Leetcode 292: Nim Game

最新推荐文章于 2024-12-02 00:00:26 发布

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最新推荐文章于 2024-12-02 00:00:26 发布

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原文链接：http://www.cnblogs.com/liangmou/p/7997381.html

本文介绍了一种判断Nim游戏胜负的算法实现。通过三种不同的方法：取模运算、动态规划以及递归缓存，来确定玩家是否能在给定石堆数量的情况下赢得游戏。

You are playing the following Nim Game with your friend: There is a heap of stones on the table, each time one of you take turns to remove 1 to 3 stones. The one who removes the last stone will be the winner. You will take the first turn to remove the stones.

Both of you are very clever and have optimal strategies for the game. Write a function to determine whether you can win the game given the number of stones in the heap.

For example, if there are 4 stones in the heap, then you will never win the game: no matter 1, 2, or 3 stones you remove, the last stone will always be removed by your friend.

 1 public class Solution {
 2     public bool CanWinNim(int n) {
 3         return n % 4 != 0;
 4     }
 5 }
 6 
 7 public class Solution1 {
 8     public bool CanWinNim(int n) {
 9         bool dp0 = true, dp1 = true, dp2 = true;
10         
11         for (int i = 3; i < n; i++)
12         {
13             var dp = !dp0 || !dp1 || !dp2;
14             dp0 = dp1;
15             dp1 = dp2;
16             dp2 = dp;
17         }
18         
19         return dp2;
20     }
21 }
22 
23 public class Solution2 {
24     private Dictionary<int, bool> cache = new Dictionary<int, bool>();
25     
26     public bool CanWinNim(int n) {
27         if (n <= 3) return true;
28         
29         if (!cache.ContainsKey(n))
30         {
31             cache[n] = !CanWinNim(n - 1) || !CanWinNim(n - 2) || !CanWinNim(n - 3);    
32         }      
33         
34         return cache[n];
35     }
36 }