Push Operation on Stack in DSA C++ - Time & Space Complexity

Time Complexity: Push Operation on Stack

O(1)

Understanding Time Complexity

We want to understand how the time needed to add an item to a stack changes as the stack grows.

How does pushing an element affect the total work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void push(int value) {
    if (top == capacity - 1) {
        // Stack is full, resize or error
        return;
    }
    top++;
    arr[top] = value;
}
    

This code adds a new value to the top of the stack if there is space.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Assigning the new value to the top position in the array.
• How many times: Exactly once per push call.

How Execution Grows With Input

Each push does the same small amount of work no matter how many items are already in the stack.

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

Pattern observation: The work stays constant even as the stack grows.

Final Time Complexity

Time Complexity: O(1)

This means pushing an item takes the same short time no matter how big the stack is.

Common Mistake

[X] Wrong: "Pushing takes longer as the stack gets bigger because it has to move all the items."

[OK] Correct: The push operation only adds one item at the top without moving others, so time stays the same.

Interview Connect

Knowing that push is a quick, constant-time operation helps you explain stack efficiency clearly in interviews.

Self-Check

"What if the stack needs to resize its array when full? How would the time complexity of push change then?"

Practice

1. What does the push operation do in a stack?

easy

A. Checks if the stack is empty

B. Removes the top element from the stack

C. Returns the bottom element of the stack

D. Adds an element to the top of the stack

Solution

1. Step 1: Understand stack behavior

   A stack follows Last In First Out (LIFO) principle, where elements are added or removed from the top.

2. Step 2: Define push operation

   The push operation adds a new element on top of the existing stack elements.

3. Final Answer:

   Adds an element to the top of the stack -> Option D

4. Quick Check:

   Push = Add top element [OK]

Hint: Push means add element on top of stack [OK]

Common Mistakes:

• Confusing push with pop operation
• Thinking push removes elements
• Assuming push checks stack emptiness

2. Which of the following is the correct syntax to push an integer 10 onto a stack named stk in C++ STL?

easy

A. stk.push(10);

B. stk.add(10);

C. stk.insert(10);

D. stk.append(10);

Solution

1. Step 1: Recall C++ STL stack methods

   The standard method to add an element to a stack is push().

2. Step 2: Match correct syntax

   Using stk.push(10); correctly pushes 10 onto the stack.

3. Final Answer:

   stk.push(10); -> Option A

4. Quick Check:

   push() is the correct method [OK]

Hint: Use push() to add elements in C++ stack [OK]

Common Mistakes:

• Using add(), insert(), or append() which are not stack methods
• Forgetting parentheses after push
• Confusing vector methods with stack

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

std::stack<int> stk;
stk.push(5);
stk.push(10);
stk.push(15);
int topElement = stk.top();

What is the value of topElement?

medium

A. 15

B. 10

C. 0

D. 5

Solution

1. Step 1: Trace push operations

   Elements pushed in order: 5, then 10, then 15. Stack top is last pushed element.

2. Step 2: Identify top element

   The top element after pushes is 15, as it was pushed last.

3. Final Answer:

   15 -> Option A

4. Quick Check:

   Last pushed = top element = 15 [OK]

Hint: Top element is last pushed value [OK]

Common Mistakes:

• Choosing first pushed element as top
• Confusing top() with pop()
• Assuming stack is empty initially

4. Identify the error in the following code snippet that tries to push an element onto a stack:

std::stack<int> stk;
stk.push 20;

medium

A. Using wrong data type for stack

B. Stack not declared properly

C. Missing parentheses in push call

D. No error in the code

Solution

1. Step 1: Check push syntax

   The push method requires parentheses around the argument, like push(20).

2. Step 2: Identify syntax error

   Code uses stk.push 20; missing parentheses, causing a syntax error.

3. Final Answer:

   Missing parentheses in push call -> Option C

4. Quick Check:

   push() needs parentheses [OK]

Hint: Always use parentheses with push() [OK]

Common Mistakes:

• Omitting parentheses after push
• Confusing push with pop syntax
• Assuming stack declaration is wrong

5. Given an empty stack, what will be the state of the stack after executing the following code?

std::stack<int> stk;
stk.push(1);
stk.push(2);
stk.push(3);
stk.pop();
stk.push(4);

Choose the correct sequence of elements from top to bottom.

hard

A. 3 -> 2 -> 1 -> null

B. 4 -> 2 -> 1 -> null

C. 1 -> 2 -> 4 -> null

D. 2 -> 4 -> 1 -> null

Solution

1. Step 1: Trace push and pop operations

   Push 1, stack: 1
   Push 2, stack: 2 -> 1
   Push 3, stack: 3 -> 2 -> 1
   Pop removes top (3), stack: 2 -> 1
   Push 4, stack: 4 -> 2 -> 1

2. Step 2: Write final stack state

   Top to bottom: 4 -> 2 -> 1 -> null

3. Final Answer:

   4 -> 2 -> 1 -> null -> Option B

4. Quick Check:

   Push/pop order = 4,2,1 [OK]

Hint: Pop removes top; next push adds new top [OK]

Common Mistakes:

• Ignoring pop effect on stack
• Assuming push adds at bottom
• Mixing order of elements after pop