Stack Implementation Using Array in DSA Python - Time & Space Complexity

Time Complexity: Stack Implementation Using Array

O(1)

Understanding Time Complexity

We want to understand how fast stack operations run when using an array.

How does the time to push or pop change as the stack grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Stack:
    def __init__(self, capacity):
        self.array = [None] * capacity
        self.top = -1
        self.capacity = capacity

    def push(self, value):
        if self.top == self.capacity - 1:
            return False  # stack full
        self.top += 1
        self.array[self.top] = value
        return True

    def pop(self):
        if self.top == -1:
            return None  # stack empty
        value = self.array[self.top]
        self.top -= 1
        return value

This code creates a stack using an array and supports push and pop operations.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single step assignments and index updates in push and pop.
• How many times: Each push or pop runs once per call, no loops inside.

How Execution Grows With Input

Each push or pop does a fixed number of steps regardless of stack size.

Input Size (n)	Approx. Operations
10	4 steps per push/pop
100	4 steps per push/pop
1000	4 steps per push/pop

Pattern observation: The time stays the same no matter how big the stack is.

Final Time Complexity

Time Complexity: O(1)

This means each push or pop takes the same short time no matter how many items are in the stack.

Common Mistake

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

[OK] Correct: The code only changes one position in the array each time, so the size does not affect the time.

Interview Connect

Knowing that stack operations run in constant time helps you explain why stacks are efficient for many tasks like undo or expression evaluation.

Self-Check

"What if the array needs to resize dynamically when full? How would the time complexity change?"

Practice

1. What is the main purpose of using an array to implement a stack?

easy

A. To allow random access to elements

B. To store elements in a first-in, first-out (FIFO) order

C. To sort elements automatically

D. To store elements in a last-in, first-out (LIFO) order

Solution

1. Step 1: Understand stack behavior

   A stack stores elements so that the last element added is the first one removed, called LIFO.

2. Step 2: Role of array in stack

   An array helps store elements in order and access the last added element easily for push/pop operations.

3. Final Answer:

   To store elements in a last-in, first-out (LIFO) order -> Option D

4. Quick Check:

   Stack = LIFO [OK]

Hint: Stack means last-in, first-out order [OK]

Common Mistakes:

• Confusing stack with queue (FIFO)
• Thinking array sorts elements automatically
• Assuming random access is main stack feature

2. Which of the following is the correct way to initialize an empty stack using an array in Python?

easy

A. stack = []

B. stack = {}

C. stack = ()

D. stack = null

Solution

1. Step 1: Identify Python data types for stack

   An array-like structure for stack is a list, initialized with square brackets [].

2. Step 2: Check each option

   stack = [] uses [], which is a list. stack = {} is a dictionary, () is a tuple, null (no data).

3. Final Answer:

   stack = [] -> Option A

4. Quick Check:

   Empty list = empty stack [OK]

Hint: Use [] to create empty list for stack [OK]

Common Mistakes:

• Using {} which creates a dictionary
• Using () which creates a tuple
• Assigning null instead of a list

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

stack = []
stack.append(10)
stack.append(20)
stack.pop()
print(stack)

medium

A. [10, 20]

B. [20]

C. [10]

D. []

Solution

1. Step 1: Trace push operations

   stack.append(10) adds 10, stack becomes [10]. Then stack.append(20) adds 20, stack becomes [10, 20].

2. Step 2: Trace pop operation

   stack.pop() removes last element 20, stack becomes [10].

3. Final Answer:

   [10] -> Option C

4. Quick Check:

   Pop removes last item, stack left with [10] [OK]

Hint: Pop removes last pushed element [OK]

Common Mistakes:

• Thinking pop removes first element
• Confusing append with insert
• Expecting stack to be empty after pop

4. Identify the error in the following stack implementation code:

stack = []
stack.push(5)
stack.append(10)
print(stack)

medium

A. 'push' method does not exist for list

B. Missing initialization of stack

C. Cannot append to list

D. print statement syntax error

Solution

1. Step 1: Check list methods

   Python lists use append() to add elements, not push().

2. Step 2: Identify error

   stack.push(5) causes AttributeError because 'push' is not a list method.

3. Final Answer:

   'push' method does not exist for list -> Option A

4. Quick Check:

   Use append(), not push() for list [OK]

Hint: Use append() to add elements to list [OK]

Common Mistakes:

• Using push() instead of append()
• Assuming push() is valid for Python lists
• Ignoring error messages

5. Given a stack implemented using an array, how can you check if the stack is empty before popping an element to avoid errors?

hard

A. Check if stack is null

B. Check if stack's length is zero using len(stack) == 0

C. Try popping and catch exceptions if stack is empty

D. Use stack[0] == null to check emptiness

Solution

1. Step 1: Understand stack emptiness check

   To avoid errors, check if stack has no elements by verifying its length is zero.

2. Step 2: Evaluate options

   Check if stack's length is zero using len(stack) == 0 correctly checks length with len(stack) == 0. Try popping and catch exceptions if stack is empty is valid but less efficient. Check if stack is null checks null which is incorrect. Use stack[0] == null to check emptiness checks first element which may cause error if empty.

3. Final Answer:

   Check if stack's length is zero using len(stack) == 0 -> Option B

4. Quick Check:

   Empty stack means length zero [OK]

Hint: Use len(stack) == 0 to check empty stack [OK]

Common Mistakes:

• Checking stack is null instead of empty
• Accessing stack[0] without checking length
• Relying only on try-except without condition