Merge Two Sorted Arrays Without Extra Space in DSA Rust - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of merging two sorted arrays without extra space

What is the state of the two arrays after merging them without extra space using the given Rust code?

DSA Rust

fn merge(arr1: &mut [i32], arr2: &mut [i32]) {
    let n = arr1.len();
    let m = arr2.len();
    let mut i = 0;
    while i < n {
        if arr1[i] > arr2[0] {
            arr1[i] = std::mem::replace(&mut arr2[0], arr1[i]);
            let mut first = arr2[0];
            let mut k = 1;
            while k < m && arr2[k] < first {
                arr2[k - 1] = arr2[k];
                k += 1;
            }
            arr2[k - 1] = first;
        }
        i += 1;
    }
}

fn main() {
    let mut arr1 = vec![1, 5, 9, 10, 15, 20];
    let mut arr2 = vec![2, 3, 8, 13];
    merge(&mut arr1, &mut arr2);
    println!("arr1: {:?}", arr1);
    println!("arr2: {:?}", arr2);
}

A arr1: [1, 3, 5, 8, 9, 10], arr2: [2, 13, 15, 20]

B arr1: [1, 2, 3, 5, 8, 9], arr2: [10, 13, 15, 20]

C arr1: [1, 2, 3, 5, 8, 10], arr2: [9, 13, 15, 20]

D arr1: [1, 2, 3, 5, 8, 9], arr2: [13, 10, 15, 20]

💡 Hint

Focus on how the smallest elements are swapped and the second array is kept sorted.

The algorithm swaps elements from arr1 with the smallest element in arr2 if arr1's element is greater. Then it repositions the swapped element in arr2 to keep arr2 sorted. After processing all elements, arr1 contains the smallest elements and arr2 the larger ones.

🧠 Conceptual

intermediate

Understanding the time complexity of merging without extra space

What is the time complexity of merging two sorted arrays without extra space using the swapping and insertion method?

A O(n * m), where n and m are the lengths of the two arrays

B O(n + m), linear time

C O(n log m), logarithmic insertion time

D O(n^2), quadratic time

💡 Hint

Consider the nested loops: one iterating over arr1 and one shifting elements in arr2.

For each element in arr1, the algorithm may shift multiple elements in arr2 to maintain sorted order, leading to O(n * m) time complexity.

🔧 Debug

advanced

Identify the bug causing incorrect merge result

Given the following Rust code snippet for merging two sorted arrays without extra space, which line causes the bug leading to incorrect final arrays?

DSA Rust

fn merge(arr1: &mut [i32], arr2: &mut [i32]) {
    let n = arr1.len();
    let m = arr2.len();
    let mut i = 0;
    while i < n {
        if arr1[i] > arr2[0] {
            arr1[i] = arr2[0];
            let mut first = arr2[0];
            let mut k = 1;
            while k < m && arr2[k] < first {
                arr2[k - 1] = arr2[k];
                k += 1;
            }
            arr2[k - 1] = first;
        }
        i += 1;
    }
}

A let mut first = arr2[0]; // should be mutable reference

B while k < m && arr2[k] < first { ... } // incorrect loop condition

C arr2[k - 1] = first; // wrong placement of element

D arr1[i] = arr2[0]; // overwriting without swapping

💡 Hint

Check how elements are swapped between arrays.

The line arr1[i] = arr2[0]; overwrites arr1[i] without saving its original value, losing data. It should swap values to preserve both elements.

📝 Syntax

advanced

Identify the syntax error in the Rust merge function

Which option contains a syntax error in the Rust code for merging two sorted arrays without extra space?

DSA Rust

fn merge(arr1: &mut [i32], arr2: &mut [i32]) {
    let n = arr1.len();
    let m = arr2.len();
    let mut i = 0;
    while i < n {
        if arr1[i] > arr2[0] {
            arr1[i] = std::mem::replace(&mut arr2[0], arr1[i]);
            let mut first = arr2[0];
            let mut k = 1;
            while k < m && arr2[k] < first {
                arr2[k - 1] = arr2[k];
                k += 1;
            }
            arr2[k - 1] = first;
        }
        i += 1;
    }
}

A Missing semicolon after std::mem::replace(&mut arr2[0], arr1[i])

B Using 'while' instead of 'for' loop for k

C Incorrect function signature missing 'mut' keyword

D Using 'let' inside while loop is invalid

💡 Hint

Look carefully at line endings and Rust syntax rules.

Rust requires semicolons after statements. The missing semicolon after the std::mem::replace call causes a syntax error.

🚀 Application

expert

Resulting arrays after merging with given inputs

Given arr1 = [4, 6, 8, 10] and arr2 = [1, 2, 3, 7, 9], what are the arrays after merging without extra space using the standard swapping method?

A arr1: [1, 2, 3, 4], arr2: [7, 6, 8, 9, 10]

B arr1: [1, 2, 3, 6], arr2: [4, 7, 8, 9, 10]

C arr1: [1, 2, 3, 4], arr2: [6, 7, 8, 9, 10]

D arr1: [1, 2, 3, 7], arr2: [4, 6, 8, 9, 10]

💡 Hint

Remember arr1 should hold the smallest elements after merging.

The smallest four elements go to arr1 in sorted order, and the remaining elements go to arr2 sorted.

Practice

1. What is the main goal when merging two sorted arrays without extra space?

easy

A. Sort each array separately using extra space

B. Combine both arrays into one sorted sequence without using extra memory

C. Copy elements from one array to another without sorting

D. Create a new array to hold merged elements

Solution

1. Step 1: Understand the problem requirement

   The problem asks to merge two sorted arrays into a sorted sequence without using extra space, meaning no new arrays can be created.

2. Step 2: Identify the correct approach

   We must rearrange elements within the given arrays to maintain sorted order combined, without additional memory.

3. Final Answer:

   Combine both arrays into one sorted sequence without using extra memory -> Option B

4. Quick Check:

   Merge without extra space = Combine in place [OK]

Hint: Merge by swapping elements, no new arrays needed [OK]

Common Mistakes:

• Trying to create a new array for merged result
• Sorting arrays separately without merging
• Ignoring the no extra space constraint

2. Which Rust syntax correctly declares two mutable sorted arrays for merging without extra space?

easy

A. let mut arr1 = [1, 3, 5]; let mut arr2 = [2, 4, 6];

B. let arr1 = [1, 3, 5]; let arr2 = [2, 4, 6];

C. mut arr1 = [1, 3, 5]; mut arr2 = [2, 4, 6];

D. let mut arr1 = (1, 3, 5); let mut arr2 = (2, 4, 6);

Solution

1. Step 1: Identify correct Rust mutable array declaration

   In Rust, arrays are declared with let mut for mutability and square brackets for arrays.

2. Step 2: Check each option

   let mut arr1 = [1, 3, 5]; let mut arr2 = [2, 4, 6]; uses let mut with arrays correctly. let arr1 = [1, 3, 5]; let arr2 = [2, 4, 6]; misses mut keyword. mut arr1 = [1, 3, 5]; mut arr2 = [2, 4, 6]; misses let keyword. let mut arr1 = (1, 3, 5); let mut arr2 = (2, 4, 6); uses tuples, not arrays.

3. Final Answer:

   let mut arr1 = [1, 3, 5]; let mut arr2 = [2, 4, 6]; -> Option A

4. Quick Check:

   Mutable arrays use let mut and [] [OK]

Hint: Use let mut and square brackets for mutable arrays [OK]

Common Mistakes:

• Forgetting mut keyword for mutable arrays
• Using tuples instead of arrays
• Missing let keyword

3. What will be the content of arrays after merging arr1 = [1, 4, 7] and arr2 = [2, 5, 6] without extra space using the gap method?

medium

A. ]7 ,6 ,5[ = 2rra ,]4 ,2 ,1[ = 1rra

B. arr1 = [1, 4, 5], arr2 = [2, 6, 7]

C. rr1 = [1, 2, 4], arr2 = [5, 6, 7]

D. arr1 = [1, 2, 4], arr2 = [5, 6, 7]

Solution

1. Step 1: Apply gap method to merge arrays

   Start with gap = ceil((3+3)/2) = 3. Compare and swap elements at gap distance across arrays until gap reduces to 0.

2. Step 2: Final arrays after merging

   After applying gap method, arr1 becomes [1, 2, 4] and arr2 becomes [5, 6, 7], maintaining sorted order without extra space.

3. Final Answer:

   arr1 = [1, 2, 4], arr2 = [5, 6, 7] -> Option D

4. Quick Check:

   Gap method merges arrays in place [OK]

Hint: Use gap method to compare and swap elements at decreasing gaps [OK]

Common Mistakes:

• Not reducing gap correctly
• Swapping elements incorrectly across arrays
• Confusing array indices during merge

4. Identify the error in this Rust code snippet for merging two sorted arrays without extra space:

let mut arr1 = [1, 5, 9];
let mut arr2 = [2, 6, 8];
for i in 0..arr1.len() {
    if arr1[i] > arr2[0] {
        let temp = arr1[i];
        arr1[i] = arr2[0];
        arr2[0] = temp;
    }
    arr2.sort();
}

medium

A. Using let temp causes ownership error in Rust

B. Swapping elements between arr1 and arr2 is not allowed

C. Sorting arr2 inside the loop is inefficient and incorrect

D. The loop range should be arr2.len() instead of arr1.len()

Solution

1. Step 1: Analyze the loop and sorting inside it

   The code sorts arr2 inside the loop for every iteration, which is inefficient and unnecessary.

2. Step 2: Correct approach for sorting arr2

   Sorting arr2 should be done once after all swaps, not inside the loop, to improve performance and correctness.

3. Final Answer:

   Sorting arr2 inside the loop is inefficient and incorrect -> Option C

4. Quick Check:

   Sort arr2 once after loop [OK]

Hint: Sort arr2 once after loop, not inside it [OK]

Common Mistakes:

• Sorting arr2 repeatedly inside loop
• Confusing loop ranges
• Misunderstanding Rust ownership with temp variable

5. Given two sorted arrays arr1 = [1, 3, 5, 7] and arr2 = [0, 2, 6, 8, 9], how can you merge them without extra space so that after merging, arr1 contains the first 4 smallest elements and arr2 contains the remaining elements sorted? Choose the correct final arrays.

hard

A. arr1 = [0, 1, 2, 3], arr2 = [5, 6, 7, 8, 9]

B. arr1 = [1, 2, 3, 5], arr2 = [0, 6, 7, 8, 9]

C. arr1 = [0, 1, 3, 5], arr2 = [2, 6, 7, 8, 9]

D. arr1 = [0, 1, 3, 6], arr2 = [2, 5, 7, 8, 9]

Solution

1. Step 1: Understand merging without extra space for unequal sizes

   We must rearrange elements so arr1 holds smallest 4 elements and arr2 holds the rest, both sorted.

2. Step 2: Apply gap method or swapping approach

   By comparing and swapping elements between arrays and sorting arr2, final arrays become arr1 = [0, 1, 2, 3] and arr2 = [5, 6, 7, 8, 9].

3. Final Answer:

   arr1 = [0, 1, 2, 3], arr2 = [5, 6, 7, 8, 9] -> Option A

4. Quick Check:

   First 4 smallest in arr1, rest in arr2 [OK]

Hint: Place smallest elements in arr1 by swapping, then sort arr2 [OK]

Common Mistakes:

• Not handling different array sizes correctly
• Failing to keep both arrays sorted after merge
• Assuming extra space is allowed