Merge Two Sorted Arrays Without Extra Space in DSA Rust - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean to merge two sorted arrays without extra space?

It means combining two sorted arrays into one sorted sequence without using any additional storage like another array. The elements are rearranged within the original arrays.

beginner

Why can't we just concatenate and sort when merging without extra space?

Concatenating requires extra space to hold all elements together. Sorting after concatenation also needs extra space or modifies the original arrays beyond allowed limits.

intermediate

What is the main idea behind the gap method for merging two sorted arrays without extra space?

The gap method compares elements at a certain gap distance and swaps them if out of order, gradually reducing the gap until it becomes 1, ensuring the arrays are merged and sorted.

intermediate

In the gap method, how is the gap value updated after each pass?

The gap is updated by dividing it by 2 and rounding up (gap = (gap + 1) / 2) until it becomes 1, which is the final pass.

intermediate

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

The time complexity is approximately O((n + m) log(n + m)), where n and m are the sizes of the two arrays.

What is the main challenge when merging two sorted arrays without extra space?

A Rearranging elements without using extra memory

B Sorting arrays individually

C Creating a new array to hold merged elements

D Ignoring the order of elements

The key challenge is to merge while rearranging elements only within the original arrays, without extra memory.

Which method is commonly used to merge two sorted arrays without extra space?

A Merge sort with extra array

B Bubble sort

C Quick sort

D Gap method

The gap method efficiently merges arrays without extra space by comparing and swapping elements at a gap distance.

How is the gap value changed in each iteration of the gap method?

A Gap is halved and rounded up

B Gap stays the same

C Gap is doubled

D Gap is set to zero

The gap is halved and rounded up each time to gradually reduce the distance between compared elements.

What happens when the gap becomes 1 in the gap method?

A Algorithm stops immediately

B Arrays are split again

C Final pass to ensure arrays are fully merged and sorted

D Extra space is allocated

When gap is 1, the method performs the final comparisons and swaps to complete the merge.

What is the space complexity of merging two sorted arrays without extra space using the gap method?

A O(n + m)

B O(1)

C O(log(n + m))

D O(n * m)

The gap method uses constant extra space, O(1), since it rearranges elements in place.

Explain how the gap method merges two sorted arrays without extra space.

Think about comparing pairs of elements separated by a gap and shrinking that gap step by step.

Describe the advantages of merging two sorted arrays without extra space compared to using extra memory.

Consider memory usage and efficiency in constrained environments.

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