Merge Two Sorted Arrays Without Extra Space in DSA C++ - Build from Scratch

Merge Two Sorted Arrays Without Extra Space

📖 Scenario: You have two sorted arrays representing two sorted lists of numbers. You want to combine them into one sorted sequence without using extra space for another array.Imagine you have two shelves with sorted books by height, and you want to rearrange the books so that all books on the first shelf are the smallest ones and all books on the second shelf are the bigger ones, keeping the order sorted.

🎯 Goal: Build a program that merges two sorted arrays into sorted order without using extra space. The first array should contain the smallest elements and the second array the larger elements after merging.

📋 What You'll Learn

Create two sorted arrays with exact values

Use a variable to track the size of the first array

Implement the merge logic without extra space

Print the two arrays after merging

💡 Why This Matters

🌍 Real World

Merging sorted data streams or lists without extra memory is useful in memory-limited devices or when working with large datasets.

💼 Career

Understanding in-place merging helps in optimizing algorithms and is a common interview question for software engineering roles.

1

Create two sorted arrays

Create two sorted arrays called arr1 and arr2 with these exact values: arr1 = {1, 5, 9, 10, 15, 20} and arr2 = {2, 3, 8, 13}

DSA C++

# Create two sorted arrays arr1 and arr2 with given values
# Your code here

Hint

Use C++ array initialization syntax with exact values.

2

Add size variables for the arrays

Create two integer variables called n and m to store the sizes of arr1 and arr2 respectively. Set n = 6 and m = 4.

DSA C++

int arr1[] = {1, 5, 9, 10, 15, 20};
int arr2[] = {2, 3, 8, 13};
// Create variables n and m for sizes of arr1 and arr2
# Your code here

Hint

Count the number of elements in each array and assign to n and m.

3

Merge the two arrays without extra space

Write a nested for loop to merge arr1 and arr2 without extra space. Use for (int i = 0; i < n; i++) and inside it for (int j = 0; j < m; j++). Inside the inner loop, if arr1[i] > arr2[j], swap arr1[i] and arr2[j]. After the loops, sort arr2 using std::sort(arr2, arr2 + m);

DSA C++

int arr1[] = {1, 5, 9, 10, 15, 20};
int arr2[] = {2, 3, 8, 13};
int n = 6;
int m = 4;
// Merge arr1 and arr2 without extra space
# Your code here

Hint

Use nested loops to compare and swap elements, then sort the second array.

4

Print the merged arrays

Print the elements of arr1 and arr2 separated by spaces. Use two for loops: one for arr1 from 0 to n, and one for arr2 from 0 to m. Print a newline between the two arrays.

DSA C++

int arr1[] = {1, 5, 9, 10, 15, 20};
int arr2[] = {2, 3, 8, 13};
int n = 6;
int m = 4;

for (int i = 0; i  arr2[j]) {
            int temp = arr1[i];
            arr1[i] = arr2[j];
            arr2[j] = temp;
        }
    }
}

std::sort(arr2, arr2 + m);

// Print arr1 and arr2 elements
# Your code here

Hint

Use two loops to print each array's elements separated by spaces, then print a newline.

Practice

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

easy

A. Copy elements from one array to another without sorting

B. Sort each array separately using extra space

C. Create a new array to hold merged elements

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

Solution

1. Step 1: Understand the problem requirement

   The problem asks 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 combined, without allocating new memory.

3. Final Answer:

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

4. Quick Check:

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

Hint: Think in-place rearrangement, no new arrays needed [OK]

Common Mistakes:

• Assuming extra space is allowed
• Trying to merge by creating a new array
• Sorting arrays separately without merging

2. Which of the following C++ code snippets correctly swaps two elements without using extra space?

easy

A. a = a + b; b = a - b; a = a - b;

B. temp = a; a = b; b = temp;

C. a = b; b = a;

D. a = a * b; b = a / b; a = a / b;

Solution

1. Step 1: Analyze swapping without extra variable

   a = a + b; b = a - b; a = a - b; uses arithmetic operations to swap values without a temporary variable.

2. Step 2: Check correctness of each option

   temp = a; a = b; b = temp; uses a temporary variable, so it uses extra space. a = b; b = a; assigns a to b and then b to a, which loses original value. a = a * b; b = a / b; a = a / b; uses multiplication/division which can cause overflow or errors if b is zero.

3. Final Answer:

   a = a + b; b = a - b; a = a - b; -> Option A

4. Quick Check:

   Swap without temp = arithmetic trick [OK]

Hint: Use arithmetic swap to avoid extra variable [OK]

Common Mistakes:

• Using a temporary variable (extra space)
• Overwriting values without saving
• Using multiplication/division causing errors

3. What will be the content of arrays arr1 and arr2 after merging without extra space using the gap method?

arr1 = {1, 5, 9, 10}
arr2 = {2, 3, 8, 13}

medium

A. arr1 = {1, 2, 3, 5}, arr2 = {8, 9, 10, 13}

B. arr1 = {1, 3, 5, 8}, arr2 = {2, 9, 10, 13}

C. arr1 = {1, 2, 5, 8}, arr2 = {3, 9, 10, 13}

D. arr1 = {1, 2, 3, 8}, arr2 = {5, 9, 10, 13}

Solution

1. Step 1: Apply gap method to merge arrays

   Start with gap = ceil((4+4)/2) = 4. Compare elements at gap distance and swap if needed, then reduce gap until 0.

2. Step 2: Final sorted arrays after gap method

   After applying the method, 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 A

4. Quick Check:

   Gap method merges arrays in-place correctly [OK]

Hint: Use gap method: reduce gap, swap if needed [OK]

Common Mistakes:

• Not reducing gap properly
• Swapping wrong elements
• Confusing array indices across two arrays

4. Identify the error in the following code snippet that attempts to merge two sorted arrays without extra space:

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

medium

A. Swapping elements without checking bounds causes runtime error

B. Loop should run till m instead of n

C. Sorting arr2 inside the loop causes high time complexity

D. No error, code is optimal

Solution

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

   The code sorts arr2 inside the loop for every swap, which is inefficient and increases time complexity to O(n*m*log m).

2. Step 2: Identify the performance issue

   Sorting arr2 repeatedly is costly; better methods avoid sorting inside the loop.

3. Final Answer:

   Sorting arr2 inside the loop causes high time complexity -> Option C

4. Quick Check:

   Sorting inside loop = inefficient [OK]

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

Common Mistakes:

• Ignoring time complexity impact
• Assuming swap causes runtime error
• Confusing loop bounds

5. Given two sorted arrays arr1 = {10, 12, 15, 18} and arr2 = {2, 5, 20, 25}, how can you merge them without extra space so that after merging, arr1 contains the first four smallest elements and arr2 contains the remaining elements sorted?

hard

A. Swap elements only if arr1[i] is greater than arr2[j] without sorting arr2

B. Use the gap method to compare and swap elements across arrays until fully merged

C. Sort both arrays separately and then concatenate

D. Copy all elements to a new array, sort it, then copy back

Solution

1. Step 1: Understand the gap method for merging

   The gap method reduces the gap between compared elements and swaps if needed, working across both arrays without extra space.

2. Step 2: Apply gap method to given arrays

   By repeatedly comparing and swapping elements at the gap distance, arr1 will hold the smallest elements and arr2 the larger ones, both sorted.

3. Final Answer:

   Use the gap method to compare and swap elements across arrays until fully merged -> Option B

4. Quick Check:

   Gap method merges sorted arrays in-place [OK]

Hint: Use gap method for in-place merge without extra space [OK]

Common Mistakes:

• Using extra arrays violating constraints
• Sorting arrays separately without merging
• Swapping without sorting arr2 leads to wrong order