Merge Sort as Divide and Conquer in DSA Rust - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind the 'Divide and Conquer' approach in Merge Sort?

Divide the list into smaller parts, sort each part, then combine them back into a sorted list.

beginner

In Merge Sort, what happens after dividing the list into two halves?

Each half is sorted recursively using Merge Sort before merging them.

intermediate

Why is Merge Sort considered efficient for large lists?

Because it breaks the problem into smaller parts and merges sorted parts efficiently, running in O(n log n) time.

beginner

What is the role of the 'merge' step in Merge Sort?

To combine two sorted lists into one sorted list by comparing elements one by one.

beginner

Show the base case for the recursive Merge Sort function.

When the list has zero or one element, it is already sorted, so return it as is.

What is the first step in Merge Sort?

A Divide the list into two halves

B Merge two sorted lists

C Sort the entire list at once

D Find the largest element

Merge Sort starts by dividing the list into two halves before sorting.

What is the time complexity of Merge Sort?

A O(n log n)

B O(log n)

C O(n^2)

D O(n)

Merge Sort runs in O(n log n) time due to dividing and merging steps.

What does the 'merge' function do in Merge Sort?

A Splits the list into halves

B Finds the middle element

C Combines two sorted lists into one sorted list

D Removes duplicates

The merge function combines two sorted lists into a single sorted list.

When does the recursive Merge Sort stop dividing the list?

A When the list has two elements

B When the list is fully sorted

C After dividing 3 times

D When the list is empty or has one element

The base case is when the list has zero or one element, which is already sorted.

Which of these is NOT a characteristic of Merge Sort?

A Works by merging sorted halves

B Is an in-place sorting algorithm

C Uses divide and conquer

D Has O(n log n) time complexity

Merge Sort is not in-place because it requires extra space for merging.

Explain how Merge Sort uses the divide and conquer approach to sort a list.

Think about breaking the problem into smaller parts and combining results.

Describe the merge step in Merge Sort and why it is important.

Focus on how two sorted parts become one sorted whole.

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