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

Time Complexity: Check if Stack is Empty or Full

O(1)

Understanding Time Complexity

We want to understand how fast we can check if a stack is empty or full.

This helps us know how much time these checks take as the stack size changes.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Stack:
    def __init__(self, capacity):
        self.capacity = capacity
        self.items = []

    def is_empty(self):
        return len(self.items) == 0

    def is_full(self):
        return len(self.items) == self.capacity

This code checks if the stack has no items or if it has reached its capacity.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking the length of the list (stack items).
• How many times: Once per call to is_empty or is_full.

How Execution Grows With Input

The length check is a simple operation that takes the same time no matter how many items are in the stack.

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

Pattern observation: The time to check does not grow with the number of items; it stays constant.

Final Time Complexity

Time Complexity: O(1)

This means checking if the stack is empty or full takes the same small amount of time no matter how big the stack is.

Common Mistake

[X] Wrong: "Checking if a stack is full or empty takes longer as the stack grows because it needs to look at all items."

[OK] Correct: The check only looks at the count of items, not each item, so it takes the same time regardless of stack 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 a list? How would the time complexity of checking if it is empty or full change?"

Practice

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

easy

A. If the stack has exactly one element

B. If the stack is full

C. If the stack has more than one element

D. If the stack has no elements

Solution

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

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

2. Step 2: Identify what empty means for a stack

   An empty stack means it has zero elements, so isEmpty() returns true if no elements are present.

3. Final Answer:

   If the stack has no elements -> Option D

4. Quick Check:

   Empty stack means no elements = true [OK]

Hint: Empty stack means zero elements inside [OK]

Common Mistakes:

• Confusing empty with full
• Thinking it checks for one element
• Assuming it checks for capacity

2. Which of the following is the correct syntax to check if a stack named stack is full in Python assuming max size is stored in max_size and current size in top?

easy

A. if top == max_size: print('Stack is full')

B. if top > max_size: print('Stack is full')

C. if top < max_size: print('Stack is full')

D. if top != max_size: print('Stack is full')

Solution

1. Step 1: Understand stack full condition

   A stack is full when the current top index equals the maximum allowed size.

2. Step 2: Match condition with syntax

   The correct check is top == max_size to confirm fullness.

3. Final Answer:

   if top == max_size: print('Stack is full') -> Option A

4. Quick Check:

   Full stack when top equals max size [OK]

Hint: Full stack means top equals max size [OK]

Common Mistakes:

• Using greater than instead of equal
• Using less than for full check
• Using not equal instead of equal

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

class Stack:
    def __init__(self, max_size):
        self.stack = []
        self.max_size = max_size
    def isFull(self):
        return len(self.stack) == self.max_size
    def isEmpty(self):
        return len(self.stack) == 0

s = Stack(2)
s.stack.append(10)
s.stack.append(20)
print(s.isFull())
print(s.isEmpty())

medium

A. False\nTrue

B. True\nTrue

C. True\nFalse

D. False\nFalse

Solution

1. Step 1: Check stack contents after append

   Two elements (10, 20) are added, so length is 2 which equals max_size.

2. Step 2: Evaluate isFull and isEmpty

   isFull() returns True because length equals max_size; isEmpty() returns False because stack is not empty.

3. Final Answer:

   True False -> Option C

4. Quick Check:

   Stack full = True, empty = False [OK]

Hint: Full if length equals max size; empty if length zero [OK]

Common Mistakes:

• Confusing isFull and isEmpty return values
• Ignoring stack length after append
• Assuming stack is empty after append

4. Find the error in the following code that checks if a stack is empty:

class Stack:
    def __init__(self):
        self.stack = []
    def isEmpty(self):
        if self.stack == 0:
            return True
        else:
            return False

s = Stack()
print(s.isEmpty())

medium

A. Missing return statement in isEmpty

B. Comparing list to integer zero causes error

C. Stack initialization is incorrect

D. Print statement syntax is wrong

Solution

1. Step 1: Analyze the isEmpty condition

   The code compares self.stack == 0, but self.stack is a list, not a number.

2. Step 2: Identify correct way to check empty list

   To check if list is empty, use len(self.stack) == 0 or simply not self.stack.

3. Final Answer:

   Comparing list to integer zero causes error -> Option B

4. Quick Check:

   List cannot be compared to number 0 [OK]

Hint: Check list emptiness with length or not operator [OK]

Common Mistakes:

• Comparing list directly to 0
• Forgetting list length check
• Using wrong comparison operator

5. You have a stack with max size 3. After pushing 3 elements, you pop one element and then check if the stack is full or empty. What will be the correct output of isFull() and isEmpty() methods?

class Stack:
    def __init__(self, max_size):
        self.stack = []
        self.max_size = max_size
    def push(self, val):
        if len(self.stack) < self.max_size:
            self.stack.append(val)
    def pop(self):
        if not self.isEmpty():
            return self.stack.pop()
    def isFull(self):
        return len(self.stack) == self.max_size
    def isEmpty(self):
        return len(self.stack) == 0

s = Stack(3)
s.push(1)
s.push(2)
s.push(3)
s.pop()
print(s.isFull())
print(s.isEmpty())

hard

A. False\nFalse

B. True\nFalse

C. False\nTrue

D. True\nTrue

Solution

1. Step 1: Track stack size after operations

   Initially push 3 elements, stack size = 3 (full). After pop, size reduces to 2.

2. Step 2: Evaluate isFull and isEmpty

   Since size is 2 and max_size is 3, isFull() returns False. Stack is not empty, so isEmpty() returns False.

3. Final Answer:

   False False -> Option A

4. Quick Check:

   Stack size 2 < max size 3, not empty [OK]

Hint: Pop reduces size; full only if size equals max [OK]

Common Mistakes:

• Assuming stack is still full after pop
• Assuming stack is empty after pop
• Ignoring size changes after pop