Approach

To design a stack that supports the operations push, pop, top, and retrieve the minimum element in constant time, we can utilize two stacks: one for the main stack operations and another one specifically for tracking the minimum elements. Here's a structured framework for implementing this:

1. Initialize Two Stacks:

• Main Stack: To hold all the elements.

• Min Stack: To keep track of the minimum elements.

• Push Operation:

• Push the element onto the main stack.

• If the min stack is empty or the new element is less than or equal to the top of the min stack, push it onto the min stack.

• Pop Operation:

• Pop the element from the main stack.

• If the popped element is equal to the top of the min stack, pop it from the min stack as well.

• Top Operation:

• Return the top element of the main stack without removing it.

• Retrieve Minimum Element:

• Return the top element of the min stack.

Key Points

• Constant Time Operations: Each of the operations should execute in O(1) time complexity.

• Space Complexity: The space complexity remains O(n) for storing elements, where n is the number of elements in the stack.

• Data Integrity: Ensure that both stacks maintain their integrity during operations to avoid errors.

Standard Response

Here is a sample implementation of the stack in Python:

class MinStack:
 def __init__(self):
 self.main_stack = []
 self.min_stack = []

 def push(self, x: int) -> None:
 self.main_stack.append(x)
 # Push onto min_stack only if it's empty or the new element is a new minimum
 if not self.min_stack or x <= self.min_stack[-1]:
 self.min_stack.append(x)

 def pop(self) -> None:
 if self.main_stack:
 popped = self.main_stack.pop()
 # If the popped element is the current minimum, pop it from min_stack as well
 if popped == self.min_stack[-1]:
 self.min_stack.pop()

 def top(self) -> int:
 return self.main_stack[-1] if self.main_stack else None

 def get_min(self) -> int:
 return self.min_stack[-1] if self.min_stack else None

Tips & Variations

Common Mistakes to Avoid:

• Not Handling Empty Stacks: Ensure to check if the stack is empty before performing operations like pop or top.

• Incorrect Minimum Management: Always check the current minimum correctly during push and pop operations to avoid inaccuracies.

Alternative Ways to Answer:

• Using a Linked List: Instead of using arrays for stacks, a linked list can also be implemented to handle dynamic memory allocation.

• Using a Single Stack with Tuple: Store tuples in the main stack that include both the value and the current minimum up to that point.

Role-Specific Variations:

• Technical Roles: Emphasize time complexity analysis and edge cases in your explanation.

• Managerial Roles: Focus on how this stack design can be applied in real-world scenarios, such as managing tasks or resources efficiently.

Follow-Up Questions:

• How would you handle thread safety for this stack implementation?

• Can you explain the trade-offs of using two stacks versus a single stack with complex data structures?

• What would you do differently if you needed to support additional operations, such as retrieving the maximum element?

This structured response not only provides a solid framework for designing the required stack but also encourages candidates to think critically about their design choices and how to communicate them effectively during interviews