Daily Coding Problem: Problem #746 [Easy]

Oddly, this is also Daily Coding Problem: Problem #794 [Easy], and Daily Coding Problem: Problem #43, and it's one of the problems in the Daily Coding Problem book.

This problem was asked by Amazon.

Implement a stack that has the following methods:

• push(val), which pushes an element onto the stack
• pop(), which pops off and returns the topmost element of the stack. If there are no elements in the stack, then it should throw an error or return null.
• max(), which returns the maximum value in the stack currently. If there are no elements in the stack, then it should throw an error or return null.

Each method should run in constant time.

Analysis

The specification is an abstract stack. It doesn't specify the implementation, which could be a fixed-size array, a linked list, or a variably-sized array, like in Python or a Go slice. I chose to do a linked list implementation.

The problem statement wants a max() method for the abstract stack. That's where some implementation complications arise. The problem statement doesn't specify a type for the values that reside on the stack. I chose integers because I didn't think about it too hard, but strings have a lexicographic ordering: "aaa" < "aaaa" < "z" for example.

The "run in constant time" constraint points at a particular implementation for the max() method. Pushing and popping elements from the head of a linked list is the dictionary definition of "constant time". Why not add a second linked list to the max-stack-type whose values are the maximum value of the values pushed on the abstract stack so far? This doubles the time it takes to push or pop an element, but that's still constant no matter how large the stack gets.

That's what I did: specify a max-stack type that contains two different, internal stacks. One stack keeps track of the values passed in via push(value), and returned via pop(), the second internal stack keeps track of the maximum value of the values in the first stack.

Code

This is the Daily Coding Problem book's solution, albeit they use Python's variable-length arrays instead of a linked list for the two stacks.

Interview Analysis

It's clear that adding the max() method to the abstract stack interface got done so as to prevent people from just spewing a stack implementation from memory. Adding max() means thinking harder about the problem, and candidates write more code than just manipulating slices in Python.

It's probably a good idea for the candidate to talk about what decisions they make as they outline a solution, including noting any vagueness in the problem statement, like what type(s) are the input values?

The "constant time" constraint almost certainly exists to keep candidates from wandering off into a vail of tears involving an array of stack elements sorted by value which gets resized and resorted on every push and pop. It also lets the interviewer see if the candidate understands what "constant time" means in the algorithm context.

The interviewer could reasonably expect design choices like

• plain stack implementation as slice or array or linked list
• max value stack element per value stack element, or keeping a minimum number on the max value stack
• only integer values, or only string values or some other choice
• full-blown Object Oriented Design, with completely hidden implementation, or just enough OOD to get by. Go can do some abstract type enforcement with an interface type.
• consideration given to errors returned or exceptions thrown, which in some languages might mean checked vs unchecked exceptions in the classes methods