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

Recall & Review

beginner

What is the main idea behind the Merge Sort algorithm?

Merge Sort works by dividing the list into smaller parts, sorting each part, and then joining them back together in order.

beginner

What are the two main steps in the Merge Sort process?

1. Divide the list into halves until each part has one element.
2. Merge the parts back together in sorted order.

intermediate

Why is Merge Sort considered efficient for large lists?

Because it always splits the list into halves and merges them in a sorted way, it runs in about n log n time, which is faster than simple sorting methods for big lists.

intermediate

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

The worst-case time complexity of Merge Sort is O(n log n), where n is the number of elements in the list.

beginner

How does the merging step in Merge Sort work?

It takes two sorted lists and compares their first elements, picking the smaller one to add to a new list, repeating this until all elements are merged in order.

What is the first step in the Merge Sort algorithm?

A Merge two sorted lists

B Swap elements if out of order

C Compare adjacent elements

D Divide the list into halves

Merge Sort starts by dividing the list into smaller halves before sorting and merging.

What is the time complexity of Merge Sort?

A O(n^2)

B O(n log n)

C O(log n)

D O(n)

Merge Sort runs in O(n log n) time because it divides the list and merges sorted parts.

During the merge step, how are elements chosen to form the sorted list?

A The smaller element from the front of each list

B Always from the first list

C Randomly from either list

D The larger element from the back of each list

The merge step picks the smaller element from the front of each sorted list to keep order.

Which of these is NOT true about Merge Sort?

A It has a stable sorting behavior

B It uses divide and conquer

C It sorts in place without extra space

D It works well for large data sets

Merge Sort requires extra space to merge lists, so it is not an in-place sort.

What happens when the list is divided until each part has one element?

A The list is considered sorted

B The list is shuffled

C The list is reversed

D The list is merged immediately

A single element list is always sorted, so this is the base case for merging.

Explain how the Merge Sort algorithm sorts a list from start to finish.

Think about breaking down the problem and then building it back up.

Describe why Merge Sort is more efficient than simple sorting methods like Bubble Sort for large lists.

Focus on how the algorithm handles big data differently.

Practice

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

easy

A. Pick the smallest element and place it at the beginning repeatedly

B. Divide the list into halves, sort each half, then merge them

C. Compare each element with every other element and swap if needed

D. Build a sorted list by inserting elements one by one

Solution

1. Step 1: Understand the divide and conquer approach

   Merge Sort splits the list into two halves recursively until each sublist has one element.

2. Step 2: Merge sorted halves

   Then it merges these small sorted lists back together in order to form a sorted list.

3. Final Answer:

   Divide the list into halves, sort each half, then merge them -> Option B

4. Quick Check:

   Merge Sort = Divide and conquer [OK]

Hint: Remember: split, sort halves, then merge [OK]

Common Mistakes:

• Confusing Merge Sort with Bubble Sort
• Thinking it sorts by swapping adjacent elements
• Believing it sorts by inserting elements one by one

2. Which of the following is the correct way to declare the merge function header in C# for Merge Sort?

easy

A. void Merge(int[] arr, int left, int mid, int right)

B. int Merge(int arr[], int left, int mid, int right)

C. void merge(int arr[], int start, int end)

D. int merge(int[] arr, int left, int right)

Solution

1. Step 1: Identify correct parameter types and names

   The merge function typically takes the array and three indices: left, mid, and right to merge two sorted halves.

2. Step 2: Check C# syntax for method declaration

   In C#, arrays are declared as int[] arr and the function returns void because it modifies the array in place.

3. Final Answer:

   void Merge(int[] arr, int left, int mid, int right) -> Option A

4. Quick Check:

   Correct signature = void Merge(int[] arr, int left, int mid, int right) [OK]

Hint: Look for void return and correct parameters [OK]

Common Mistakes:

• Using incorrect return type (int instead of void)
• Wrong parameter types or order
• Using lowercase function names in C#

3. What will be the output of the following C# code snippet using Merge Sort on array [4, 1, 3, 2]?

int[] arr = {4, 1, 3, 2};
MergeSort(arr, 0, arr.Length - 1);
Console.WriteLine(string.Join(", ", arr));

medium

A. 1, 3, 2, 4

B. 4, 3, 2, 1

C. 1, 2, 3, 4

D. 2, 1, 3, 4

Solution

1. Step 1: Apply Merge Sort to the array [4, 1, 3, 2]

   Split into [4,1] and [3,2], sort each half to [1,4] and [2,3].

2. Step 2: Merge the two sorted halves

   Merging [1,4] and [2,3] results in [1, 2, 3, 4].

3. Final Answer:

   1, 2, 3, 4 -> Option C

4. Quick Check:

   Sorted array = 1, 2, 3, 4 [OK]

Hint: Merge halves stepwise to get sorted array [OK]

Common Mistakes:

• Confusing merge order and producing unsorted output
• Not splitting array correctly
• Printing before sorting completes

4. Identify the bug in this Merge Sort merge function snippet:

void Merge(int[] arr, int left, int mid, int right) {
  int n1 = mid - left + 1;
  int n2 = right - mid;
  int[] L = new int[n1];
  int[] R = new int[n2];
  for (int i = 0; i < n1; i++) L[i] = arr[left + i];
  for (int j = 0; j < n2; j++) R[j] = arr[mid + 1 + j];
  // merging logic follows
}

medium

A. Incorrect array sizes for L and R

B. Loop conditions should use < instead of <= to avoid out of bounds

C. Wrong indices used for copying elements

D. Missing return statement in void function

Solution

1. Step 1: Check array size calculations

   The size of the left array should be mid - left + 1 to include the mid element; the right array size is correct as right - mid.

2. Step 2: Analyze loop conditions for copying elements

   Loops should use < to avoid out of bounds errors.

3. Final Answer:

   Incorrect array sizes for L and R -> Option A

4. Quick Check:

   Left array size must be mid - left + 1 [OK]

Hint: Array size for left = mid - left + 1 [OK]

Common Mistakes:

• Using <= causes index out of range errors
• Miscalculating array sizes
• Confusing mid index offsets

5. Given a large dataset with many duplicate values, how can you modify the Merge Sort algorithm to maintain stability (keep duplicates in original order)?

hard

A. Change Merge Sort to Quick Sort for better stability

B. Sort duplicates separately after Merge Sort completes

C. Use a hash set to remove duplicates before sorting

D. When merging, if elements are equal, take element from left subarray first

Solution

1. Step 1: Understand stability in sorting

   A stable sort keeps equal elements in the same order as original.

2. Step 2: Modify merge step to preserve order

   When merging, if elements are equal, always pick from the left subarray first to keep original order.

3. Final Answer:

   When merging, if elements are equal, take element from left subarray first -> Option D

4. Quick Check:

   Stable merge = pick left element first on ties [OK]

Hint: Pick left element first when equal during merge [OK]

Common Mistakes:

• Removing duplicates before sorting changes data
• Assuming Quick Sort is stable (it is not)
• Sorting duplicates separately after merge