Last Remaining Number
Recursion
Given the integer n, you have a list of all integers in the range [1, n] sorted in a strictly increasing order. Performing the following steps:
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.
Return the last remaining number.
Write a recursive function to solve this problem. The input contains 1 positive integer n with 1 <= n <= 109
Important Info:
You must solve this problem using recursion. If you do not use recursion, then you will not get any points for this assignment.
Example 1:
Input: 4
Output: 2
Explanation: (bold indicate that the number is removed at that step)
arr = [1, 2, 3, 4]
arr = [2, 4]
arr = [2]
Example 2:
Input: 9
Output: 6
Explanation: (bold indicate that the number is removed at that step)
arr = [1, 2, 3, 4, 5, 6, 7, 8, 9]
arr = [2, 4, 6, 8]
arr = [2, 6]
arr = [6]
