Algorithm


Problem Name: 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

Code Examples

#1 Code Example with Javascript Programming

Code - Javascript Programming


const lastRemaining = function(n) {
  let left = true
  let remaining = n
  let step = 1
  let head = 1
  while (remaining > 1) {
    if (left || remaining % 2 === 1) {
      head = head + step
    }
    remaining = remaining >> 1
    step = step * 2
    left = !left
  }
  return head
}
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Input

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cmd
n = 9

Output

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6

#2 Code Example with Python Programming

Code - Python Programming


class Solution:
    def lastRemaining(self, n):
        head, left, step, remaining = 1, 1, 1, n
        while remaining > 1:
            if left or remaining % 2: head += step
            left = 1 - left
            step *= 2
            remaining //= 2
        return head
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Input

x
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cmd
n = 1

Output

x
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cmd
1
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