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

Time Complexity: Array Deletion at Beginning

O(n)

Understanding Time Complexity

When we delete an element from the start of an array, the computer must adjust the rest of the elements.

We want to know how the time needed changes as the array gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void deleteAtBeginning(int arr[], int *size) {
    for (int i = 0; i < *size - 1; i++) {
        arr[i] = arr[i + 1];
    }
    (*size)--;
}
    

This code removes the first element by shifting all other elements one position left.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that shifts elements left.
• How many times: It runs once for each element except the first, so roughly n-1 times.

How Execution Grows With Input

As the array size grows, the number of shifts grows almost the same way.

Input Size (n)	Approx. Operations
10	9 shifts
100	99 shifts
1000	999 shifts

Pattern observation: The work grows roughly in a straight line with the number of elements.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete the first element grows directly with the array size.

Common Mistake

[X] Wrong: "Deleting the first element is always fast and takes constant time."

[OK] Correct: Because the array needs to move all other elements to fill the gap, which takes time proportional to the array size.

Interview Connect

Understanding this helps you explain why some data structures are better for certain operations, showing your grasp of efficiency.

Self-Check

"What if we deleted the last element instead of the first? How would the time complexity change?"

Practice

1. What happens to the elements of an array when you delete the first element (at the beginning)?

easy

A. All elements shift one position to the right, and the last element is removed.

B. All elements shift one position to the left, and the first element is removed.

C. The array size increases by one.

D. The array remains unchanged.

Solution

1. Step 1: Understand deletion at beginning

   Deleting the first element means removing the element at index 0.

2. Step 2: Effect on remaining elements

   All other elements move one position left to fill the gap.

3. Final Answer:

   All elements shift one position to the left, and the first element is removed. -> Option B

4. Quick Check:

   Deletion at start shifts elements left [OK]

Hint: Deleting start shifts all elements left by one [OK]

Common Mistakes:

• Thinking elements shift right instead of left
• Assuming array size increases
• Believing array stays unchanged

2. Which of the following C code snippets correctly deletes the first element of an integer array arr of size n by shifting elements left?

easy

A. for(int i = 0; i < n; i++) { arr[i] = arr[i]; } n--;

B. for(int i = n - 1; i > 0; i--) { arr[i] = arr[i - 1]; } n++;

C. for(int i = 0; i < n - 1; i++) { arr[i] = arr[i + 1]; } n--;

D. for(int i = 1; i < n; i++) { arr[i] = arr[i - 1]; } n--;

Solution

1. Step 1: Identify correct loop for shifting left

   The loop must start from index 0 and assign arr[i] = arr[i+1] up to n-2.

2. Step 2: Check array size update

   After shifting, size decreases by 1 (n--).

3. Final Answer:

   for(int i = 0; i < n - 1; i++) { arr[i] = arr[i + 1]; } n--; -> Option C

4. Quick Check:

   Shift left from 0 to n-2, then reduce size [OK]

Hint: Shift elements left from 0 to n-2, then decrease size [OK]

Common Mistakes:

• Looping backwards instead of forwards
• Increasing size instead of decreasing
• Incorrect loop bounds causing overwrite

3. What is the output array after deleting the first element from int arr[] = {10, 20, 30, 40, 50}; using the correct deletion method?

medium

A. [50, 40, 30, 20]

B. [10, 20, 30, 40]

C. [30, 40, 50]

D. [20, 30, 40, 50]

Solution

1. Step 1: Remove first element 10

   Deleting first element removes 10 from the array.

2. Step 2: Shift remaining elements left

   Elements 20, 30, 40, 50 shift left to fill index 0 to 3.

3. Final Answer:

   [20, 30, 40, 50] -> Option D

4. Quick Check:

   First element removed, others shifted left [OK]

Hint: After deletion, array starts from second element [OK]

Common Mistakes:

• Leaving original first element in array
• Removing last element instead
• Reversing array order

4. Consider this code snippet for deleting the first element of an array:

for(int i = 1; i < n; i++) { arr[i-1] = arr[i]; } n--;

What is the error in this code?

medium

A. The loop correctly shifts elements; no error present.

B. The loop should start from i = 0, not 1.

C. The array size should be increased, not decreased.

D. The assignment should be arr[i] = arr[i-1], not arr[i-1] = arr[i].

Solution

1. Step 1: Analyze loop start and assignments

   The loop starts at i=1 and assigns arr[i-1] = arr[i], shifting elements left correctly.

2. Step 2: Check array size update

   Decreasing n by 1 after shifting is correct to reflect deletion.

3. Final Answer:

   The loop correctly shifts elements; no error present. -> Option A

4. Quick Check:

   Loop from 1 with arr[i-1]=arr[i] shifts left [OK]

Hint: Loop from 1 with arr[i-1]=arr[i] shifts left correctly [OK]

Common Mistakes:

• Thinking loop must start at 0 for shifting left
• Confusing assignment direction
• Incorrectly changing array size

5. You have an array int arr[] = {5, 10, 15, 20, 25, 30}; and size n = 6. You delete the first element twice using the correct deletion method. What is the resulting array and size?

hard

A. Array: [15, 20, 25, 30], Size: 4

B. Array: [10, 15, 20, 25, 30], Size: 5

C. Array: [5, 10, 15, 20], Size: 4

D. Array: [20, 25, 30], Size: 3

Solution

1. Step 1: First deletion removes 5

   After first deletion, array becomes [10, 15, 20, 25, 30], size 5.

2. Step 2: Second deletion removes 10

   After second deletion, array becomes [15, 20, 25, 30], size 4.

3. Final Answer:

   Array: [15, 20, 25, 30], Size: 4 -> Option A

4. Quick Check:

   Two deletions remove first two elements, size reduces by 2 [OK]

Hint: Each deletion removes first element and reduces size by one [OK]

Common Mistakes:

• Not updating size after each deletion
• Deleting wrong elements
• Confusing array indexes after shifts