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390. Elimination Game

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

• Java
• C++
• Python
• Go

• 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;
      }
  };
  

• 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
  
  

• 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
  }
  

All Problems

All Solutions