Merge Two Sorted Arrays Without Extra Space in DSA Java - 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 array or storage beyond the given arrays.

beginner

Why can't we simply concatenate and sort the two arrays to merge without extra space?

Concatenating requires extra space to hold combined elements, and sorting after concatenation is inefficient. The goal is to merge in-place without extra storage and maintain sorted order efficiently.

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 in-place.

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 / 2) + (gap % 2)) until it becomes 0, which ends the process.

intermediate

What are the time and space complexities of merging two sorted arrays without extra space using the Gap method?

Time complexity is O((n + m) log(n + m)) where n and m are array sizes, due to gap reduction passes. Space complexity is O(1) since no extra space is used.

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

A Maintaining sorted order without extra storage

B Finding the maximum element

C Reversing the arrays

D Counting duplicates

The key challenge is to merge while keeping the arrays sorted without using extra space.

In the Gap method, what happens when the gap becomes 1?

A The process restarts

B The arrays are reversed

C The arrays are fully merged and sorted

D The arrays are split

When gap is 1, the final pass ensures the arrays are fully merged and sorted.

Which of these is NOT a step in the Gap method?

A Compare and swap elements at gap distance

B Use extra array to store merged elements

C Repeat until gap is 1

D Reduce gap after each pass

The Gap method does not use extra arrays; it merges in-place.

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

A O(1)

B O(n)

C O(n + m)

D O(log(n + m))

The Gap method uses constant extra space, so space complexity is O(1).

If the first array is [1, 5, 9] and the second is [2, 6, 10], what is the merged output after merging without extra space?

A [1, 2, 5, 6, 9, 10]

B [1, 5, 6] and [2, 9, 10]

C ]01 ,9 ,6[ dna ]5 ,2 ,1[

D [1, 2, 5] and [6, 9, 10]

The arrays remain separate but sorted: first array [1, 2, 5], second array [6, 9, 10].

Explain the Gap method for merging two sorted arrays without extra space.

Think about comparing elements at a distance and shrinking that distance.

Describe why merging two sorted arrays without extra space is useful and what challenges it solves.

Consider memory limits and efficiency.

Practice

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

easy

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

B. Copy all elements into a new array and sort it

C. Sort each array separately without merging

D. Use a temporary 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 additional arrays or large memory allocation.

2. Step 2: Identify the correct approach

   Using in-place techniques like swapping elements between arrays and sorting them ensures no extra space is used.

3. Final Answer:

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

4. Quick Check:

   Merge without extra space = Combine in-place [OK]

Hint: Remember: no extra array means in-place merging [OK]

Common Mistakes:

• Thinking extra array is allowed
• Sorting arrays separately without merging
• Using extra memory for temporary storage

2. Which of the following Java code snippets correctly swaps elements between two arrays arr1 and arr2 at indices i and j without extra space?

easy

A. arr1[i] = arr1[j]; arr2[j] = arr2[i];

B. arr1[i] = arr2[j]; arr2[j] = arr1[i];

C. int temp = arr2[j]; arr1[i] = arr2[j]; arr2[j] = temp;

D. int temp = arr1[i]; arr1[i] = arr2[j]; arr2[j] = temp;

Solution

1. Step 1: Check the swap logic

   Swapping requires a temporary variable to hold one value while assigning the other to avoid overwriting.

2. Step 2: Verify correct use of temp variable

   int temp = arr1[i]; arr1[i] = arr2[j]; arr2[j] = temp; uses a temp variable to hold arr1[i], then assigns arr2[j] to arr1[i], and finally assigns temp to arr2[j], correctly swapping values.

3. Final Answer:

   int temp = arr1[i]; arr1[i] = arr2[j]; arr2[j] = temp; -> Option D

4. Quick Check:

   Swap needs temp variable = int temp = arr1[i]; arr1[i] = arr2[j]; arr2[j] = temp; [OK]

Hint: Always use a temp variable to swap two values safely [OK]

Common Mistakes:

• Assigning without temp causes overwriting
• Swapping elements within the same array incorrectly
• Confusing indices during swap

3. Given two sorted arrays arr1 = [1, 5, 9, 10] and arr2 = [2, 3, 8, 13], after applying the merge without extra space algorithm, what will be the final state of arr1 and arr2?

medium

A. arr1 = [1, 2, 3, 8], arr2 = [5, 9, 10, 13]

B. arr1 = [1, 2, 3, 5], arr2 = [8, 9, 10, 13]

C. arr1 = [1, 3, 5, 8], arr2 = [2, 9, 10, 13]

D. arr1 = [1, 2, 5, 8], arr2 = [3, 9, 10, 13]

Solution

1. Step 1: Compare and swap elements between arrays

   Start comparing last element of arr1 with first of arr2. Swap if arr1 element is greater. After swaps, sort both arrays.

2. Step 2: Final sorted arrays after merging

   After swapping and sorting, arr1 becomes [1, 2, 3, 5] and arr2 becomes [8, 9, 10, 13].

3. Final Answer:

   arr1 = [1, 2, 3, 5], arr2 = [8, 9, 10, 13] -> Option B

4. Quick Check:

   In-place merge sorts arrays = arr1 = [1, 2, 3, 5], arr2 = [8, 9, 10, 13] [OK]

Hint: Swap bigger arr1 elements with smaller arr2, then sort both [OK]

Common Mistakes:

• Not sorting arrays after swapping
• Swapping incorrectly leading to unsorted arrays
• Mixing indices during swaps

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

for (int i = 0; i < arr1.length; i++) {
  if (arr1[i] > arr2[0]) {
    int temp = arr1[i];
    arr1[i] = arr2[0];
    arr2[0] = temp;
    Arrays.sort(arr2);
  }
}

medium

A. Using Arrays.sort on arr1 instead of arr2 is required

B. Swapping elements without checking arr2 length causes error

C. Sorting arr2 inside the loop causes unnecessary repeated sorting

D. Loop should run until arr2.length instead of arr1.length

Solution

1. Step 1: Analyze sorting inside the loop

   The code sorts arr2 inside the loop every time a swap happens, which is inefficient and slows down the algorithm.

2. Step 2: Suggest optimization

   Sorting arr2 once after all swaps or using a better approach like gap method improves performance.

3. Final Answer:

   Sorting arr2 inside the loop causes unnecessary repeated sorting -> Option C

4. Quick Check:

   Repeated sorting inside loop = inefficiency [OK]

Hint: Avoid sorting inside loops; sort once after swaps [OK]

Common Mistakes:

• Sorting arr2 repeatedly inside loop
• Confusing loop limits between arrays
• Ignoring performance impact of repeated sorting

5. You have two sorted arrays arr1 = [1, 4, 7, 8, 10] and arr2 = [2, 3, 9]. Using the gap method to merge without extra space, what is the final state of both arrays?

hard

A. arr1 = [1, 2, 3, 4, 7], arr2 = [8, 9, 10]

B. arr1 = [1, 2, 3, 4, 9], arr2 = [7, 8, 10]

C. arr1 = [1, 3, 4, 7, 8], arr2 = [2, 9, 10]

D. arr1 = [1, 2, 4, 7, 8], arr2 = [3, 9, 10]

Solution

1. Step 1: Calculate initial gap and compare elements

   Total length is 8, initial gap = ceil(8/2) = 4. Compare elements at gap distance and swap if needed, then reduce gap.

2. Step 2: Perform gap reductions and swaps

   After successive gap reductions (4, 2, 1), arrays become sorted as arr1 = [1, 2, 3, 4, 7] and arr2 = [8, 9, 10].

3. Final Answer:

   arr1 = [1, 2, 3, 4, 7], arr2 = [8, 9, 10] -> Option A

4. Quick Check:

   Gap method sorts arrays in-place = arr1 = [1, 2, 3, 4, 7], arr2 = [8, 9, 10] [OK]

Hint: Use gap method: reduce gap, swap if needed, repeat until gap=0 [OK]

Common Mistakes:

• Not reducing gap correctly
• Swapping wrong elements across arrays
• Confusing gap calculation with array lengths