Check if Stack is Empty or Full in DSA Rust - 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 these checks affect the program speed.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

struct Stack {
    data: Vec<i32>,
    capacity: usize,
}

impl Stack {
    fn is_empty(&self) -> bool {
        self.data.is_empty()
    }

    fn is_full(&self) -> bool {
        self.data.len() == self.capacity
    }
}
    

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

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking the length of the vector or if it is empty.
• How many times: These checks happen once per call, no loops or recursion.

How Execution Grows With Input

Checking if the stack is empty or full takes the same time no matter the size.

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

Pattern observation: The operation count stays the same even if the stack grows.

Final Time Complexity

Time Complexity: O(1)

This means checking if the stack is empty or full takes the same short time no matter how many items are inside.

Common Mistake

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

[OK] Correct: The check only looks at the count or emptiness, which is stored and accessed instantly, not by scanning all items.

Interview Connect

Knowing these checks are very fast helps you explain stack operations clearly and confidently in interviews.

Self-Check

"What if the stack was implemented using a linked list instead of a vector? How would the time complexity of checking if it is full or empty change?"

Practice

1. What does the is_empty() method of a stack typically check?

easy

A. If the stack has more than one element

B. If the stack is full and cannot accept more elements

C. If the stack has exactly one element

D. If the stack has no elements inside

Solution

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

   This method checks whether the stack contains any elements or not.

2. Step 2: Interpret the meaning of empty stack

   An empty stack means it has zero elements inside, so is_empty() returns true only in this case.

3. Final Answer:

   If the stack has no elements inside -> Option D

4. Quick Check:

   Empty stack means no elements [OK]

Hint: Empty means zero elements inside the stack [OK]

Common Mistakes:

• Confusing empty with full
• Thinking empty means one element
• Assuming empty means stack is null

2. Which of the following is the correct Rust syntax to check if a stack named stack is full assuming it has a fixed capacity stored in capacity and current size in size?

easy

A. if stack.len() == capacity { /* full */ }

B. if stack.size == capacity { /* full */ }

C. if stack.is_full() { /* full */ }

D. if stack.size > capacity { /* full */ }

Solution

1. Step 1: Identify how to get current stack size

   In Rust, len() method is commonly used to get the current number of elements in a collection like a stack.

2. Step 2: Compare current size with capacity

   If stack.len() equals capacity, the stack is full.

3. Final Answer:

   if stack.len() == capacity { /* full */ } -> Option A

4. Quick Check:

   Use len() to check size [OK]

Hint: Use stack.len() to get current size in Rust [OK]

Common Mistakes:

• Using stack.size instead of stack.len()
• Checking size > capacity instead of == capacity
• Assuming is_full() method exists by default

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

struct Stack {
    elements: Vec<i32>,
    capacity: usize,
}

impl Stack {
    fn is_full(&self) -> bool {
        self.elements.len() == self.capacity
    }

    fn is_empty(&self) -> bool {
        self.elements.is_empty()
    }
}

fn main() {
    let stack = Stack { elements: vec![1, 2, 3], capacity: 3 };
    println!("{} {}", stack.is_empty(), stack.is_full());
}

medium

A. false true

B. true false

C. false false

D. true true

Solution

1. Step 1: Check if stack is empty

   The stack has elements [1, 2, 3], so is_empty() returns false.

2. Step 2: Check if stack is full

   The stack capacity is 3 and current length is 3, so is_full() returns true.

3. Final Answer:

   false true -> Option A

4. Quick Check:

   Elements present = not empty, length == capacity = full [OK]

Hint: Empty false if elements exist; full true if length equals capacity [OK]

Common Mistakes:

• Thinking stack is empty when it has elements
• Confusing is_empty() and is_full() return values
• Ignoring capacity when checking full

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

struct Stack {
    elements: Vec<i32>,
}

impl Stack {
    fn is_empty(&self) -> bool {
        self.elements.len() = 0
    }
}

medium

A. Vec<i32> cannot be used to store stack elements

B. Missing return type in is_empty method

C. Using '=' instead of '==' for comparison in is_empty method

D. is_empty method should take mutable self parameter

Solution

1. Step 1: Check the comparison operator in is_empty

   The code uses single '=' which is assignment, not comparison. It should use '==' to compare length with zero.

2. Step 2: Confirm other parts are correct

   The return type bool is present, Vec<i32> is valid, and self does not need to be mutable for this check.

3. Final Answer:

   Using '=' instead of '==' for comparison in is_empty method -> Option C

4. Quick Check:

   Use '==' for comparison, not '=' [OK]

Hint: Use '==' to compare values, '=' is assignment [OK]

Common Mistakes:

• Using '=' instead of '==' in conditions
• Forgetting return type bool
• Making self mutable unnecessarily

5. You have a stack with capacity 5 and current elements [10, 20, 30]. You want to write a Rust function can_push that returns true if the stack is not full and false otherwise. Which implementation is correct?

struct Stack {
    elements: Vec<i32>,
    capacity: usize,
}

impl Stack {
    fn can_push(&self) -> bool {
        // Choose correct condition
    }
}

hard

A. self.elements.len() <= self.capacity

B. self.elements.len() < self.capacity

C. self.elements.len() == self.capacity

D. self.elements.len() > self.capacity

Solution

1. Step 1: Understand when pushing is allowed

   You can push only if the stack is not full, meaning current size is less than capacity.

2. Step 2: Choose the correct comparison

   If length is less than capacity, pushing is possible. If equal or more, stack is full or invalid.

3. Final Answer:

   self.elements.len() < self.capacity -> Option B

4. Quick Check:

   Push allowed if size < capacity [OK]

Hint: Push allowed only if current size less than capacity [OK]

Common Mistakes:

• Using <= instead of < allows overflow
• Checking == means no room left
• Using > is logically incorrect