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 divides the list into two halves, sorts each half, and then merges the two sorted halves back together.

beginner

What is the time complexity of Merge Sort in the average and worst cases?

The time complexity of Merge Sort is O(n log n) for both average and worst cases.

intermediate

Why does Merge Sort require extra space?

Merge Sort needs extra space to hold temporary arrays during the merging process because it combines two sorted lists into one.

intermediate

Explain the merge step in Merge Sort.

The merge step takes two sorted halves and compares their elements one by one, placing the smaller element into a new array until all elements are merged in sorted order.

intermediate

Is Merge Sort a stable sorting algorithm? Why or why not?

Yes, Merge Sort is stable because it preserves the relative order of equal elements during the merge step.

What technique does Merge Sort use to sort the array?

A Divide and conquer

B Greedy

C Dynamic programming

D Brute force

Merge Sort splits the array into smaller parts, sorts them, and merges them back, which is divide and conquer.

What is the space complexity of Merge Sort?

A O(1)

B O(n log n)

C O(log n)

D O(n)

Merge Sort requires O(n) extra space for temporary arrays during merging.

During the merge step, what happens when elements from both halves are equal?

A The element from the right half is chosen first

B The element from the left half is chosen first

C Both elements are skipped

D The algorithm stops

To maintain stability, the element from the left half is chosen first when elements are equal.

Which of the following is true about Merge Sort's performance?

A It always divides the array into halves

B It has a worst-case time complexity of O(n^2)

C It is faster than Quick Sort in all cases

D It sorts in place without extra memory

Merge Sort always divides the array into two halves recursively.

What is the base case for the recursive Merge Sort function?

A When the array has more than two elements

B When the array is fully sorted

C When the array has one or zero elements

D When the array is empty

The base case is when the array has one or zero elements, which are already sorted.

Describe step-by-step how Merge Sort sorts an array of numbers.

Think about splitting, sorting smaller parts, and merging.

Explain why Merge Sort is considered a stable sorting algorithm.

Focus on how equal elements are handled during merging.

Practice

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

easy

A. Select the smallest element and place it at the beginning

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

C. Sort the array by repeatedly swapping adjacent elements

D. Build a heap and extract elements in sorted order

Solution

1. Step 1: Understand the divide and conquer approach

   Merge sort splits the array into two halves recursively until single elements remain.

2. Step 2: Merge sorted halves

   It then merges these sorted halves to produce a fully sorted array.

3. Final Answer:

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

4. Quick Check:

   Merge Sort = Divide, Sort, Merge [OK]

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

Common Mistakes:

• Confusing merge sort with bubble sort
• Thinking merge sort swaps adjacent elements
• Mixing merge sort with selection sort

2. Which of the following is the correct way to declare the merge function header in C++ for merge sort?

easy

A. int mergeSort(int arr[], int left, int right);

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

C. void mergeSort(int arr[], int left, int right);

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

Solution

1. Step 1: Identify the merge function role

   The merge function combines two sorted parts; it does not return a value, so it should be void.

2. Step 2: Check parameter list

   It takes the array and three indices: left, mid, and right to merge subarrays.

3. Final Answer:

   void merge(int arr[], int left, int mid, int right); -> Option D

4. Quick Check:

   Merge function = void with arr and indices [OK]

Hint: Merge combines parts, returns nothing [OK]

Common Mistakes:

• Using int return type for merge
• Confusing merge with mergeSort function
• Wrong parameter order or missing parameters

3. What will be the output of the following code snippet after applying merge sort on the array?

int arr[] = {5, 2, 9, 1};
mergeSort(arr, 0, 3);
for(int i = 0; i < 4; i++) std::cout << arr[i] << " ";

medium

A. 5 2 9 1

B. 9 5 2 1

C. 1 2 5 9

D. 2 1 5 9

Solution

1. Step 1: Apply merge sort on the array

   The array {5, 2, 9, 1} is split and sorted recursively to {1, 2, 5, 9}.

2. Step 2: Print the sorted array

   The for loop prints elements in sorted order: 1 2 5 9.

3. Final Answer:

   1 2 5 9 -> Option C

4. Quick Check:

   Sorted array = 1 2 5 9 [OK]

Hint: Merge sort outputs sorted array ascending [OK]

Common Mistakes:

• Printing original array without sorting
• Confusing merge sort with reverse sort
• Off-by-one errors in indices

4. Identify the error in the following merge sort code snippet:

void merge(int arr[], int left, int mid, int right) {
  int n1 = mid - left;
  int n2 = right - mid;
  int L[n1], R[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...
}

medium

A. Incorrect calculation of n1 and n2 sizes

B. Wrong indexing in copying elements to L array

C. Using variable-length arrays which is invalid in C++

D. Missing return statement in void function

Solution

1. Step 1: Check size calculations

   n1 = mid - left is missing +1 (should be mid - left + 1) to include the mid element; n2 = right - mid is correct.

2. Step 2: Check copying to L array

   Copying starts at left + i for i < n1, which goes up to mid-1, missing arr[mid].

3. Step 3: Identify the main error

   The error causes wrong indexing/range when copying elements to L array.

4. Final Answer:

   Incorrect calculation of n1 and n2 sizes -> Option A

5. Quick Check:

   Subarray size calculation off by one [OK]

Hint: Check array copy indices carefully [OK]

Common Mistakes:

• Off-by-one errors in subarray sizes
• Using variable-length arrays in C++
• Ignoring void function return type

5. Given an array with many duplicate elements, how can merge sort be adapted to maintain the relative order of equal elements (stable sort)?

hard

A. Always pick the element from the left subarray first when merging equals

B. Always pick the element from the right subarray first when merging equals

C. Swap equal elements randomly during merge

D. Use quicksort instead of merge sort

Solution

1. Step 1: Understand stability in sorting

   A stable sort keeps equal elements in their original relative order.

2. Step 2: Apply stability in merge step

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

3. Final Answer:

   Always pick the element from the left subarray first when merging equals -> Option A

4. Quick Check:

   Stable merge = left element first on equals [OK]

Hint: Pick left element first on ties to keep order [OK]

Common Mistakes:

• Picking right element first breaks stability
• Random swaps destroy order
• Confusing merge sort with quicksort stability