Elimination game

We will recursively eleminate people from beginning to end and then return backword with the same logic until only one person left, then return that.

class Solution:
    def lastRemaining(self, n: int) -> int:
        def eliminate(numbersCount, isForward, base, step):
            if numbersCount == 1:
                return base + 1
            if isForward or numbersCount % 2 == 1:
                base += step // 2

            step *= 2
            numbersCount //= 2
            return eliminate(numbersCount, not isForward, base, step)

        return eliminate(n, True, 0, 2)

Time Complexity: O(n)
Space Complexity: O(n)