Insertion Sort Algorithm in DSA C# - Build from Scratch

Insertion Sort Algorithm

📖 Scenario: You have a list of numbers that you want to arrange from smallest to largest. This is like organizing books on a shelf by their height, one by one.

🎯 Goal: Build a program that sorts a list of numbers using the insertion sort method, showing how the list becomes ordered step by step.

📋 What You'll Learn

Create an integer array called numbers with the exact values: 8, 3, 5, 4, 6

Create an integer variable called n that stores the length of the numbers array

Use a for loop with variable i starting from 1 to n - 1 to iterate over the array

Inside the loop, create an integer variable called key that stores numbers[i]

Use a while loop with variable j starting from i - 1 to move elements greater than key one position ahead

After sorting, print the sorted array elements separated by spaces

💡 Why This Matters

🌍 Real World

Sorting is used in organizing data like names, prices, or dates to find information quickly.

💼 Career

Understanding sorting algorithms is important for software developers to write efficient code for data handling.

1

Create the initial array

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

DSA C#

# Your code here

Hint

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

2

Add the length variable

Create an integer variable called n that stores the length of the numbers array

DSA C#

int[] numbers = {8, 3, 5, 4, 6};
# Your code here

Hint

Use numbers.Length to get the array size.

3

Implement the insertion sort logic

Use a for loop with variable i from 1 to n - 1. Inside it, create an integer variable key equal to numbers[i]. Then use a while loop with variable j starting from i - 1 to move elements greater than key one position ahead and finally place key in the correct position.

DSA C#

int[] numbers = {8, 3, 5, 4, 6};
int n = numbers.Length;
# Your code here

Hint

Remember to move elements greater than key one step right inside the while loop.

4

Print the sorted array

Print the elements of the numbers array separated by spaces using Console.WriteLine and string.Join

DSA C#

int[] numbers = {8, 3, 5, 4, 6};
int n = numbers.Length;
for (int i = 1; i = 0 && numbers[j] > key)
    {
        numbers[j + 1] = numbers[j];
        j--;
    }
    numbers[j + 1] = key;
}
# Your code here

Hint

Use Console.WriteLine(string.Join(" ", numbers)); to print the sorted array.

Practice

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

easy

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

B. It divides the array into halves and sorts each half recursively.

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

D. It selects the smallest element and swaps it with the first unsorted element.

Solution

1. Step 1: Understand insertion sort process

   Insertion sort takes one element at a time and inserts it into the correct position in the already sorted part of the array.

2. Step 2: Compare with other sorting methods

   Other options describe merge sort (B), bubble sort (C), and selection sort (D), which are different algorithms.

3. Final Answer:

   It builds the sorted array one element at a time by inserting elements in their 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 insertion sort divides array recursively
• Mixing up selection sort with insertion sort

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

easy

A. for (int i = 0; i < n; i++)

B. for (int i = 1; i <= n; i++)

C. for (int i = n - 1; i >= 0; i--)

D. for (int i = 1; i < n; 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 conditions

   The loop runs while i < n to cover all elements. for (int i = 1; i < n; i++) matches this.

3. Final Answer:

   for (int i = 1; i < n; i++) -> Option D

4. Quick Check:

   Start from 1 to n-1 for insertion sort loop [OK]

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

Common Mistakes:

• Starting loop at 0 instead of 1
• Using <= n instead of < n causing out-of-bounds
• Counting backwards incorrectly

3. What will be the output array after applying insertion sort on int[] arr = {4, 3, 2, 1}?

medium

A. [1, 3, 2, 4]

B. [4, 3, 2, 1]

C. [1, 2, 3, 4]

D. [2, 3, 4, 1]

Solution

1. Step 1: Trace insertion sort on given array

   Start with 4 (sorted). Insert 3 before 4 -> [3,4,2,1]. Insert 2 before 3 -> [2,3,4,1]. Insert 1 before 2 -> [1,2,3,4].

2. Step 2: Confirm final sorted array

   The array is sorted in ascending order: [1, 2, 3, 4].

3. Final Answer:

   [1, 2, 3, 4] -> Option C

4. Quick Check:

   Insertion sort sorts ascending -> [1, 2, 3, 4] [OK]

Hint: Insertion sort sorts array ascending step-by-step [OK]

Common Mistakes:

• Assuming array stays unchanged
• Mixing up positions during insertion
• Stopping before fully sorting

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

for (int i = 1; i < arr.Length; i++) {
    int key = arr[i];
    int j = i + 1;
    while (j >= 0 && arr[j] > key) {
        arr[j + 1] = arr[j];
        j--;
    }
    arr[j + 1] = key;
}

medium

A. The variable j should start at i - 1 instead of i + 1.

B. The while loop condition should use j < arr.Length instead of j >= 0.

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

D. The array index arr[j + 1] causes out-of-bounds error.

Solution

1. Step 1: Check initialization of j

   In insertion sort, j starts at the element before i, so it should be i - 1, not i + 1.

2. Step 2: Verify while loop condition and shifting

   The condition j >= 0 is correct to move backwards. The shifting logic is correct if j starts properly.

3. Final Answer:

   The variable j should start at i - 1 instead of i + 1. -> Option A

4. Quick Check:

   j starts at i-1 to compare previous elements [OK]

Hint: j must start left of i to compare previous elements [OK]

Common Mistakes:

• Starting j at i+1 causing wrong comparisons
• Incorrect while loop boundary causing errors
• Misplacing key assignment inside loop

5. Given a nearly sorted array int[] arr = {1, 2, 4, 3, 5, 6}, how many element shifts will insertion sort perform to fully sort it?

hard

A. 2

B. 1

C. 3

D. 4

Solution

1. Step 1: Identify where shifts occur

   Only the element 3 is out of order. It needs to be inserted before 4.

2. Step 2: Count shifts to insert 3

   To insert 3, j=2 (arr[2]=4 > 3), shift arr[3]=arr[2] (1 shift), j=1 (arr[1]=2 < 3), stop. Place arr[2]=3 (not a shift).

3. Step 3: Check if other shifts occur

   No other elements need shifting. Total shifts = 1.

4. Final Answer:

   1 -> Option B

5. Quick Check:

   One shift when inserting 3 [OK]

Hint: Count only elements moved to insert out-of-place items [OK]

Common Mistakes:

• Counting swaps instead of shifts
• Ignoring that placing key is not a shift
• Assuming all elements shift