Merge Sort Algorithm in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to find the middle index for splitting the array.

DSA C++

int mid = (left [1] right) / 2;

Drag options to blanks, or click blank then click option'

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction instead of addition.

Using multiplication which is incorrect here.

The middle index is found by adding left and right, then dividing by 2.

2fill in blank

medium

Complete the code to merge two sorted halves by comparing elements.

DSA C++

if (leftArr[i] [1] rightArr[j]) { merged[k++] = leftArr[i++]; } else { merged[k++] = rightArr[j++]; }

Drag options to blanks, or click blank then click option'

A<=

B<

C>=

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using > instead of < causes wrong order.

Using <= or >= can cause duplicates or errors.

We pick the smaller element first, so we use < to compare.

3fill in blank

hard

Fix the error in the recursive call to sort the right half.

DSA C++

mergeSort(arr, [1], right);

Drag options to blanks, or click blank then click option'

Amid

Bright - 1

Cmid + 1

Dleft

Attempts:

3 left

💡 Hint

Common Mistakes

Using mid instead of mid + 1 causes overlap.

Using right - 1 misses the last element.

The right half starts from mid + 1 to right.

4fill in blank

hard

Fill both blanks to copy remaining elements from left and right arrays after merging.

DSA C++

while (i < n1) merged[k++] = leftArr[1]; while (j < n2) merged[k++] = rightArr[2];

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A[i++]

B[j++]

C[k++]

D[i]

Attempts:

3 left

💡 Hint

Common Mistakes

Using [k++] causes wrong indexing.

Not incrementing i or j causes infinite loops.

We copy remaining elements by using i++ and j++ to move indices.

5fill in blank

hard

Fill all three blanks to copy merged array back to original array.

DSA C++

for (int idx = 0; idx < n1 + n2; idx++) arr[1] = merged[2]; [3]

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A[left + idx]

B[idx]

C// end of copying

D[idx + left]

Attempts:

3 left

💡 Hint

Common Mistakes

Using arr[idx] overwrites wrong part of array.

Missing the comment line is okay but less clear.

We copy merged elements back starting at left index. The comment marks end of copying.

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