zoukankan      html  css  js  c++  java
  • 【leetcode】1025. Divisor Game

    题目如下:

    Alice and Bob take turns playing a game, with Alice starting first.

    Initially, there is a number N on the chalkboard.  On each player's turn, that player makes a move consisting of:

    • Choosing any x with 0 < x < N and N % x == 0.
    • Replacing the number N on the chalkboard with N - x.

    Also, if a player cannot make a move, they lose the game.

    Return True if and only if Alice wins the game, assuming both players play optimally.

    Example 1:

    Input: 2
    Output: true
    Explanation: Alice chooses 1, and Bob has no more moves.
    

    Example 2:

    Input: 3
    Output: false
    Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.
    

    Note:

    1. 1 <= N <= 1000

    解题思路:假设当前操作是Bob选择,我们可以定义一个集合dic = {},里面存储的元素Bob必输的局面。例如当前N=1,那么Bob无法做任何移动,是必输的场面,记dic[1] = 1。那么对于Alice来说,在轮到自己操作的时候,只有选择一个x,使得N-x在这个必输的集合dic里面,这样就是必胜的策略。因此对于任意一个N,只要存在 N%x == 0 并且N-x in dic,那么这个N对于Alice来说就是必胜的。只要计算一遍1~1000所有的值,把必输的N存入dic中,最后判断Input是否在dic中即可得到结果。

    代码如下:

    class Solution(object):
        dic = {1:1}
        def init(self):
            for i in range(2,1000+1):
                flag = False
                for j in range(1,i):
                    if i % j == 0 and i - j in self.dic:
                        flag = True
                        break
                if flag == False:
                    self.dic[i] = 1
    
        def divisorGame(self, N):
            """
            :type N: int
            :rtype: bool
            """
            if len(self.dic) == 1:
                self.init()
            return N not in self.dic
  • 相关阅读:
    robotframework使用之 下拉框处理
    Python操作MySQL
    Python发送邮件
    Redis 常用命令
    安装htop教程及坑
    探索式测试-概述
    Git相关命令教程
    [精华][推荐]SSO CAS单点登录框架学习 环境搭建
    [精华][推荐]SSO CAS单点登录框架学习 搭建详细步骤及源码
    [精华][推荐]CAS实现单点登录实例源码
  • 原文地址:https://www.cnblogs.com/seyjs/p/10744033.html
Copyright © 2011-2022 走看看