Insertion Sort Algorithm in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind the Insertion Sort algorithm?

Insertion Sort builds the sorted list one element at a time by taking each element and inserting it into its correct position among the already sorted elements.

beginner

How does Insertion Sort handle the elements during sorting?

It picks elements one by one from the unsorted part and inserts them into the correct position in the sorted part by shifting larger elements to the right.

intermediate

What is the time complexity of Insertion Sort in the worst case?

The worst-case time complexity is O(n²), where n is the number of elements, because each insertion may require shifting all previously sorted elements.

intermediate

Why is Insertion Sort efficient for nearly sorted data?

Because it only shifts elements when necessary, if the data is almost sorted, fewer shifts are needed, making it close to O(n) time.

beginner

Show the state of the array after inserting the element 5 into the sorted subarray [1, 3, 7, 9].

After inserting 5, the array becomes [1, 3, 5, 7, 9]. The element 5 is placed between 3 and 7 by shifting 7 and 9 to the right.

What does Insertion Sort do with each new element from the unsorted part?

A Inserts it into the correct position in the sorted part

B Swaps it with the last element

C Ignores it if it is smaller

D Deletes it

Insertion Sort takes each element and inserts it into the correct position in the sorted part by shifting elements as needed.

What is the best-case time complexity of Insertion Sort?

A O(n²)

B O(n log n)

C O(n)

D O(log n)

When the array is already sorted, Insertion Sort only compares each element once, resulting in O(n) time.

Which of these is true about Insertion Sort?

A It is the fastest sorting algorithm for large data

B It always uses extra memory

C It sorts by dividing the array into halves

D It is a stable sorting algorithm

Insertion Sort is stable because it does not change the relative order of equal elements.

In Insertion Sort, what happens when the current element is smaller than elements in the sorted part?

A The current element is swapped with the first element

B Those elements are shifted right to make space

C The array is reversed

D The current element is discarded

Elements larger than the current element are shifted right to insert the current element in the correct position.

Which scenario makes Insertion Sort perform poorly?

A Array is sorted in reverse order

B Array is already sorted

C Array is nearly sorted

D Array has all equal elements

Reverse sorted arrays cause maximum shifts, leading to worst-case O(n²) time.

Explain how Insertion Sort works step-by-step on an example array.

Think about how you sort playing cards in your hand.

Describe the time complexity of Insertion Sort and when it performs best and worst.

Consider how many shifts happen in different input orders.

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