Push Operation on Stack in DSA Rust - Time & Space Complexity

Time Complexity: Push Operation on Stack

O(1)

Understanding Time Complexity

We want to understand how long it takes to add an item to a stack.

Specifically, how the time changes as the stack grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

struct Stack {
    elements: Vec<i32>,
}

impl Stack {
    fn push(&mut self, value: i32) {
        self.elements.push(value);
    }
}

This code adds a new value to the top of the stack using a vector.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding one element to the vector (stack).
• How many times: Once per push call.

How Execution Grows With Input

Each push adds one item. Usually, this takes the same small amount of time no matter how big the stack is.

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

Pattern observation: The time stays about the same no matter how many items are in the stack.

Final Time Complexity

Time Complexity: O(1)

This means adding an item takes a constant amount of time regardless of stack size.

Common Mistake

[X] Wrong: "Push takes longer as the stack grows because it has to move all elements."

[OK] Correct: The vector adds at the end, so it does not move existing elements each time. Occasionally it resizes, but that cost is spread out over many pushes.

Interview Connect

Knowing push is fast and constant time helps you explain why stacks are good for quick adds and removes.

Self-Check

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

Practice

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

easy

A. Removes the top element from the stack

B. Adds an element to the top of the stack

C. Returns the bottom element of the stack

D. Checks if the stack is empty

Solution

1. Step 1: Understand stack behavior

   A stack follows Last In First Out (LIFO) principle, where elements are added or removed from the top.

2. Step 2: Define push operation

   The push operation adds a new element on top of the existing elements in the stack.

3. Final Answer:

   Adds an element to the top of the stack -> Option B

4. Quick Check:

   Push = Add top element [OK]

Hint: Push always adds to the top of the stack [OK]

Common Mistakes:

• Confusing push with pop operation
• Thinking push removes elements
• Assuming push adds to the bottom

2. Which of the following is the correct Rust syntax to push an element 5 onto a stack implemented as a Vec<i32> named stack?

easy

A. stack.push(5);

B. stack.add(5);

C. stack.insert(5);

D. stack.append(5);

Solution

1. Step 1: Recall Rust Vec push method

   In Rust, Vec has a method push to add elements at the end (top of stack).

2. Step 2: Check method names

   add, insert, and append have different meanings or require different parameters.

3. Final Answer:

   stack.push(5); -> Option A

4. Quick Check:

   Vec push method = stack.push(5); [OK]

Hint: Use .push() to add elements to Vec stack [OK]

Common Mistakes:

• Using .add() which does not exist for Vec
• Confusing .insert() which needs index
• Using .append() which merges vectors

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

let mut stack = Vec::new();
stack.push(10);
stack.push(20);
stack.push(30);
println!("{:?}", stack);

medium

A. [10, 20, 30]

B. [30, 20, 10]

C. [10, 20]

D. Compilation error

Solution

1. Step 1: Trace push operations

   Elements 10, 20, and 30 are pushed in order, so stack contains [10, 20, 30].

2. Step 2: Understand Vec print format

   Printing with {:?} shows elements in insertion order, so output is [10, 20, 30].

3. Final Answer:

   [10, 20, 30] -> Option A

4. Quick Check:

   Push order preserved in Vec print [OK]

Hint: Vec prints elements in insertion order [OK]

Common Mistakes:

• Assuming stack prints top element first
• Confusing push order with pop order
• Expecting reversed output

4. Identify the error in this Rust code that tries to push an element onto a stack:

let stack = Vec::new();
stack.push(100);

medium

A. Missing semicolon after push

B. Vec::new() is incorrect syntax

C. push method does not exist for Vec

D. stack is immutable, cannot push

Solution

1. Step 1: Check variable mutability

   The variable stack is declared immutable by default, so push cannot modify it.

2. Step 2: Understand push method requirements

   push requires the vector to be mutable to add elements.

3. Final Answer:

   stack is immutable, cannot push -> Option D

4. Quick Check:

   Mutable vector needed for push [OK]

Hint: Declare stack as mutable with 'mut' to push [OK]

Common Mistakes:

• Forgetting to add 'mut' keyword
• Thinking Vec::new() is wrong syntax
• Assuming push is not a Vec method

5. You want to implement a stack using a Rust Vec<i32> and push elements 1, 2, 3 in that order. After pushing, you want to print the stack from top to bottom. Which code snippet correctly achieves this?

hard

A. let mut stack = Vec::new();
stack.push(1);
stack.push(2);
stack.push(3);
for i in stack.iter() {
println!("{}", i);
}

B. let mut stack = Vec::new();
stack.push(3);
stack.push(2);
stack.push(1);
for i in stack.iter() {
println!("{}", i);
}

C. let mut stack = Vec::new();
stack.push(1);
stack.push(2);
stack.push(3);
for i in stack.iter().rev() {
println!("{}", i);
}

D. let mut stack = Vec::new();
stack.push(1);
stack.push(2);
stack.push(3);
for i in stack.into_iter() {
println!("{}", i);
}

Solution

1. Step 1: Push elements in order

   Elements 1, 2, 3 are pushed in order, so stack is [1, 2, 3] with 3 at top.

2. Step 2: Print from top to bottom

   To print from top (last pushed) to bottom, iterate in reverse order using iter().rev().

3. Final Answer:

   Code snippet with stack.iter().rev() -> Option C

4. Quick Check:

   Reverse iteration prints top to bottom [OK]

Hint: Use .iter().rev() to print stack top to bottom [OK]

Common Mistakes:

• Printing in normal order shows bottom to top
• Pushing elements in reverse order
• Using into_iter() which consumes the stack