Array Deletion at End in DSA Python - 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 item 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.

def delete_at_end(arr):
    if len(arr) == 0:
        return None
    return arr.pop()

This code removes the last item from the array if it exists.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Removing the last element using pop()
• How many times: Exactly once per call, no loops or recursion

How Execution Grows With Input

Removing the last item takes the same amount of time no matter how big the array is.

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

Pattern observation: The time stays constant as the array grows.

Final Time Complexity

Time Complexity: O(1)

This means removing the last item takes the same short time no matter how big the array is.

Common Mistake

[X] Wrong: "Removing the last item takes longer if the array is bigger because it has to shift elements."

[OK] Correct: When deleting at the end, no elements need to move. Only the last item is removed, so time stays the same.

Interview Connect

Knowing that deleting at the end is very fast helps you choose the right data structure and method in real problems.

Self-Check

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

Practice

1. What happens when you delete the last element from an array in Python using pop()?

easy

A. The first element is removed and the array size stays the same.

B. The last element is removed and the array size decreases by one.

C. The array is cleared completely.

D. The array becomes empty but elements remain.

Solution

1. Step 1: Understand the pop() method

   The pop() method removes the last element from the array (list) by default.

2. Step 2: Effect on array size

   After removal, the array size decreases by one because one element is deleted.

3. Final Answer:

   The last element is removed and the array size decreases by one. -> Option B

4. Quick Check:

   pop() removes last element [OK]

Hint: pop() removes last item and shrinks array [OK]

Common Mistakes:

• Thinking pop() removes the first element
• Assuming pop() clears the whole array
• Believing array size stays the same after pop()

2. Which of the following is the correct syntax to delete the last element from a list named arr in Python?

easy

A. arr.pop()

B. arr.delete()

C. pop(arr)

D. arr.remove_last()

Solution

1. Step 1: Identify the correct method for deletion at end

   In Python, pop() is the method used to remove the last element from a list.

2. Step 2: Check syntax correctness

   The correct syntax is arr.pop(). Other options are invalid or do not exist in Python.

3. Final Answer:

   arr.pop() -> Option A

4. Quick Check:

   pop() is correct syntax [OK]

Hint: Use arr.pop() to remove last element [OK]

Common Mistakes:

• Using arr.delete() which is invalid
• Trying pop(arr) instead of arr.pop()
• Using arr.remove_last() which does not exist

3. What is the output of the following code?

arr = [10, 20, 30, 40]
arr.pop()
print(arr)

medium

A. [10, 20, 30]

B. [20, 30, 40]

C. [10, 20, 30, 40]

D. [10, 20, 40]

Solution

1. Step 1: Understand pop() effect on arr

   The pop() removes the last element, which is 40.

2. Step 2: Print the updated array

   After removal, the array becomes [10, 20, 30].

3. Final Answer:

   [10, 20, 30] -> Option A

4. Quick Check:

   Last element removed, array shrinks [OK]

Hint: pop() removes last element, print updated list [OK]

Common Mistakes:

• Expecting original array unchanged
• Removing first element instead of last
• Confusing pop() with remove()

4. Find the error in the following code that tries to delete the last element from arr:

arr = [1, 2, 3]
arr.pop(0)
print(arr)

medium

A. pop() deletes the entire array

B. pop() cannot take any arguments

C. pop() should be replaced with remove()

D. pop(0) removes the first element, not the last

Solution

1. Step 1: Analyze pop(0) usage

   pop(0) removes the element at index 0, which is the first element, not the last.

2. Step 2: Identify correct method to delete last element

   To delete the last element, pop() should be called without arguments.

3. Final Answer:

   pop(0) removes the first element, not the last -> Option D

4. Quick Check:

   pop(index) removes element at index [OK]

Hint: pop() without argument removes last element [OK]

Common Mistakes:

• Assuming pop() cannot take arguments
• Using pop(0) to remove last element
• Confusing pop() with remove()

5. Given the list arr = [5, 10, 15, 20, 25], you want to remove the last two elements using pop(). Which code snippet correctly achieves this?

hard

A. arr.pop(1)
arr.pop(0)

B. arr.pop(3)
arr.pop(2)

C. arr.pop()
arr.pop()

D. arr.pop(0)
arr.pop(1)

Solution

1. Step 1: Understand pop() without argument

   Calling pop() without arguments removes the last element each time.

2. Step 2: Apply pop() twice to remove last two elements

   Calling arr.pop() twice removes 25 then 20, the last two elements.

3. Step 3: Check other options

   Options A, B, and C use indices that become invalid or remove wrong elements after first pop.

4. Final Answer:

   arr.pop() followed by arr.pop() -> Option C

5. Quick Check:

   pop() twice removes last two elements [OK]

Hint: Use pop() twice to remove last two elements [OK]

Common Mistakes:

• Using pop() with fixed indices without updating
• Removing first elements instead of last
• Assuming pop() clears multiple elements at once