Merge Sort as Divide and Conquer in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to split the array into two halves.

DSA Rust

let mid = arr.len() [1] 2;

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

A/

B*

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using + or * instead of division to find the middle.

We divide the length by 2 to find the middle index for splitting.

2fill in blank

medium

Complete the code to recursively sort the left half of the array.

DSA Rust

let left = merge_sort(&arr[0..[1]]);

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

Amid

Barr.len()

C0

Darr.len() / 2 + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using arr.len() which is the full length, not half.

The left half is from index 0 up to mid (exclusive).

3fill in blank

hard

Fix the error in the merge function call to combine sorted halves.

DSA Rust

merge(&left, &[1])

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

Aarr

Bleft

Cmid

Dright

Attempts:

3 left

💡 Hint

Common Mistakes

Passing arr or mid instead of right to merge.

We merge the left and right sorted halves, so the second argument must be right.

4fill in blank

hard

Fill both blanks to complete the merge function signature.

DSA Rust

fn merge(left: &[i32], [1]: &[i32]) -> Vec<i32> { [2] }

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

Aright

Bright: &[i32]

CVec::new()

Dreturn Vec::new()

Attempts:

3 left

💡 Hint

Common Mistakes

Missing parameter name or type, or missing return statement.

The second parameter must be named with type, and the function returns a new vector.

5fill in blank

hard

Fill all three blanks to complete the merge logic for comparing elements.

DSA Rust

if left[i] [1] right[j] { result.push(left[i]); i += [2]; } else { result.push(right[j]); j += [3]; }

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

A<=

B1

C2

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong comparison operators or increment values.

We compare elements with <= and increment indices by 1 after pushing.

Practice

1. What is the main idea behind the Merge Sort algorithm in the context of divide and conquer?

easy

A. Select a pivot and partition the array around it

B. Sort the array by swapping adjacent elements repeatedly

C. Build a heap and extract elements in sorted order

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

Solution

1. Step 1: Understand divide and conquer in Merge Sort

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

2. Step 2: Merge sorted halves

   After splitting, it merges the sorted halves back together to form a sorted array.

3. Final Answer:

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

4. Quick Check:

   Divide and conquer = split, sort, merge [OK]

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

Common Mistakes:

• Confusing Merge Sort with Bubble Sort
• Thinking Merge Sort uses a pivot like Quick Sort
• Ignoring the merge step after dividing

2. Which of the following is the correct Rust function signature for a merge sort function that sorts a mutable slice of integers?

easy

A. fn merge_sort(arr: Vec<i32>) -> Vec<i32>

B. fn merge_sort(arr: &mut [i32])

C. fn merge_sort(arr: &[i32]) -> &[i32]

D. fn merge_sort(arr: &mut Vec<i32>) -> ()

Solution

1. Step 1: Identify mutable slice parameter

   Merge sort modifies the array in place, so it needs a mutable slice: &mut [i32].

2. Step 2: Check function return type

   In-place sorting returns nothing, so return type is omitted (unit type).

3. Final Answer:

   fn merge_sort(arr: &mut [i32]) -> Option B

4. Quick Check:

   Mutable slice input, no return [OK]

Hint: Use &mut [i32] for in-place sorting in Rust [OK]

Common Mistakes:

• Using immutable slice &[i32] when mutation is needed
• Returning a new vector instead of sorting in place
• Incorrect return type for in-place function

3. What will be the output of the following Rust code snippet using merge sort on the array [4, 1, 3, 2]?

fn main() {
    let mut arr = [4, 1, 3, 2];
    merge_sort(&mut arr);
    println!("{:?}", arr);
}

fn merge_sort(arr: &mut [i32]) {
    let mid = arr.len() / 2;
    if mid == 0 { return; }
    merge_sort(&mut arr[..mid]);
    merge_sort(&mut arr[mid..]);
    let mut merged = arr.to_vec();
    merge(&arr[..mid], &arr[mid..], &mut merged[..]);
    arr.copy_from_slice(&merged);
}

fn merge(left: &[i32], right: &[i32], merged: &mut [i32]) {
    let mut i = 0;
    let mut j = 0;
    let mut k = 0;
    while i < left.len() && j < right.len() {
        if left[i] <= right[j] {
            merged[k] = left[i];
            i += 1;
        } else {
            merged[k] = right[j];
            j += 1;
        }
        k += 1;
    }
    while i < left.len() {
        merged[k] = left[i];
        i += 1;
        k += 1;
    }
    while j < right.len() {
        merged[k] = right[j];
        j += 1;
        k += 1;
    }
}

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: Trace recursive splitting

   Array splits into [4,1] and [3,2], then further into single elements.

2. Step 2: Merge sorted halves

   Merge [4] and [1] into [1,4], merge [3] and [2] into [2,3], then merge [1,4] and [2,3] into [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 halves step-by-step to get sorted array [OK]

Common Mistakes:

• Confusing merge order causing wrong output
• Forgetting to copy merged array back
• Incorrect base case stopping recursion too early

4. Identify the bug in this Rust merge sort implementation snippet:

fn merge_sort(arr: &mut [i32]) {
    let mid = arr.len() / 2;
    if arr.len() <= 1 { return; }
    merge_sort(&mut arr[..mid]);
    merge_sort(&mut arr[mid..]);
    let mut merged = arr.to_vec();
    merge(&arr[..mid], &arr[mid..], &mut merged[..]);
    arr.copy_from_slice(&merged);
}

medium

A. The base case condition is correct; no bug here

B. The slices passed to merge overlap and cause incorrect merging

C. The merge function is called with immutable slices, but merged is mutable

D. The base case condition should check if mid == 0, not arr.len() <= 1

Solution

1. Step 1: Check base case

   The condition if arr.len() <= 1 { return; } correctly handles arrays of length 0 or 1.

2. Step 2: Verify recursive calls

   Disjoint mutable slices arr[..mid] and arr[mid..] are sorted independently.

3. Step 3: Examine merge

   Immutable borrows of disjoint slices to merge are temporary; writes to separate merged vec. No overlap or borrow issues.

4. Final Answer:

   The base case condition is correct; no bug here -> Option A

5. Quick Check:

   Disjoint slices + temporary borrows = safe [OK]

Hint: Verify disjoint slices and borrow lifetimes; this is correct [OK]

Common Mistakes:

• Ignoring slice borrowing rules in Rust
• Confusing base case condition with bug
• Assuming immutable slices cause errors with mutable writes

5. Given a large array of integers with many duplicate values, how can you modify the merge step in merge sort to optimize performance by reducing unnecessary copying?

hard

A. Skip copying elements when both halves have equal values during merge

B. Avoid merging duplicates by sorting only unique elements

C. Use a stable merge that avoids copying duplicates by referencing indices

D. Count duplicates and merge them as a single element to reduce size

Solution

1. Step 1: Understand stable merge importance

   Stable merge preserves order of equal elements and can optimize by referencing indices instead of copying repeatedly.

2. Step 2: Avoid unnecessary copying of duplicates

   By using indices and stable merge logic, duplicates are merged efficiently without extra copying.

3. Final Answer:

   Use a stable merge that avoids copying duplicates by referencing indices -> Option C

4. Quick Check:

   Stable merge optimizes duplicate handling [OK]

Hint: Use stable merge to handle duplicates efficiently [OK]

Common Mistakes:

• Trying to merge duplicates as single element (loses data)
• Skipping copying equal elements breaks stability
• Sorting only unique elements changes array content