390 Elimination Game

You have a list arr of all integers in the range [1, n] sorted in a strictly increasing order. Apply the following algorithm on arr:

• Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.
• Repeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.
• Keep repeating the steps again, alternating left to right and right to left, until a single number remains.

Given the integer n, return the last number that remains in arr.

Example 1:

Input: n = 9
Output: 6
Explanation:
arr = [1, 2, 3, 4, 5, 6, 7, 8, 9]
arr = [2, 4, 6, 8]
arr = [2, 6]
arr = [6]

Example 2:

Input: n = 1
Output: 1

Constraints:

• 1 <= n <= 109

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class Solution:
    def lastRemaining(self, n: int) -> int:
        def helper(n, from_left):
            if n == 1:
                return 1
            if from_left:
                # remove odd
                return 2 * helper(n // 2, False)
            elif n % 2 == 1:
                # remove odd
                return 2 * helper(n // 2, True)
            else:
                # remove even
                # [1 2 3 4 5 6 ] ==> [1 3 5] == 2 * [1 2 3] - 1
                return 2 * helper(n // 2, True) - 1
        return helper(n, True)