Merge Sort Algorithm in DSA C# - Build from Scratch

Merge Sort Algorithm

📖 Scenario: You are working on a program that needs to sort a list of numbers efficiently. Sorting helps organize data so it is easier to search and analyze.Merge Sort is a popular sorting method that splits the list into smaller parts, sorts each part, and then merges them back together in order.

🎯 Goal: Build a program that uses the Merge Sort algorithm to sort a list of integers in ascending order.

📋 What You'll Learn

Create an integer array with specific values

Write a helper method to merge two sorted arrays

Write the recursive Merge Sort method

Print the sorted array after applying Merge Sort

💡 Why This Matters

🌍 Real World

Sorting data is essential in many applications like organizing contacts, searching efficiently, and preparing data for reports.

💼 Career

Understanding Merge Sort helps in software development roles that require efficient data processing and algorithm optimization.

1

Create the integer array

Create an integer array called numbers with these exact values: 38, 27, 43, 3, 9, 82, 10.

DSA C#

// Create the integer array called numbers with the given values
// Your code here

Hint

Use int[] numbers = { ... }; to create the array with the exact values.

2

Write the merge helper method

Write a static method called Merge that takes two sorted integer arrays left and right and returns a new sorted integer array containing all elements from both arrays merged in ascending order.

DSA C#

int[] numbers = {38, 27, 43, 3, 9, 82, 10};

// Write the Merge method below
// Your code here

Hint

The Merge method compares elements from both arrays and adds the smaller one to the result array until all elements are merged.

3

Write the recursive MergeSort method

Write a static method called MergeSort that takes an integer array array and returns a sorted integer array using the Merge Sort algorithm. It should split the array into halves, recursively sort each half, and merge them using the Merge method.

DSA C#

int[] numbers = {38, 27, 43, 3, 9, 82, 10};

static int[] Merge(int[] left, int[] right)
{
    // Merge method code
}

// Write the MergeSort method below
// Your code here

Hint

Split the array into two halves, recursively sort each half, then merge them.

4

Print the sorted array

Call the MergeSort method on the numbers array and print the sorted array elements separated by spaces using Console.WriteLine.

DSA C#

int[] numbers = {38, 27, 43, 3, 9, 82, 10};

static int[] Merge(int[] left, int[] right)
{
    // Merge method code
}

static int[] MergeSort(int[] array)
{
    // MergeSort method code
}

// Call MergeSort on numbers and print the sorted array
// Your code here

Hint

Use string.Join(" ", sortedNumbers) to join array elements with spaces for printing.

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