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

Solutions (Rust)

1. Solution

impl Solution {
    pub fn last_remaining(n: i32) -> i32 {
        if n == 1 {
            return 1;
        }

        2 * Self::last_remaining_rev(n / 2)
    }

    pub fn last_remaining_rev(n: i32) -> i32 {
        if n == 1 {
            return 1;
        }

        2 * Self::last_remaining(n / 2) - 1 + n % 2
    }
}