Implement a Maximum-Tracking Stack
Problem Description
Design and implement a stack-like data structure that supports the following operations efficiently:
push(x): Adds integerxto the top of the stack.pop(): Removes and returns the element at the top of the stack.top(): Returns the element at the top of the stack without removing it.peekMax(): Returns the maximum value currently in the stack without removing it.popMax(): Removes and returns the maximum value currently in the stack. If the maximum value appears multiple times, remove the occurrence closest to the top of the stack.
Assumptions:
pop,top,peekMax, andpopMaxoperations will only be called when the stack is non-empty.
Deliverables:
- Provide an optimal implementation of the data structure.
- Analyze the time complexity of each operation (
push,pop,top,peekMax,popMax).
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Core dilemma
The central engineering conflict is maintaining efficient O(1) or O(logN) access to the maximum element while simultaneously supporting standard LIFO stack operations and, critically, an O(1) or O(logN) `popMax` operation that removes an arbitrary element from the logical 'middle' of the stack, which is inherently O(N) for a simple array-backed stack. The 'closest to top' constraint for `popMax` further complicates solutions involving sorted structures.
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Implement a Maximum-Tracking Stack
Problem Description
Design and implement a stack-like data structure that supports the following operations efficiently:
push(x): Adds integerxto the top of the stack.pop(): Removes and returns the element at the top of the stack.top(): Returns the element at the top of the stack without removing it.peekMax(): Returns the maximum value currently in the stack without removing it.popMax(): Removes and returns the maximum value currently in the stack. If the maximum value appears multiple times, remove the occurrence closest to the top of the stack.
Assumptions:
pop,top,peekMax, andpopMaxoperations will only be called when the stack is non-empty.
Deliverables:
- Provide an optimal implementation of the data structure.
- Analyze the time complexity of each operation (
push,pop,top,peekMax,popMax).