Question

390. Elimination Game

中文文档

Description

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

Solution 1

class Solution:
  def lastRemaining(self, n: int) -> int:
    a1, an = 1, n
    i, step, cnt = 0, 1, n
    while cnt > 1:
      if i % 2:
        an -= step
        if cnt % 2:
          a1 += step
      else:
        a1 += step
        if cnt % 2:
          an -= step
      cnt >>= 1
      step <<= 1
      i += 1
    return a1

class Solution {
  public int lastRemaining(int n) {
    int a1 = 1, an = n, step = 1;
    for (int i = 0, cnt = n; cnt > 1; cnt >>= 1, step <<= 1, ++i) {
      if (i % 2 == 1) {
        an -= step;
        if (cnt % 2 == 1) {
          a1 += step;
        }
      } else {
        a1 += step;
        if (cnt % 2 == 1) {
          an -= step;
        }
      }
    }
    return a1;
  }
}

class Solution {
public:
  int lastRemaining(int n) {
    int a1 = 1, an = n, step = 1;
    for (int i = 0, cnt = n; cnt > 1; cnt >>= 1, step <<= 1, ++i) {
      if (i % 2) {
        an -= step;
        if (cnt % 2) a1 += step;
      } else {
        a1 += step;
        if (cnt % 2) an -= step;
      }
    }
    return a1;
  }
};

func lastRemaining(n int) int {
  a1, an, step := 1, n, 1
  for i, cnt := 0, n; cnt > 1; cnt, step, i = cnt>>1, step<<1, i+1 {
    if i%2 == 1 {
      an -= step
      if cnt%2 == 1 {
        a1 += step
      }
    } else {
      a1 += step
      if cnt%2 == 1 {
        an -= step
      }
    }
  }
  return a1
}