Push Operation on Stack in DSA C# - Time & Space Complexity

Time Complexity: Push Operation on Stack

O(1)

Understanding Time Complexity

We want to understand how the time needed to add an item to a stack changes as the stack grows.

How does the push operation behave when the stack size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public class Stack
{
    private int[] items;
    private int top = -1;

    public Stack(int size)
    {
        items = new int[size];
    }

    public void Push(int item)
    {
        items[++top] = item;
    }
}
    

This code adds a new item to the top of the stack by increasing the top index and storing the item.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single assignment to the array at the incremented top index.
• How many times: Exactly once per push call, no loops or recursion involved.

How Execution Grows With Input

Each push adds one item with a fixed number of steps, no matter how big the stack is.

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

Pattern observation: The time to push stays the same even if the stack grows larger.

Final Time Complexity

Time Complexity: O(1)

This means pushing an item takes the same short time no matter how many items are already in the stack.

Common Mistake

[X] Wrong: "Push takes longer as the stack grows because the array is bigger."

[OK] Correct: The push just places the item at the next free spot; it does not scan or move existing items, so time stays constant.

Interview Connect

Knowing that push is a quick, constant-time operation helps you explain stack efficiency clearly in interviews.

Self-Check

"What if the stack uses a dynamic array that resizes when full? How would the time complexity of push change then?"

Practice

1. What does the Push operation do in a stack?

easy

A. Adds an element to the top of the stack

B. Removes the top element from 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 stack, increasing its size by one.

3. Final Answer:

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

4. Quick Check:

   Push = Add top element [OK]

Hint: Push means add on top of stack [OK]

Common Mistakes:

• Confusing Push with Pop operation
• Thinking Push removes elements
• Assuming Push accesses bottom element

2. Which of the following is the correct syntax to push an integer value 10 onto a stack named stack in C#?

easy

A. stack.Insert(10);

B. stack.Add(10);

C. stack.Push(10);

D. stack.Push = 10;

Solution

1. Step 1: Recall Stack method for adding elements

   In C#, the Stack class uses the method Push() to add elements.

2. Step 2: Check syntax correctness

   The correct syntax is calling Push with the value inside parentheses: stack.Push(10);

3. Final Answer:

   stack.Push(10); -> Option C

4. Quick Check:

   Push method call syntax = stack.Push(value) [OK]

Hint: Use stack.Push(value) to add elements [OK]

Common Mistakes:

• Using Add or Insert which are not stack methods
• Assigning value directly to Push
• Missing parentheses in method call

3. What will be the output after executing the following C# code?

Stack<int> stack = new Stack<int>();
stack.Push(5);
stack.Push(10);
stack.Push(15);
Console.WriteLine(string.Join(", ", stack));

medium

A. 5, 10, 15

B. 15, 10, 5

C. 10, 15, 5

D. 15, 5, 10

Solution

1. Step 1: Understand push order and stack iteration

   Elements pushed are 5, then 10, then 15. Stack stores last pushed on top.

2. Step 2: Determine iteration order when printing

   Stack enumerates from top to bottom, so output order is 15, 10, 5.

3. Final Answer:

   15, 10, 5 -> Option B

4. Quick Check:

   Stack top to bottom = 15, 10, 5 [OK]

Hint: Stack prints top element first [OK]

Common Mistakes:

• Assuming stack prints in push order
• Confusing stack with queue order
• Forgetting stack is LIFO

4. Identify the error in the following C# code that tries to push elements onto a stack:

Stack<string> stack = new Stack<string>();
stack.Push "hello";
stack.Push("world");

medium

A. Push method does not exist

B. Stack cannot hold strings

C. Missing semicolon after second Push

D. Missing parentheses in first Push call

Solution

1. Step 1: Check syntax of Push calls

   The first Push call is written as stack.Push "hello"; missing parentheses.

2. Step 2: Confirm correct method usage

   Push requires parentheses around argument: stack.Push("hello");

3. Final Answer:

   Missing parentheses in first Push call -> Option D

4. Quick Check:

   Method calls need parentheses [OK]

Hint: Always use parentheses with method calls [OK]

Common Mistakes:

• Ignoring parentheses syntax
• Thinking stack can't hold strings
• Assuming missing semicolon causes error here

5. Given a stack initially empty, what will be the content of the stack after executing the following code?

Stack<int> stack = new Stack<int>();
for (int i = 1; i <= 3; i++)
{
    stack.Push(i * 2);
}
stack.Push(10);
stack.Push(stack.Pop() + 5);

hard

A. 15, 6, 4, 2

B. 10, 8, 4, 2

C. 15, 10, 6, 4, 2

D. 10, 15, 6, 4, 2

Solution

1. Step 1: Trace the for loop pushing values

   Loop pushes 2, 4, 6 in order. Stack top is 6, bottom is 2.

2. Step 2: Push 10, then pop top and push pop+5

   Push 10: stack top to bottom 10, 6, 4, 2. Pop removes 10, 10 + 5 = 15, push 15: top to bottom 15, 6, 4, 2.

3. Final Answer:

   15, 6, 4, 2 -> Option A

4. Quick Check:

   Stack after operations = 15, 6, 4, 2 [OK]

Hint: Track push/pop stepwise to find final stack [OK]

Common Mistakes:

• Confusing pop value used for new push
• Forgetting pop removes top element
• Assuming push adds without removing