Check if Stack is Empty or Full in DSA Go - Time & Space Complexity

Time Complexity: Check if Stack is Empty or Full

O(1)

Understanding Time Complexity

Checking if a stack is empty or full is a common operation in stack data structures.

We want to know how fast these checks happen as the stack size changes.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

package main

import "fmt"

type Stack struct {
  items []int
  size  int
  top   int
}

func (s *Stack) IsEmpty() bool {
  return s.top == -1
}

func (s *Stack) IsFull() bool {
  return s.top == s.size-1
}

func main() {
  stack := Stack{items: make([]int, 5), size: 5, top: -1}
  fmt.Println(stack.IsEmpty())
  fmt.Println(stack.IsFull())
}

This code defines a stack and checks if it is empty or full by comparing the top index.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Simple comparison of integers (top index with -1 or size-1).
• How many times: Each check runs once per call, no loops or recursion involved.

How Execution Grows With Input

Checking if the stack is empty or full does not depend on the number of items in the stack.

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

Pattern observation: The number of operations stays the same no matter how big the stack is.

Final Time Complexity

Time Complexity: O(1)

This means the check happens instantly, no matter how many items are in the stack.

Common Mistake

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

[OK] Correct: The check only compares two numbers, so it always takes the same short time.

Interview Connect

Knowing that these checks are very fast helps you focus on more complex stack operations during interviews.

Self-Check

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

Practice

1. What does the IsEmpty() function check in a stack data structure?

easy

A. If the stack has no elements inside

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

C. If the stack has exactly one element

D. If the stack has more than one element

Solution

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

   The IsEmpty() function checks whether the stack contains any elements or not.

2. Step 2: Identify what empty means for a stack

   An empty stack means it has zero elements inside, so no items to pop or peek.

3. Final Answer:

   If the stack has no elements inside -> Option A

4. Quick Check:

   IsEmpty() means stack is empty = true [OK]

Hint: Empty means zero elements inside stack [OK]

Common Mistakes:

• Confusing empty with full
• Thinking empty means one element
• Mixing IsEmpty with IsFull

2. Which of the following is the correct Go syntax to check if a stack is full when using a fixed size array?

easy

A. if len(stack) == 0 { /* stack is full */ }

B. if top > len(stack) { /* stack is full */ }

C. if top == len(stack) - 1 { /* stack is full */ }

D. if top == 0 { /* stack is full */ }

Solution

1. Step 1: Understand stack indexing in Go

   For a fixed size array stack, top points to the last filled index. The last valid index is length - 1.

2. Step 2: Check condition for full stack

   When top equals len(stack) - 1, the stack is full because no more elements can be added.

3. Final Answer:

   if top == len(stack) - 1 { /* stack is full */ } -> Option C

4. Quick Check:

   top == max index means full [OK]

Hint: Full means top equals last index (length - 1) [OK]

Common Mistakes:

• Using > instead of == for full check
• Checking if top == 0 for full
• Confusing length with top index

3. Given the following Go code, what will be printed?

type Stack struct {
    items []int
    top   int
}

func (s *Stack) IsEmpty() bool {
    return s.top == -1
}

func main() {
    s := Stack{items: make([]int, 5), top: -1}
    fmt.Println(s.IsEmpty())
    s.top = 4
    fmt.Println(s.IsEmpty())
}

medium

A. true\nfalse

B. false\ntrue

C. false\nfalse

D. true\ntrue

Solution

1. Step 1: Check initial top value and IsEmpty() result

   Initially, top is -1, so IsEmpty() returns true because stack is empty.

2. Step 2: Update top to 4 and check IsEmpty() again

   After setting top to 4, IsEmpty() returns false because stack now has elements.

3. Final Answer:

   true\nfalse -> Option A

4. Quick Check:

   top -1 means empty true, top 4 means not empty false [OK]

Hint: top -1 means empty, any other top means not empty [OK]

Common Mistakes:

• Assuming top 4 means empty
• Confusing slice length with top
• Ignoring initial top value

4. Find the error in this Go code snippet that checks if a stack is full:

func (s *Stack) IsFull() bool {
    return s.top == len(s.items)
}

medium

A. The function should return 's.top > len(s.items)' instead

B. The condition should be 's.top == len(s.items) - 1' to check full correctly

C. The function should check if 's.top == 0' to be full

D. No error, the code is correct

Solution

1. Step 1: Understand stack indexing for full condition

   Stack top index starts at -1 and max valid index is length - 1.

2. Step 2: Identify correct full condition

   Full means top equals last valid index, which is len(s.items) - 1, not len(s.items).

3. Final Answer:

   The condition should be 's.top == len(s.items) - 1' to check full correctly -> Option B

4. Quick Check:

   Full means top == max index (length - 1) [OK]

Hint: Full means top equals last index, not length [OK]

Common Mistakes:

• Using length instead of length - 1
• Checking top == 0 for full
• Returning wrong boolean condition

5. You have a stack implemented with a fixed size array of length 3 and a top index starting at -1. After pushing two elements, you pop one element, then push two more elements. Which statement about the stack state is correct?

hard

A. The stack is empty and top index is -1

B. The stack is not full and top index is 1

C. The stack is full but top index is 3

D. The stack is full and top index is 2

Solution

1. Step 1: Track stack operations and top index changes

   Start: top = -1 (empty). Push two elements: top = 1. Pop one element: top = 0. Push two elements: top = 2 (max index for length 3).

2. Step 2: Determine if stack is full

   Since top = 2 and max index is 2 (length 3 - 1), stack is full.

3. Final Answer:

   The stack is full and top index is 2 -> Option D

4. Quick Check:

   Push/pop changes top; top 2 means full for size 3 [OK]

Hint: Track top index after each push/pop carefully [OK]

Common Mistakes:

• Assuming top can be 3 for full
• Forgetting pop decreases top
• Confusing empty with full states