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

Time Complexity: Push Operation on Stack

O(1) amortized

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.

func (s *Stack) Push(value int) {
    s.items = append(s.items, value)
}
    

This code adds a new value to the top of the stack by appending it to the slice.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Appending an element to the slice backing the stack.
• How many times: Once per push call, no loops or recursion involved.

How Execution Grows With Input

Each push adds one element, so the work per push stays mostly the same.

Input Size (n)	Approx. Operations
10	10 simple append steps
100	100 simple append steps
1000	1000 simple append steps

Pattern observation: Each push takes about the same time, so total time grows linearly with number of pushes.

Final Time Complexity

Time Complexity: O(1) amortized

This means each push operation takes a constant amount of time on average, no matter how big the stack is.

Common Mistake

[X] Wrong: "Push takes longer as the stack grows because the array must copy all elements each time."

[OK] Correct: The slice grows by doubling size occasionally, so most pushes are fast. The costly copying happens rarely and is spread out, making average push time constant.

Interview Connect

Understanding push time helps you explain stack efficiency clearly, a key skill in many coding discussions.

Self-Check

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

Practice

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

easy

A. Returns the bottom element of the stack

B. Removes the top element from the stack

C. Adds an element to the top 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, so new elements are added on top.

2. Step 2: Define push operation

   The push operation adds a new element to the top of the stack.

3. Final Answer:

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

4. Quick Check:

   Push = Add top [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 element 5 onto a stack named s in Go?

easy

A. s.push(5)

B. s.Push(5)

C. push(s, 5)

D. s = append(s, 5)

Solution

1. Step 1: Understand Go slice as stack

   In Go, stacks are often implemented using slices. To push, append adds element at the end.

2. Step 2: Identify correct syntax

   Using append(s, 5) adds 5 to the slice s, simulating push.

3. Final Answer:

   s = append(s, 5) -> Option D

4. Quick Check:

   Go push = append slice [OK]

Hint: Use append to push in Go slices [OK]

Common Mistakes:

• Using lowercase push method which doesn't exist
• Calling push as a function without method
• Ignoring that slices need reassignment after append

3. What will be the output after executing this Go code?

stack := []int{1, 2, 3}
stack = append(stack, 4)
fmt.Println(stack)

medium

A. [1 2 3 4]

B. [4 1 2 3]

C. [1 2 3]

D. runtime error

Solution

1. Step 1: Initial stack state

   Stack slice starts as [1 2 3].

2. Step 2: Append 4 to stack

   Append adds 4 at the end, so stack becomes [1 2 3 4].

3. Final Answer:

   [1 2 3 4] -> Option A

4. Quick Check:

   Append adds at end [OK]

Hint: Append adds element at slice end [OK]

Common Mistakes:

• Expecting append to add at start
• Confusing append with insert
• Thinking append causes error without reassignment

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

var stack []int
stack.push(10)

medium

A. Stack is not initialized

B. push method does not exist for slices

C. Missing import for stack package

D. Cannot push integer 10

Solution

1. Step 1: Check stack type and methods

   Stack is a slice of int. Slices do not have a push method in Go.

2. Step 2: Identify correct push approach

   To push, use append function instead of push method.

3. Final Answer:

   push method does not exist for slices -> Option B

4. Quick Check:

   Slices lack push method [OK]

Hint: Slices use append, no push method [OK]

Common Mistakes:

• Assuming push is built-in method for slices
• Thinking stack must be initialized first
• Believing import fixes method absence

5. Given a stack implemented as a slice in Go, how would you push multiple elements 7, 8, 9 in one operation?

hard

A. stack = append(stack, []int{7, 8, 9}...)

B. stack.push(7); stack.push(8); stack.push(9)

C. append(stack, 7, 8, 9)

D. stack = append(stack, []int{7, 8, 9})

Solution

1. Step 1: Understand appending multiple elements

   To add multiple elements from a slice, use the ... operator to unpack them.

2. Step 2: Identify correct append syntax

   Using append(stack, []int{7, 8, 9}...) adds all three elements individually.

3. Final Answer:

   stack = append(stack, []int{7, 8, 9}...) -> Option A

4. Quick Check:

   Use ... to unpack slice in append [OK]

Hint: Use ... to append multiple elements at once [OK]

Common Mistakes:

• Forgetting to assign the result of append back to stack
• Using non-existent push method multiple times
• Appending slice without unpacking elements