Space Complexity of Stack Operations

Space complexity refers to the amount of extra memory used by an operation relative to the input size. In the case of stacks, most operations are performed in-place, meaning they work directly within the existing memory block. Below, we explore the space complexity of key stack operations: Push, Pop, Peek, isEmpty, and Traversal.

Summary Table

Operation	Space Complexity	Why?
Push	O(1)	Element is added at the top using constant space
Pop	O(1)	Element is removed from top without new memory
Peek	O(1)	Accesses the top element directly
isEmpty	O(1)	Returns true/false using a single flag or count
Traversal	O(1) to O(N)	O(1) if only reading top; O(N) if visiting all elements

1. Push

The push operation inserts an element at the top of the stack. It uses only a fixed amount of memory to store the incoming value.

• Space Complexity: O(1)
• Why: The new element is stored directly at the next position. No new data structures or extra allocations are needed.

2. Pop

The pop operation removes the top element from the stack.

• Space Complexity: O(1)
• Why: No extra space is required since the operation simply removes or de-references the top value.

3. Peek

The peek operation reads the top element without removing it.

• Space Complexity: O(1)
• Why: It directly accesses the top index or pointer without needing to copy or move data.

4. isEmpty

The isEmpty check determines whether the stack is empty.

• Space Complexity: O(1)
• Why: This operation typically checks a counter or pointer — both are constant-sized variables.

5. Traversal

Traversal involves visiting each element in the stack, usually from top to bottom.

• Space Complexity: O(1) to O(N)
• Why: If you're reading only the top value or using a single pointer, it's O(1). But if you're storing or printing all N elements during traversal, temporary memory like an output list or recursion stack may consume O(N).