Array Deletion at End in DSA C - Time & Space Complexity

Time Complexity: Array Deletion at End

O(1)

Understanding Time Complexity

We want to understand how fast it is to remove an element from the end of an array.

How does the time needed change as the array gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void deleteAtEnd(int arr[], int *size) {
    if (*size == 0) return; // no elements to delete
    (*size)--;
}
    

This code removes the last element by reducing the size count of the array.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Decreasing the size variable by one.
• How many times: Happens once per deletion call, no loops or recursion.

How Execution Grows With Input

Removing the last element always takes the same small step, no matter how big the array is.

Input Size (n)	Approx. Operations
10	1
100	1
1000	1

Pattern observation: The time stays constant regardless of array size.

Final Time Complexity

Time Complexity: O(1)

This means deleting the last element takes the same short time no matter how big the array is.

Common Mistake

[X] Wrong: "Deleting from the end takes longer as the array grows because we have to move many elements."

[OK] Correct: We do not move any elements when deleting at the end; we just reduce the size count, so time stays the same.

Interview Connect

Knowing that deleting at the end is very fast helps you choose the right data structure and shows you understand how arrays work under the hood.

Self-Check

"What if we changed deletion to remove the first element instead? How would the time complexity change?"

Practice

1. What happens to the size of an array when you delete an element from the end in a typical static array implementation?

easy

A. The size decreases by one

B. The size stays the same

C. The size increases by one

D. The size becomes zero

Solution

1. Step 1: Understand array size after deletion

   Deleting an element from the end means removing the last element, so the total number of elements reduces by one.

2. Step 2: Effect on array size

   The size variable or count of elements decreases by one to reflect the removal.

3. Final Answer:

   The size decreases by one -> Option A

4. Quick Check:

   Deleting last element reduces size by 1 [OK]

Hint: Deleting end element reduces size by one [OK]

Common Mistakes:

• Thinking size stays same after deletion
• Assuming size increases after deletion
• Confusing deletion with insertion

2. Which of the following is the correct way to delete the last element from an array arr of size n in C?

easy

A. free(arr[n-1]);

B. arr[n] = 0;

C. n = n - 1;

D. arr = arr - 1;

Solution

1. Step 1: Understand array deletion in C

   In static arrays, deleting means reducing the size count. So, decreasing n by 1 removes last element logically.

2. Step 2: Analyze options

   n = n - 1; correctly reduces size. arr[n] = 0; tries to set element but doesn't change size. free(arr[n-1]); is invalid as free is for dynamic memory. arr = arr - 1; is invalid pointer arithmetic.

3. Final Answer:

   n = n - 1; -> Option C

4. Quick Check:

   Decrease size variable to delete last element [OK]

Hint: Reduce size variable to delete last element [OK]

Common Mistakes:

• Using free() on static array elements
• Trying to set last element to zero without changing size
• Incorrect pointer arithmetic

3. What will be the output of the following C code?

int arr[5] = {10, 20, 30, 40, 50};
int n = 5;
n = n - 1;
for(int i = 0; i < n; i++) {
    printf("%d ", arr[i]);
}

medium

A. 10 20 30 40 50

B. 10 20 30 40

C. 20 30 40 50

D. 10 20 30

Solution

1. Step 1: Understand size after deletion

   Initially, n is 5. After n = n - 1;, n becomes 4, so loop runs from 0 to 3.

2. Step 2: Loop prints elements from index 0 to 3

   Elements printed are arr[0]=10, arr[1]=20, arr[2]=30, arr[3]=40.

3. Final Answer:

   10 20 30 40 -> Option B

4. Quick Check:

   Loop runs n=4 times, prints first 4 elements [OK]

Hint: After reducing size, loop prints fewer elements [OK]

Common Mistakes:

• Printing all 5 elements ignoring updated size
• Starting loop from 1 instead of 0
• Confusing array indices

4. Identify the error in the following code snippet that attempts to delete the last element of an array arr of size n.

void deleteEnd(int arr[], int n) {
    arr[n] = 0;
    n = n - 1;
}

medium

A. Accessing arr[n] is out of bounds

B. Size variable n should not be changed

C. Setting arr[n] to 0 deletes the element

D. Function should return the new size

Solution

1. Step 1: Check array index usage

   Array indices go from 0 to n-1. Accessing arr[n] is out of bounds and causes undefined behavior.

2. Step 2: Understand deletion logic

   To delete last element, reduce size n by 1. Setting arr[n] to 0 is invalid and does not delete element.

3. Final Answer:

   Accessing arr[n] is out of bounds -> Option A

4. Quick Check:

   Array index must be less than size [OK]

Hint: Array last index is n-1, not n [OK]

Common Mistakes:

• Using arr[n] instead of arr[n-1]
• Assuming setting element to zero deletes it
• Not updating size correctly

5. Given a dynamic array implemented with a pointer int *arr and current size n, which of the following correctly deletes the last element and updates the array size safely in C?

hard

A. free(arr[n-1]); n = n - 1;

B. arr[n-1] = 0; n = n - 1;

C. arr = arr - 1; n = n - 1;

D. n = n - 1; arr = realloc(arr, n * sizeof(int));

Solution

1. Step 1: Understand dynamic array deletion

   To delete last element, reduce size n by 1 and resize memory using realloc to avoid wasted space.

2. Step 2: Analyze options

   n = n - 1; arr = realloc(arr, n * sizeof(int)); correctly reduces size and resizes memory. arr[n-1] = 0; n = n - 1; sets element to zero but wastes memory. free(arr[n-1]); n = n - 1; incorrectly uses free on element. arr = arr - 1; n = n - 1; does invalid pointer arithmetic.

3. Final Answer:

   n = n - 1; arr = realloc(arr, n * sizeof(int)); -> Option D

4. Quick Check:

   Reduce size and resize memory with realloc [OK]

Hint: Use realloc after reducing size for dynamic arrays [OK]

Common Mistakes:

• Not resizing memory after deletion
• Using free() on array elements
• Incorrect pointer arithmetic