Merge Sort Algorithm in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to split the array into two halves.

DSA Java

int mid = [1] / 2;

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

Aarr.size()

Barr.length()

Carr.length

Darr.size

Attempts:

3 left

💡 Hint

Common Mistakes

Using arr.length() which is a method call and causes error.

Using arr.size() which is for collections, not arrays.

The length of an array in Java is accessed using arr.length.

2fill in blank

medium

Complete the code to copy the left half of the array.

DSA Java

int[] left = Arrays.copyOfRange(arr, 0, [1]);

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

Amid

Barr.length / 2

Carr.length

Dmid + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using mid + 1 which copies one extra element.

Using arr.length which copies the whole array.

The left half goes from index 0 up to but not including mid, so mid is correct.

3fill in blank

hard

Fix the error in the merge function to correctly compare elements.

DSA Java

if (left[i] [1] right[j]) {

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

A>

B<

C==

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using > which picks the larger element and breaks sorting.

Using == which does not help in ordering.

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

4fill in blank

hard

Fill both blanks to copy remaining elements after merging.

DSA Java

while (i < [1]) {
    arr[k++] = left[[2]++];
}

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

Aleft.length

Bi

Cright.length

Dj

Attempts:

3 left

💡 Hint

Common Mistakes

Using right.length instead of left.length in the condition.

Using j instead of i as the index for left array.

We copy remaining elements from left array while i < left.length, and increment i as index.

5fill in blank

hard

Fill all three blanks to complete the merge function's main loop.

DSA Java

while (i < [1] && j < [2]) {
    if (left[i] [3] right[j]) {
        arr[k++] = left[i++];
    } else {
        arr[k++] = right[j++];
    }
}

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

Aleft.length

Bright.length

C<

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using > instead of < in comparison.

Mixing up left.length and right.length in conditions.

The loop runs while i < left.length and j < right.length. The comparison uses < to pick smaller element.

Practice

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

easy

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

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

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

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 A

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 in place without merging
• Believing it picks smallest elements one by one

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

easy

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

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

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

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

Solution

1. Step 1: Identify parameters needed for merging

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

2. Step 2: Check return type and parameter order

   It returns nothing (void) and parameters match the signature in void merge(int[] arr, int left, int mid, int right).

3. Final Answer:

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

4. Quick Check:

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

Hint: Merge needs array and three indices: left, mid, right [OK]

Common Mistakes:

• Using wrong parameter order
• Returning int instead of void
• Missing mid index parameter

3. What will be the output of the following Java code snippet using Merge Sort on array {4, 1, 3, 2}?

int[] arr = {4, 1, 3, 2};
mergeSort(arr, 0, arr.length - 1);
System.out.println(Arrays.toString(arr));

medium

A. [1, 2, 3, 4]

B. [4, 3, 2, 1]

C. [1, 3, 2, 4]

D. [2, 1, 3, 4]

Solution

1. Step 1: Understand mergeSort on {4,1,3,2}

   It splits into {4,1} and {3,2}, sorts each half to {1,4} and {2,3}.

2. Step 2: Merge sorted halves

   Merging {1,4} and {2,3} results in fully sorted array {1,2,3,4}.

3. Final Answer:

   [1, 2, 3, 4] -> Option A

4. Quick Check:

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

Hint: Merge Sort always returns sorted array ascending [OK]

Common Mistakes:

• Confusing merge order
• Not sorting halves before merging
• Printing original unsorted array

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

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 + j];
  // merging logic follows...
}

medium

A. Array L should be of size n1 + 1

B. Lengths n1 and n2 should be mid - left + 1 and right - mid

C. Copying elements from arr to R should start from mid + 1

D. No bug, code is correct

Solution

1. Step 1: Check array lengths and copying ranges

   Lengths n1 = mid - left + 1 and n2 = right - mid are correct for the left half (left to mid) and right half (mid+1 to right).

2. Step 2: Verify copying elements to R array

   Copying to R starts at arr[mid], but it should start at arr[mid + 1] to avoid overlap.

3. Final Answer:

   Copying elements from arr to R should start from mid + 1 -> Option C

4. Quick Check:

   Right half copy starts at mid+1 [OK]

Hint: Right half starts copying from mid+1, not mid [OK]

Common Mistakes:

• Starting right half copy at mid instead of mid+1
• Incorrect array length calculation
• Assuming no overlap in copying

5. Given an array with many duplicate elements, how can you modify Merge Sort to maintain the original order of equal elements (stable sort)?

hard

A. When merging, always pick from the right subarray first

B. Merge Sort cannot be stable with duplicates

C. Use a hash map to track duplicates and reorder after sorting

D. When merging, if elements are equal, pick from the left subarray first

Solution

1. Step 1: Understand stability in sorting

   A stable sort keeps equal elements in their original order.

2. Step 2: Modify merge step for stability

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

3. Final Answer:

   When merging, if elements are equal, pick from the left subarray first -> Option D

4. Quick Check:

   Stable merge picks left element first on ties [OK]

Hint: Pick left element first when equal to keep order [OK]

Common Mistakes:

• Picking right element first breaks stability
• Thinking Merge Sort is unstable by default
• Using extra data structures unnecessarily