Solution: Max Stack

Understand how to implement a custom Max Stack that supports standard stack operations along with efficient retrieval and removal of the maximum element. Learn a method combining stacks and heaps to achieve optimal time complexity, including handling duplicates with unique indexing and lazy updates to keep data structures synchronized.

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Statement
Solution
- Time complexity
- Space complexity

Statement

Design a custom stack class, Max Stack, that supports the basic stack operations and can find the maximum element present in the stack.

Implement the following methods for Max Stack:

Constructor: This initializes the Max Stack object.
Void Push(int x): This pushes the provided element, x, onto the stack.
Int Pop( ): This removes and returns the element on the top of the stack.
Int Top( ): This retrieves the most recently added element on the top of the stack without removing it.
Int peekMax( ): This retrieves the maximum element in the stack without removing it.
Int popMax( ): This retrieves the maximum element in the stack and removes it. If there is more than one maximum element, remove the most recently added one (the topmost).

Constraints:

$-1000 \leq$ x $\leq 1000$
A maximum of $100$ calls can be made to Push( ), Pop( ), Top( ), peekMax( ) and popMax( ).
The Pop( ), Top( ), peekMax( ), and popMax( ) methods will always be called on a ...