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; // nothing to delete
    size = size - 1; // reduce size by one
}
    

This code removes the last element by simply 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: This operation happens once per deletion.

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 the same even if the array grows larger.

Final Time Complexity

Time Complexity: O(1)

This means deleting the last element takes a constant amount of time regardless of array size.

Common Mistake

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

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

Interview Connect

Knowing that deleting at the end is very fast helps you choose the right data structure and operation in real projects and interviews.

Self-Check

"What if we changed to deleting an element at the start of the array? 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 dynamic array?

easy

A. The size decreases by one

B. The size remains the same

C. The size increases by one

D. The size becomes zero

Solution

1. Step 1: Understand dynamic array size behavior

   When an element is deleted from the end, the array size reduces by one because one element is removed.

2. Step 2: Confirm size change after deletion

   Deleting from the end does not affect other elements, only reduces size by one.

3. Final Answer:

   The size decreases by one -> Option A

4. Quick Check:

   Size after deletion = original size - 1 [OK]

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

Common Mistakes:

• Thinking size remains same after deletion
• Assuming size increases after deletion
• Confusing deletion at end with deletion at start

2. Which of the following is the correct syntax to delete the last element from a vector named vec in C++?

easy

A. vec.erase_end();

B. vec.delete_last();

C. vec.remove_end();

D. vec.pop_back();

Solution

1. Step 1: Recall vector deletion syntax

   The standard method to remove the last element from a vector in C++ is pop_back().

2. Step 2: Verify other options

   Other methods like delete_last(), remove_end(), and erase_end() do not exist in C++ STL vector.

3. Final Answer:

   vec.pop_back(); -> Option D

4. Quick Check:

   Use pop_back() to delete last element [OK]

Hint: Use pop_back() to remove last element in vector [OK]

Common Mistakes:

• Using non-existent methods like delete_last()
• Confusing erase() with erase_end()
• Trying to use remove_end() which is invalid

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

std::vector<int> v = {10, 20, 30, 40};
v.pop_back();
for(int x : v) std::cout << x << " ";

medium

A. 10 20 30 40

B. 20 30 40

C. 10 20 30

D. 10 20 40

Solution

1. Step 1: Understand pop_back effect on vector

   pop_back() removes the last element, which is 40 in this vector.

2. Step 2: Print remaining elements

   After removal, vector contains 10, 20, 30. Loop prints these with spaces.

3. Final Answer:

   10 20 30 -> Option C

4. Quick Check:

   Last element removed, output = 10 20 30 [OK]

Hint: pop_back() removes last element before printing [OK]

Common Mistakes:

• Printing original vector without deletion
• Confusing which element is removed
• Forgetting pop_back() modifies vector

4. Identify the error in the following code that attempts to delete the last element of an array:

int arr[3] = {1, 2, 3};
arr.pop_back();

medium

A. pop_back() deletes first element, not last

B. pop_back() is not a member of built-in arrays

C. Array size is zero, cannot delete

D. No error, code is correct

Solution

1. Step 1: Check array type and methods

   Built-in arrays in C++ do not have member functions like pop_back().

2. Step 2: Understand correct usage

   pop_back() is a method of std::vector, not raw arrays.

3. Final Answer:

   pop_back() is not a member of built-in arrays -> Option B

4. Quick Check:

   pop_back() only works with vectors, not arrays [OK]

Hint: pop_back() works only on vectors, not raw arrays [OK]

Common Mistakes:

• Assuming pop_back() works on raw arrays
• Ignoring that arrays have fixed size
• Thinking pop_back() deletes first element

5. You have a vector v with elements {5, 10, 15, 20, 25}. You want to delete the last two elements and then print the vector. Which code snippet correctly does this?

hard

A. v.erase(v.end()-2, v.end()); for(auto x : v) std::cout << x << ' ';

B. v.pop_back(); for(auto x : v) std::cout << x << ' ';

C. v.remove_end(); v.remove_end(); for(auto x : v) std::cout << x << ' ';

D. v.pop_back(2); for(auto x : v) std::cout << x << ' ';

Solution

1. Step 1: Understand methods to delete multiple elements

   pop_back() removes only one element at a time. To remove two, it must be called twice. erase() can remove a range efficiently.

2. Step 2: Analyze the snippets

   The snippet v.erase(v.end()-2, v.end()); for(auto x : v) std::cout << x << ' '; correctly removes the last two elements. The snippet with a single v.pop_back(); removes only one element. remove_end() does not exist. pop_back(2) uses invalid syntax.

3. Final Answer:

   v.erase(v.end()-2, v.end()); for(auto x : v) std::cout << x << ' '; -> Option A

4. Quick Check:

   erase() with range removes last two elements efficiently [OK]

Hint: Use erase(end()-2, end()) to delete last two elements [OK]

Common Mistakes:

• Using pop_back() only once instead of twice
• Using non-existent remove_end() method
• Not knowing erase() can remove ranges