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 at the start of an array, the computer must adjust the rest of the elements.

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int[] arr = {1, 2, 3, 4, 5};
int n = arr.Length;

// Delete first element by shifting
for (int i = 1; i < n; i++) {
    arr[i - 1] = arr[i];
}
// Optional: reduce size or ignore last element
    

This code removes the first element by moving all other elements one step 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 after the first, so about n-1 times.

How Execution Grows With Input

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

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

Pattern observation: The work grows directly with the number of elements.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete the first element grows in a straight line with the array size.

Common Mistake

[X] Wrong: "Deleting the first element is quick and takes the same time no matter the array size."

[OK] Correct: Because all elements after the first must move, the time depends on how many elements there are.

Interview Connect

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

Self-Check

"What if we used a linked list instead of an array? How would the time complexity of deleting the first element change?"

Practice

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

easy

A. All elements shift one position to the left, and the last element becomes unused.

B. The array size decreases automatically by one.

C. The first element is replaced by null but others stay the same.

D. The array elements remain unchanged.

Solution

1. Step 1: Understand array fixed size in C#

   Arrays have fixed size; deleting an element does not reduce size automatically.

2. Step 2: Effect of deleting first element

   To delete the first element, all other elements shift left by one to fill the gap.

3. Final Answer:

   All elements shift one position to the left, and the last element becomes unused. -> Option A

4. Quick Check:

   Deleting first element shifts left [OK]

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

Common Mistakes:

• Thinking array size changes automatically
• Assuming elements stay in place
• Believing first element becomes null only

2. Which of the following is the correct syntax to delete the first element from an array named arr in C# by shifting elements?

easy

A. arr.RemoveAt(0);

B. for(int i = 0; i < arr.Length - 1; i++) arr[i] = arr[i + 1];

C. for(int i = 1; i < arr.Length; i++) arr[i] = arr[i - 1];

D. arr.Delete(0);

Solution

1. Step 1: Understand array element shifting

   To delete first element, shift elements left starting from index 0 to length-2.

2. Step 2: Check syntax correctness

   for(int i = 0; i < arr.Length - 1; i++) arr[i] = arr[i + 1]; correctly loops from 0 to length-2 and assigns arr[i] = arr[i+1].

3. Final Answer:

   for(int i = 0; i < arr.Length - 1; i++) arr[i] = arr[i + 1]; -> Option B

4. Quick Check:

   Loop from 0 to length-2 shifting elements left [OK]

Hint: Shift elements from index 0 to length-2 left [OK]

Common Mistakes:

• Starting loop from 1 instead of 0
• Using non-existent array methods like RemoveAt
• Assigning elements in wrong direction

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

int[] arr = {10, 20, 30, 40};
for(int i = 0; i < arr.Length - 1; i++) {
  arr[i] = arr[i + 1];
}
arr[arr.Length - 1] = 0;
for(int i = 0; i < arr.Length; i++) {
  Console.Write(arr[i] + " ");
}

medium

A. 20 30 40 0

B. 10 20 30 40

C. 0 20 30 40

D. 20 30 40 40

Solution

1. Step 1: Trace the shifting loop

   Loop shifts elements left: arr[0]=20, arr[1]=30, arr[2]=40.

2. Step 2: Set last element to 0

   arr[3] = 0 replaces old last element 40.

3. Final Answer:

   20 30 40 0 -> Option A

4. Quick Check:

   Shift left + last zero = 20 30 40 0 [OK]

Hint: Shift left then zero last element for deletion [OK]

Common Mistakes:

• Not setting last element to zero
• Confusing loop range causing wrong shifts
• Printing old array without changes

4. Identify the error in the following code that tries to delete the first element of an array arr and fix it:

int[] arr = {5, 10, 15, 20};
for(int i = 1; i < arr.Length; i++) {
  arr[i] = arr[i - 1];
}
arr[arr.Length - 1] = 0;

medium

A. Last element should not be set to zero.

B. Array size must be reduced before shifting.

C. Loop direction is wrong; should shift elements left, not right.

D. The loop should start from 0 and go to arr.Length - 2.

Solution

1. Step 1: Analyze loop direction

   The loop copies arr[i-1] to arr[i], shifting elements right, which is incorrect for deletion.

2. Step 2: Correct loop to shift elements left

   Loop should assign arr[i] = arr[i+1] starting from i=0 to length-2.

3. Final Answer:

   Loop direction is wrong; should shift elements left, not right. -> Option C

4. Quick Check:

   Shift left to delete first element [OK]

Hint: Shift elements left, not right, when deleting at start [OK]

Common Mistakes:

• Shifting elements in wrong direction
• Trying to reduce array size directly
• Ignoring last element cleanup

5. You have an array int[] arr = {3, 6, 9, 12, 15}. Write a method to delete the first element and return a new array with the remaining elements only (size reduced by one). Which approach is correct?

hard

A. Use arr.RemoveAt(0) to delete the first element.

B. Shift elements left in original array and keep the same size.

C. Set arr[0] = 0 and return the original array.

D. Create a new array of size arr.Length - 1 and copy elements from index 1 onward.

Solution

1. Step 1: Understand fixed size arrays

   Arrays in C# have fixed size; to reduce size, create a new array.

2. Step 2: Copy elements except first

   Create new array of size one less and copy elements from index 1 onward.

3. Final Answer:

   Create a new array of size arr.Length - 1 and copy elements from index 1 onward. -> Option D

4. Quick Check:

   New smaller array with elements from index 1 [OK]

Hint: Create new smaller array and copy from index 1 [OK]

Common Mistakes:

• Trying to resize original array directly
• Only shifting elements without resizing
• Using non-existent RemoveAt method on array