Array Reversal Techniques in DSA C - Time & Space Complexity

Time Complexity: Array Reversal Techniques

O(n)

Understanding Time Complexity

We want to understand how the time needed to reverse an array changes as the array gets bigger.

How does the number of steps grow when the array size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void reverseArray(int arr[], int n) {
    int start = 0, end = n - 1;
    while (start < end) {
        int temp = arr[start];
        arr[start] = arr[end];
        arr[end] = temp;
        start++;
        end--;
    }
}
    

This code reverses the elements of an array by swapping pairs from the start and end moving towards the center.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Swapping two elements inside a while loop.
• How many times: The loop runs about n/2 times, where n is the array size.

How Execution Grows With Input

As the array size grows, the number of swaps grows roughly half as fast.

Input Size (n)	Approx. Operations
10	5 swaps
100	50 swaps
1000	500 swaps

Pattern observation: The number of operations grows linearly with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to reverse the array grows directly in proportion to the array size.

Common Mistake

[X] Wrong: "Reversing an array takes constant time because we just swap elements."

[OK] Correct: Even though each swap is quick, the number of swaps grows with the array size, so total time grows too.

Interview Connect

Knowing how array reversal scales helps you understand basic array operations and prepares you for more complex problems.

Self-Check

"What if we used recursion to reverse the array instead of a loop? How would the time complexity change?"

Practice

1. What does reversing an array mean in simple terms?

easy

A. Changing the order of elements so the last becomes first and first becomes last

B. Sorting the array in ascending order

C. Removing duplicate elements from the array

D. Adding new elements at the end of the array

Solution

1. Step 1: Understand array order

   An array has elements arranged from first to last index.

2. Step 2: Define reversal

   Reversing means swapping elements so the last element moves to the first position and vice versa.

3. Final Answer:

   Changing the order of elements so the last becomes first and first becomes last -> Option A

4. Quick Check:

   Reversal = Reverse order [OK]

Hint: Reversal flips the array order front to back [OK]

Common Mistakes:

• Confusing reversal with sorting
• Thinking reversal removes elements
• Assuming reversal adds elements

2. Which of the following C code snippets correctly swaps two elements arr[i] and arr[j] for array reversal?

easy

A. arr[i] = arr[j]; arr[j] = arr[i];

B. temp = arr[j]; arr[j] = arr[i]; arr[i] = temp;

C. int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp;

D. arr[i] = arr[j]; arr[j] = temp;

Solution

1. Step 1: Use a temporary variable for swapping

   To swap two values, store one in a temporary variable to avoid overwriting.

2. Step 2: Assign values correctly

   Assign arr[i] to temp, then arr[j] to arr[i], then temp to arr[j].

3. Final Answer:

   int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; -> Option C

4. Quick Check:

   Swap uses temp variable [OK]

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

Common Mistakes:

• Overwriting one element before saving it
• Using uninitialized temp variable
• Swapping without temp causes data loss

3. What is the output of the following C code?

int arr[] = {1, 2, 3, 4, 5};
int n = 5;
for(int i = 0; i < n/2; i++) {
  int temp = arr[i];
  arr[i] = arr[n - i - 1];
  arr[n - i - 1] = temp;
}
for(int i = 0; i < n; i++) {
  printf("%d ", arr[i]);
}

medium

A. 2 1 4 3 5

B. 5 4 3 2 1

C. 1 2 3 4 5

D. 5 3 2 4 1

Solution

1. Step 1: Understand the loop swaps

   The loop swaps elements from start and end moving towards the center: arr[0] with arr[4], arr[1] with arr[3].

2. Step 2: Trace swaps

   Swap 1 and 5 -> arr = {5, 2, 3, 4, 1}; Swap 2 and 4 -> arr = {5, 4, 3, 2, 1}; middle element 3 stays same.

3. Final Answer:

   5 4 3 2 1 -> Option B

4. Quick Check:

   Reversed array = 5 4 3 2 1 [OK]

Hint: Swapping pairs from ends reverses array [OK]

Common Mistakes:

• Not swapping all pairs correctly
• Loop running too many or too few times
• Confusing indices in swap

4. Identify the error in this C code snippet intended to reverse an array:

int arr[] = {10, 20, 30, 40};
int n = 4;
for(int i = 0; i <= n/2; i++) {
  int temp = arr[i];
  arr[i] = arr[n - i - 1];
  arr[n - i - 1] = temp;
}

medium

A. Temporary variable temp is not declared

B. The swap logic is incorrect

C. Array size n is wrong

D. The loop condition should be i < n/2 instead of i <= n/2

Solution

1. Step 1: Analyze loop condition

   The loop runs from i = 0 to i <= n/2, which means it runs one extra iteration when i = n/2.

2. Step 2: Understand effect of extra iteration

   For even n=4, n/2=2, so i=2 is invalid index for swapping (out of bounds or swaps middle element twice).

3. Final Answer:

   The loop condition should be i < n/2 instead of i <= n/2 -> Option D

4. Quick Check:

   Loop runs too far, fix condition [OK]

Hint: Use i < n/2 to avoid extra swap [OK]

Common Mistakes:

• Using <= causes out-of-bound swaps
• Confusing array length with index
• Ignoring zero-based indexing

5. Given an array arr of size n, which approach is best to reverse the array in-place with minimum extra memory and why?

hard

A. Use two pointers, one at start and one at end, swap and move towards center

B. Create a new array and copy elements from end to start

C. Use recursion to swap elements from ends

D. Sort the array in descending order

Solution

1. Step 1: Compare memory usage of methods

   Creating a new array uses extra memory equal to array size; recursion uses call stack memory.

2. Step 2: Evaluate two-pointer method

   Two pointers swap elements in-place without extra memory, making it efficient and simple.

3. Final Answer:

   Use two pointers, one at start and one at end, swap and move towards center -> Option A

4. Quick Check:

   Two-pointer swap = minimal memory [OK]

Hint: Two-pointer swap reverses in-place with no extra memory [OK]

Common Mistakes:

• Using extra arrays wastes memory
• Recursion adds unnecessary stack overhead
• Sorting does not reverse original order