Stack Concept and LIFO Principle in DSA C - Time & Space Complexity

Time Complexity: Stack Concept and LIFO Principle

O(1)

Understanding Time Complexity

We want to understand how long it takes to add or remove items from a stack.

How does the time change when the stack grows bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Push operation: add item to stack
void push(int stack[], int *top, int value) {
    stack[++(*top)] = value;
}

// Pop operation: remove item from stack
int pop(int stack[], int *top) {
    return stack[(*top)--];
}
    

This code adds or removes one item from the top of the stack using the LIFO rule.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single step to add or remove one item.
• How many times: Each push or pop does this once, no loops involved.

How Execution Grows With Input

Each push or pop takes the same short time no matter how big the stack is.

Input Size (n)	Approx. Operations
10	1 operation per push or pop
100	1 operation per push or pop
1000	1 operation per push or pop

Pattern observation: Time stays the same no matter how many items are in the stack.

Final Time Complexity

Time Complexity: O(1)

This means adding or removing an item takes a fixed, quick step regardless of stack size.

Common Mistake

[X] Wrong: "Pushing or popping takes longer as the stack grows because it has more items."

[OK] Correct: Each push or pop only changes the top item, so time does not grow with stack size.

Interview Connect

Knowing that stack operations are quick and constant time helps you explain efficient data handling in many programs.

Self-Check

"What if we had to search for an item inside the stack before popping? How would the time complexity change?"