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 the push operation behave when the stack size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Push operation on stack
void push(int stack[], int *top, int value, int max_size) {
    if (*top == max_size - 1) {
        // Stack overflow
        return;
    }
    (*top)++;
    stack[*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: Single assignment to the stack array at the top position.
• How many times: Exactly once per push call, no loops or recursion involved.

How Execution Grows With Input

Each push does a fixed number of steps regardless of stack size.

Input Size (n)	Approx. Operations
10	3 steps (check, increment, assign)
100	3 steps
1000	3 steps

Pattern observation: The number of steps stays the same no matter how big the stack is.

Final Time Complexity

Time Complexity: O(1)

This means pushing an item takes the same short time no matter how many items are already in the stack.

Common Mistake

[X] Wrong: "Push takes longer as the stack grows because it has to move all items."

[OK] Correct: Push only adds one item at the top without moving others, so time does not grow with stack size.

Interview Connect

Knowing push is always quick helps you explain why stacks are efficient for adding data, a key skill in many coding problems.

Self-Check

"What if the stack was implemented using a linked list instead of an array? How would the time complexity of push change?"

Practice

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

easy

A. Checks if the stack is empty

B. Adds an element to the top of the stack

C. Removes the top element from the stack

D. Returns the bottom element of the stack

Solution

1. Step 1: Understand stack operations

   A stack is a data structure where elements are added or removed from the top only.

2. Step 2: Define push operation

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

3. Final Answer:

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

4. Quick Check:

   Push means add on top = C [OK]

Hint: Push always adds on top of stack [OK]

Common Mistakes:

• Confusing push with pop operation
• Thinking push removes elements
• Mixing stack with queue operations

2. Which of the following is the correct syntax to push an element 5 onto a stack named s in C?

easy

A. s.push = 5;

B. s.push(5);

C. push(5, s);

D. push(s, 5);

Solution

1. Step 1: Understand typical C stack push syntax

   In C, stack operations are usually functions where the stack is passed as the first argument.

2. Step 2: Match syntax with parameters

   The correct function call to push 5 onto stack s is push(s, 5);.

3. Final Answer:

   push(s, 5); -> Option D

4. Quick Check:

   Function push(stack, value) = A [OK]

Hint: In C, function push(stack, value) is standard [OK]

Common Mistakes:

• Using object.method syntax (not C style)
• Swapping argument order
• Assigning value instead of calling function

3. What will be the content of the stack after executing the following code?

int stack[5];
int top = -1;
// Push function
void push(int val) {
  if(top < 4) {
    top++;
    stack[top] = val;
  }
}

push(10);
push(20);
push(30);

medium

A. [10, 20, 30]

B. [30, 20, 10]

C. [10, 20]

D. Empty stack

Solution

1. Step 1: Trace each push call

   Initially, top = -1. After push(10), top=0, stack[0]=10. After push(20), top=1, stack[1]=20. After push(30), top=2, stack[2]=30.

2. Step 2: List stack content from bottom to top

   Stack elements from index 0 to top (2) are [10, 20, 30].

3. Final Answer:

   [10, 20, 30] -> Option A

4. Quick Check:

   Push adds at top increasing index = B [OK]

Hint: Stack stores pushed elements in order at increasing top index [OK]

Common Mistakes:

• Reversing order of elements
• Confusing top index with element values
• Assuming stack is empty after pushes

4. Identify the error in the following push function for a stack of size 3:

int stack[3];
int top = 0;
void push(int val) {
  if(top <= 3) {
    stack[top] = val;
    top++;
  }
}

medium

A. Condition should be top < 3, not top <= 3

B. top should be incremented before assignment

C. stack array size should be 4

D. top should start at -1, not 0

Solution

1. Step 1: Analyze top and condition

   top starts at 0, which is valid for empty stack at index 0. The condition allows top to be 3, which is out of bounds for stack[3] (indices 0 to 2).

2. Step 2: Correct the condition

   Change condition to top < 3 to prevent overflow and invalid access.

3. Final Answer:

   Condition should be top < 3, not top <= 3 -> Option A

4. Quick Check:

   Stack max index 2 means top < 3 [OK]

Hint: Check array bounds: top must be less than size [OK]

Common Mistakes:

• Allowing top to equal array size causing overflow
• Starting top at -1 but not adjusting code
• Incrementing top before assignment causing skip

5. Given a stack implemented with an array of size 4 and top = 2 currently, what will happen if we try to push two more elements without popping?
Choose the correct behavior.

hard

A. Both pushes fail immediately due to full stack

B. Both pushes succeed, stack size automatically increases

C. First push succeeds, second push causes stack overflow

D. First push causes overflow, second push is not attempted

Solution

1. Step 1: Understand current stack state

   Array size is 4, so valid indices are 0 to 3. top=2 means top element is at index 2, so one slot remains at index 3.

2. Step 2: Push two elements

   First push increments top to 3 and stores element at index 3 (valid). Second push tries to increment top to 4, which is out of bounds, causing overflow.

3. Final Answer:

   First push succeeds, second push causes stack overflow -> Option C

4. Quick Check:

   Array size 4, top max index 3, overflow after that [OK]

Hint: Stack size fixed; overflow after last index [OK]

Common Mistakes:

• Assuming stack auto-expands
• Thinking both pushes fail immediately
• Confusing top index with count