Check if Stack is Empty or Full in DSA Java - Time & Space Complexity

Time Complexity: Check if Stack is Empty or Full

O(1)

Understanding Time Complexity

Checking if a stack is empty or full is a common operation in stack data structures.

We want to know how fast these checks happen as the stack size changes.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public class Stack {
    private int[] arr;
    private int top;
    private int capacity;

    public Stack(int size) {
        arr = new int[size];
        capacity = size;
        top = -1;
    }

    public boolean isEmpty() {
        return top == -1;
    }

    public boolean isFull() {
        return top == capacity - 1;
    }
}
    

This code defines a stack and checks if it is empty or full by comparing the top index.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Simple comparison of the top index with fixed values.
• How many times: Each check runs once per call, no loops or recursion involved.

How Execution Grows With Input

These checks do not depend on the stack size; they always do the same small work.

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

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

Final Time Complexity

Time Complexity: O(1)

This means the check happens instantly, no matter how many items are in the stack.

Common Mistake

[X] Wrong: "Checking if the stack is full or empty takes longer as the stack grows."

[OK] Correct: These checks only compare numbers and do not look through the stack, so their speed does not change with size.

Interview Connect

Knowing that these checks are very fast helps you focus on more complex stack operations during interviews.

Self-Check

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

Practice

1. What does the isEmpty() method in a stack typically check?

easy

A. If the stack has exactly one element

B. If the stack is full

C. If the stack has no elements

D. If the stack is initialized

Solution

1. Step 1: Understand the purpose of isEmpty()

   The isEmpty() method checks whether the stack contains any elements or not.

2. Step 2: Identify the condition checked

   If the stack has no elements, it is empty, so isEmpty() returns true.

3. Final Answer:

   If the stack has no elements -> Option C

4. Quick Check:

   Empty stack means no elements = true [OK]

Hint: Empty means zero elements in stack [OK]

Common Mistakes:

• Confusing isEmpty() with isFull()
• Thinking isEmpty() checks for one element
• Assuming isEmpty() checks initialization

2. Which of the following is the correct syntax to check if a stack named stack is full in Java?

easy

A. stack.isEmpty();

B. stack.isFull();

C. stack.full();

D. stack.isFilled();

Solution

1. Step 1: Identify the standard method name for full check

   In stack implementations, the method to check if the stack is full is usually named isFull().

2. Step 2: Match the correct syntax

   The correct syntax to call this method on a stack object named stack is stack.isFull();.

3. Final Answer:

   stack.isFull(); -> Option B

4. Quick Check:

   Method to check full = isFull() [OK]

Hint: Full check method is isFull() [OK]

Common Mistakes:

• Using isEmpty() to check full
• Using non-existent methods like full()
• Misspelling method names

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

class Stack {
  int maxSize = 3;
  int top = -1;
  int[] arr = new int[maxSize];

  boolean isFull() {
    return top == maxSize - 1;
  }

  boolean isEmpty() {
    return top == -1;
  }

  void push(int val) {
    if (!isFull()) {
      arr[++top] = val;
      System.out.println("Pushed " + val);
    } else {
      System.out.println("Stack is full");
    }
  }
}

public class Main {
  public static void main(String[] args) {
    Stack stack = new Stack();
    stack.push(10);
    stack.push(20);
    stack.push(30);
    stack.push(40);
  }
}

medium

A. Pushed 10
Pushed 20
Pushed 30
Stack is full

B. Pushed 10
Pushed 20
Pushed 30
Pushed 40

C. Stack is full
Stack is full
Stack is full
Stack is full

D. Pushed 10
Pushed 20
Stack is full
Stack is full

Solution

1. Step 1: Trace push operations and stack state

   Initially, top = -1. Each push increments top and adds value if stack not full. Max size is 3, so max top index is 2.

2. Step 2: Check each push call

   Push 10: top becomes 0, prints "Pushed 10".
   Push 20: top becomes 1, prints "Pushed 20".
   Push 30: top becomes 2, prints "Pushed 30".
   Push 40: top is 2 (full), so prints "Stack is full".

3. Final Answer:

   Pushed 10 Pushed 20 Pushed 30 Stack is full -> Option A

4. Quick Check:

   Stack max size 3, 4th push fails [OK]

Hint: Stack full when top == maxSize-1 [OK]

Common Mistakes:

• Assuming push always succeeds
• Ignoring top index limits
• Confusing isEmpty() with isFull()

4. Find the error in this stack implementation snippet that checks if the stack is empty:

public boolean isEmpty() {
  if (top == 0) {
    return true;
  } else {
    return false;
  }
}

medium

A. No error, the code is correct

B. The method should return false when top == 0

C. The method should check if top == maxSize

D. The condition should be top == -1 to check empty

Solution

1. Step 1: Understand stack empty condition

   In stack, empty means no elements pushed, so top is usually -1.

2. Step 2: Identify incorrect condition

   The code checks top == 0, which means one element is present, so it is wrong for empty check.

3. Final Answer:

   The condition should be top == -1 to check empty -> Option D

4. Quick Check:

   Empty stack top = -1 [OK]

Hint: Empty stack top is -1, not 0 [OK]

Common Mistakes:

• Checking top == 0 for empty
• Confusing full and empty conditions
• Returning wrong boolean values

5. You have a stack with max size 5 and current top = 3. Which of the following statements is true about the stack's state?

hard

A. The stack is neither full nor empty

B. The stack is empty

C. The stack is full

D. The stack has exactly 5 elements

Solution

1. Step 1: Understand stack indexing and size

   Stack max size is 5, so valid top indices are 0 to 4. top = 3 means 4 elements are present (indices 0,1,2,3).

2. Step 2: Determine if stack is full or empty

   Full means top == maxSize - 1 which is 4 here, so not full.
   Empty means top == -1, so not empty.
   Therefore, stack is neither full nor empty.

3. Final Answer:

   The stack is neither full nor empty -> Option A

4. Quick Check:

   top=3, maxSize=5 means partial fill [OK]

Hint: Full if top = maxSize-1, empty if top = -1 [OK]

Common Mistakes:

• Assuming top=3 means full
• Confusing top index with element count
• Thinking top=3 means empty