Peek Top Element of Stack in DSA Rust - Time & Space Complexity

Time Complexity: Peek Top Element of Stack

O(1)

Understanding Time Complexity

We want to understand how long it takes to look at the top item of a stack.

How does the time needed change when the stack grows bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

struct Stack {
    elements: Vec<i32>,
}

impl Stack {
    fn peek(&self) -> Option<i32> {
        self.elements.last().copied()
    }
}
    

This code returns the top element of the stack without removing it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Accessing the last element of a vector.
• How many times: Exactly once per peek call.

How Execution Grows With Input

Looking at the top element takes the same time no matter how big the stack is.

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

Pattern observation: The time stays constant as the stack grows.

Final Time Complexity

Time Complexity: O(1)

This means peeking the top element takes the same short time no matter how many items are in the stack.

Common Mistake

[X] Wrong: "Peeking takes longer if the stack is bigger because it has to check many elements."

[OK] Correct: Peeking only looks at the last element directly, so it does not depend on stack size.

Interview Connect

Knowing that peek is a constant time operation helps you explain stack efficiency clearly and confidently.

Self-Check

"What if the stack was implemented using a linked list instead of a vector? How would the time complexity of peek change?"

Practice

1. What does the peek operation do in a stack data structure?

easy

A. Returns the top element without removing it

B. Removes the top element and returns it

C. Adds a new element to the top

D. Checks if the stack is empty

Solution

1. Step 1: Understand stack operations

   A stack stores elements in a last-in, first-out order. Common operations include push, pop, and peek.

2. Step 2: Define peek operation

   Peek returns the top element without removing it, allowing you to see the current top value safely.

3. Final Answer:

   Returns the top element without removing it -> Option A

4. Quick Check:

   Peek = top element without removal [OK]

Hint: Peek shows top without changing stack [OK]

Common Mistakes:

• Confusing peek with pop operation
• Thinking peek adds elements
• Assuming peek checks emptiness

2. Which of the following Rust code snippets correctly peeks the top element of a stack implemented as a Vec<i32> named stack?

easy

A. let top = stack.last();

B. let top = stack[0];

C. let top = stack.pop();

D. let top = stack.first();

Solution

1. Step 1: Understand Rust Vec methods for stack

   In Rust, Vec can be used as a stack. pop() removes and returns the last element, last() returns a reference to the last element without removing it.

2. Step 2: Identify correct peek method

   Peek means to see the top element without removing it, so stack.last() is correct. stack.pop() removes it, stack[0] accesses the first element, and stack.first() returns the first element, not the top.

3. Final Answer:

   let top = stack.last(); -> Option A

4. Quick Check:

   Peek = stack.last() [OK]

Hint: Use .last() to peek top element in Rust Vec stack [OK]

Common Mistakes:

• Using pop() which removes element
• Accessing first() instead of last()
• Using index 0 which is bottom of stack

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

let mut stack = vec![10, 20, 30];
if let Some(top) = stack.last() {
    println!("{}", top);
} else {
    println!("Stack is empty");
}

medium

A. 20

B. 30

C. 10

D. Stack is empty

Solution

1. Step 1: Understand stack contents and last()

   The stack vector contains [10, 20, 30]. The last element is 30.

2. Step 2: Trace the if let statement

   The stack.last() returns Some(&30), so the if block prints 30.

3. Final Answer:

   30 -> Option B

4. Quick Check:

   stack.last() = 30 [OK]

Hint: stack.last() returns top element reference [OK]

Common Mistakes:

• Printing bottom element instead of top
• Confusing last() with pop() output
• Assuming stack is empty

4. Identify the error in the following Rust code that tries to peek the top element of a stack and fix it:

let stack = vec![1, 2, 3];
let top = stack.pop().unwrap();
println!("Top element: {}", top);

medium

A. No error, code works correctly

B. pop() removes element; use last() to peek instead

C. unwrap() causes panic; use expect() instead

D. stack should be mutable to use pop()

Solution

1. Step 1: Check mutability for pop()

   pop() removes the last element, so the vector must be mutable. Here, stack is immutable.

2. Step 2: Fix by making stack mutable

   Change let stack = vec![1, 2, 3]; to let mut stack = vec![1, 2, 3]; to allow pop().

3. Final Answer:

   stack should be mutable to use pop() -> Option D

4. Quick Check:

   pop() needs mutable stack [OK]

Hint: pop() requires mutable stack variable [OK]

Common Mistakes:

• Ignoring mut keyword error
• Confusing pop() with peek operation
• Assuming unwrap() always safe

5. Given a stack implemented as Vec<i32>, write a Rust function peek_top that returns the top element as Option<i32> without removing it. What is the correct implementation?

hard

A. fn peek_top(stack: &mut Vec<i32>) -> Option<i32> { stack.pop() }

B. fn peek_top(stack: &Vec<i32>) -> i32 { *stack.last().unwrap() }

C. fn peek_top(stack: &Vec<i32>) -> Option<i32> { stack.last().copied() }

D. fn peek_top(stack: Vec<i32>) -> Option<i32> { stack.first().copied() }

Solution

1. Step 1: Understand function requirements

   The function must peek without removing, so it should borrow stack immutably and return Option<i32>.

2. Step 2: Analyze options

   fn peek_top(stack: &Vec<i32>) -> Option<i32> { stack.last().copied() } uses stack.last().copied() which returns Option<i32> by copying the reference. fn peek_top(stack: &mut Vec<i32>) -> Option<i32> { stack.pop() } removes element (pop), fn peek_top(stack: &Vec<i32>) -> i32 { *stack.last().unwrap() } unwraps and returns i32 (not Option), fn peek_top(stack: Vec<i32>) -> Option<i32> { stack.first().copied() } uses first() which is bottom element.

3. Final Answer:

   fn peek_top(stack: &Vec<i32>) -> Option<i32> { stack.last().copied() } -> Option C

4. Quick Check:

   Peek returns Option with copied last element [OK]

Hint: Use last().copied() for safe peek returning Option<i32> [OK]

Common Mistakes:

• Using pop() which removes element
• Returning i32 instead of Option<i32>
• Accessing first() instead of last()