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

Time Complexity: Stack Concept and LIFO Principle

O(1)

Understanding Time Complexity

We want to understand how the time to perform stack operations changes as the number of items grows.

Specifically, how fast can we add or remove items following the Last In First Out rule?

Scenario Under Consideration

Analyze the time complexity of the following stack operations.

public class Stack {
    private int[] data;
    private int top = -1;

    public Stack(int size) {
        data = new int[size];
    }

    public void push(int value) {
        data[++top] = value;
    }

    public int pop() {
        return data[top--];
    }
}
    

This code shows how to add (push) and remove (pop) items from a stack using an array.

Identify Repeating Operations

Look for repeated actions that take time.

• Primary operation: Adding or removing one item at the top of the stack.
• How many times: Each push or pop happens once per operation, no loops inside.

How Execution Grows With Input

Each push or pop takes the same small amount of time no matter how many items are in the stack.

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

Pattern observation: The time stays the same even as the stack grows larger.

Final Time Complexity

Time Complexity: O(1)

This means each push or pop operation takes a constant, fixed amount of time regardless of stack size.

Common Mistake

[X] Wrong: "Pushing or popping takes longer as the stack gets bigger because there are more items."

[OK] Correct: Each operation only touches the top item, so it does not depend on how many items are below.

Interview Connect

Understanding that stack operations are fast and simple helps you explain why stacks are useful in many programs and algorithms.

Self-Check

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

Practice

1. What does the LIFO principle mean in the context of a stack?

easy

A. First In, First Out - the first element added is the first to be removed

B. Last In, First Out - the last element added is the first to be removed

C. Elements are removed randomly

D. Elements are removed based on their value

Solution

1. Step 1: Understand the LIFO principle

   LIFO means the last item you put in is the first one you take out.

2. Step 2: Apply to stack behavior

   Stacks follow LIFO, so the last pushed element is popped first.

3. Final Answer:

   Last In, First Out - the last element added is the first to be removed -> Option B

4. Quick Check:

   LIFO = Last In, First Out [OK]

Hint: Remember stack like a stack of plates, last on top removed first [OK]

Common Mistakes:

• Confusing LIFO with FIFO
• Thinking elements are removed randomly
• Assuming removal depends on element value

2. Which of the following is the correct way to push an element '5' onto a stack named stack in Java?

easy

A. stack.insert(5);

B. stack.add(5);

C. stack.put(5);

D. stack.push(5);

Solution

1. Step 1: Recall Java Stack method for adding elements

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

2. Step 2: Match method with given options

   Only stack.push(5); correctly uses the stack push method.

3. Final Answer:

   stack.push(5); -> Option D

4. Quick Check:

   Use push() to add elements to stack [OK]

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

Common Mistakes:

• Using add() which is for lists, not stacks
• Using insert() or put() which are invalid for Stack
• Confusing stack methods with other collections

3. What will be the output of the following Java code?

Stack<Integer> stack = new Stack<>();
stack.push(10);
stack.push(20);
stack.push(30);
System.out.println(stack.pop());
System.out.println(stack.pop());

medium

A. 30\n20

B. 30\n10

C. 20\n30

D. 10\n20

Solution

1. Step 1: Trace push operations

   Elements pushed in order: 10 (bottom), 20, 30 (top).

2. Step 2: Trace pop operations

   First pop removes 30, second pop removes 20.

3. Final Answer:

   30\n20 -> Option A

4. Quick Check:

   Stack pops last pushed first: 30 then 20 [OK]

Hint: Pop returns last pushed element first [OK]

Common Mistakes:

• Assuming pop removes from bottom
• Mixing order of popped elements
• Confusing push and pop effects

4. Identify the error in the following Java code snippet using a stack:

Stack<String> stack = new Stack<>();
stack.push("apple");
stack.push("banana");
String fruit = stack.pop();
System.out.println(stack.peek());
stack.pop();
stack.pop();

medium

A. Using peek() instead of pop() is incorrect

B. Stack cannot hold String objects

C. Calling pop() on an empty stack causes EmptyStackException

D. push() method is not defined for Stack

Solution

1. Step 1: Trace stack operations

   Push "apple", then "banana". Pop removes "banana". Peek shows "apple". Next pop removes "apple".

2. Step 2: Identify error on last pop

   Last pop tries to remove from empty stack, causing EmptyStackException.

3. Final Answer:

   Calling pop() on an empty stack causes EmptyStackException -> Option C

4. Quick Check:

   Pop on empty stack throws exception [OK]

Hint: Pop more times than pushes causes error [OK]

Common Mistakes:

• Ignoring exception on empty pop
• Thinking peek removes element
• Believing stack can't hold Strings

5. Given a stack with elements pushed in this order: 1, 2, 3, 4, 5. Which sequence of pop operations will produce the output 5 4 3 and leave the stack with elements 1 2 remaining?

hard

A. Pop three times consecutively

B. Pop once, push 6, then pop twice

C. Pop twice, push 7, then pop once

D. Pop once, pop twice, push 8

Solution

1. Step 1: Understand initial stack order

   Stack top is 5, bottom is 1 after pushing 1 to 5.

2. Step 2: Pop three times consecutively

   Pop removes 5, then 4, then 3, leaving 1 and 2 in stack.

3. Final Answer:

   Pop three times consecutively -> Option A

4. Quick Check:

   3 pops remove top 3 elements [OK]

Hint: Pop as many times as output elements needed [OK]

Common Mistakes:

• Adding elements unnecessarily
• Confusing push and pop order
• Expecting output without popping