Merge Two Sorted Arrays Without Extra Space in DSA C - 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 extra array or memory for storage.

intermediate

Why is it challenging to merge two sorted arrays without extra space?

Because you cannot use extra memory to hold elements temporarily, so you must rearrange elements within the original arrays carefully to keep them sorted.

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.

advanced

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 constraint when merging two sorted arrays without extra space?

A No extra memory can be used

B Arrays must be of equal size

C Arrays must be merged into a new array

D Only one array can be modified

The key constraint is to merge without using any extra memory.

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

A Bubble sort

B Insertion sort

C Quick sort

D Gap method

The gap method efficiently merges arrays in-place without extra space.

How is the initial gap calculated in the gap method for arrays of size n and m?

A n + m

B (n + m) / 2

C n * m

D max(n, m)

The initial gap is usually half of the total length (n + m) / 2.

What happens when two elements compared at the gap distance are out of order?

A They are swapped

B They are left as is

C The gap is increased

D The arrays are merged immediately

Out of order elements are swapped to move towards sorted order.

When does the gap method stop?

A When gap becomes 0

B When arrays are reversed

C When gap becomes 1 and no swaps are needed

D After one pass

The method stops when gap is 1 and arrays are fully sorted.

Explain the steps of the gap method to merge two sorted arrays without extra space.

Think about comparing pairs with decreasing distance.

Why is merging two sorted arrays without extra space useful in real life?

Consider devices with limited RAM.

Practice

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

easy

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

B. Sort each array separately 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 task is to merge two sorted arrays into a single sorted sequence without using extra space, meaning no additional arrays or large buffers.

2. Step 2: Identify the correct approach

   We must rearrange elements within the given arrays to maintain sorted order without allocating extra memory.

3. Final Answer:

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

4. Quick Check:

   Merge without extra space = Combine in place [OK]

Hint: Merge by swapping elements, no extra array needed [OK]

Common Mistakes:

• Thinking extra array is allowed
• Sorting arrays separately without merging
• Copying elements without sorting

2. Which of the following C code snippets correctly declares two sorted arrays for merging without extra space?

easy

A. int arr1[] = (1, 3, 5); int arr2[] = (2, 4, 6);

B. int arr1 = {1, 3, 5}; int arr2 = {2, 4, 6};

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

D. int arr1[] = {1, 3, 5}; int arr2[] = {2, 4, 6};

Solution

1. Step 1: Check array declaration syntax in C

   Arrays in C are declared using curly braces {} with type and square brackets [].

2. Step 2: Validate each option

   int arr1[] = {1, 3, 5}; int arr2[] = {2, 4, 6}; uses correct syntax: int arr[] = {elements}; Options A, B, and D use invalid syntax for arrays in C.

3. Final Answer:

   int arr1[] = {1, 3, 5}; int arr2[] = {2, 4, 6}; -> Option D

4. Quick Check:

   C arrays use {} for initialization [OK]

Hint: Use curly braces {} to initialize arrays in C [OK]

Common Mistakes:

• Using parentheses () or square brackets [] for initialization
• Missing data type or brackets
• Assigning arrays without braces

3. Given two sorted arrays:
arr1 = {1, 4, 7, 8, 10}
arr2 = {2, 3, 9}
After merging without extra space, what will be the content of arr1?

medium

A. [1, 2, 3, 4, 8]

B. [1, 2, 3, 4, 7]

C. [1, 2, 3, 7, 8]

D. [1, 3, 4, 7, 8]

Solution

1. Step 1: Understand merging without extra space

   We merge by comparing elements and swapping to keep smallest elements in arr1.

2. Step 2: Merge process

   Initial arr1: [1,4,7,8,10], arr2: [2,3,9]
   Compare 10 (arr1 last) and 2 (arr2 first), swap -> arr1: [1,4,7,8,2], arr2: [10,3,9]
   Sort arr2: [3,9,10]
   Repeat swaps and sorts until arr1 holds smallest 5 elements:
   Final arr1: [1,2,3,4,7]

3. Final Answer:

   [1, 2, 3, 4, 7] -> Option B

4. Quick Check:

   Smallest 5 elements in arr1 after merge = [1,2,3,4,7] [OK]

Hint: Keep smallest elements in first array by swapping [OK]

Common Mistakes:

• Not sorting arr2 after swaps
• Assuming arr1 remains unchanged
• Mixing elements without sorting

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

for (int i = 0; i < n; i++) {
  if (arr1[i] > arr2[0]) {
    int temp = arr1[i];
    arr1[i] = arr2[0];
    arr2[0] = temp;
    sort(arr2, arr2 + m);
  }
}

medium

A. Using sort() without including <algorithm> header

B. Swapping elements incorrectly between arrays

C. Sorting arr2 inside the loop causes inefficiency

D. Loop should run from 0 to m instead of n

Solution

1. Step 1: Analyze the loop and sorting

   The code swaps elements and sorts arr2 inside the loop for every iteration.

2. Step 2: Identify inefficiency

   Sorting arr2 in every iteration is costly and inefficient; better to optimize sorting or use a different approach.

3. Final Answer:

   Sorting arr2 inside the loop causes inefficiency -> Option C

4. Quick Check:

   Sorting inside loop = inefficient [OK]

Hint: Avoid sorting inside loops for better performance [OK]

Common Mistakes:

• Ignoring performance impact of repeated sorting
• Confusing array sizes for loop limits
• Assuming swap logic is incorrect

5. You have two sorted arrays:
arr1 = {1, 5, 9, 10, 15, 20}
arr2 = {2, 3, 8, 13}
Using the gap method to merge without extra space, what is the final state of arr2 after merging?

hard

A. [10, 13, 15, 20]

B. [8, 9, 10, 15]

C. [8, 13, 15, 20]

D. [9, 10, 13, 15]

Solution

1. Step 1: Understand the gap method

   The gap method compares elements at a gap distance and swaps if out of order, reducing gap until 1.

2. Step 2: Apply gap method to arrays

   Initial arr1: [1,5,9,10,15,20], arr2: [2,3,8,13]
   After merging, arr1 holds smallest elements: [1,2,3,5,8,9]
   arr2 holds remaining elements: [10,13,15,20]

3. Step 3: Final arr2 state

   arr2 after merge is [10, 13, 15, 20].

4. Final Answer:

   [10, 13, 15, 20] -> Option A

5. Quick Check:

   Gap method final arr2 = [10, 13, 15, 20] [OK]

Hint: Gap method sorts by comparing distant elements [OK]

Common Mistakes:

• Confusing final positions of elements in arr2
• Assuming arr2 remains unchanged
• Misapplying gap calculation