrectly
• Misplacing key assignment

5. Given the array [3, 0, -2, 5, 1], after the second iteration (i=2) of insertion sort, what will the array look like?

hard

A. [0, 3, -2, 5, 1]

B. [0, -2, 3, 5, 1]

C. [-2, 0, 3, 5, 1]

D. [3, 0, -2, 5, 1]

Solution

1. Step 1: Trace first iteration (i=1)

   key=0, compare with 3, shift 3 right, insert 0 at index 0 -> [0,3,-2,5,1]

2. Step 2: Trace second iteration (i=2)

   key=-2, compare with 3 and 0, shift both right, insert -2 at index 0 -> [-2,0,3,5,1]

3. Final Answer:

   [-2, 0, 3, 5, 1] -> Option C

4. Quick Check:

   After 2 iterations, array is partially sorted [OK]

Hint: After i-th iteration, first i+1 elements are sorted [OK]

Common Mistakes:

• Not shifting all larger elements
• Inserting key at wrong position
• Confusing iteration count with index