Nim游戏:有n堆石子,每堆个数不一,两人依次捡石子,每次只能从一堆中至少捡一个.捡走最后一个石子胜. 先手胜负:将所有堆的石子数进行异或(xor),最后值为0则先手输,否则先手胜. ================================ Anti-Nim游戏:游戏与Nim游戏基本相同,只是捡走最后一个石子者输. 先手胜负:将所有堆的石子数进行异或(xor),如果异或结果为0且所有堆的石子数全为1,或者异或结果为0且存在数量大于1的石子堆,则先手胜.否则先手输. 该题即是Anti-Ni…

题意:n堆石头,拿走最后一块的输 思路:SJ定理:先手必胜当且仅当:(1)游戏的SG函数不为0且游戏中某个单一游戏的SG函数大于1:(2)游戏的SG函数为0且游戏中没有单一游戏的SG函数大于1. 参考:[博弈]Anti,Multi,Every-SG 代码: #include<set> #include<map> #include<stack> #include<cmath> #include<queue> #include<vector&g…

NIM游戏,NIM游戏变形,威佐夫博弈以及巴什博奕总结 经典NIM游戏: 一共有N堆石子,编号1..n,第i堆中有个a[i]个石子. 每一次操作Alice和Bob可以从任意一堆石子中取出任意数量的石子,至少取一颗,至多取出这一堆剩下的所有石子. 两个人轮流行动,取走最后一个的人胜利.Alice为先手. 我们定义: P:表示当前局面下先手必败 N:表示当前局面下先手必胜 N,P状态的转移满足如下性质: 1.合法操作集合为空的局面为P 2.可以移动到P的局面为N,这个很好理解,以为只要能转换到P局面…

转自http://blog.sina.com.cn/s/blog_63e4cf2f0100tq4i.html 今天在POJ做了一道博弈题..进而了解到了阶梯博弈...下面阐述一下我对于阶梯博弈的理解..  首先是对阶梯博弈的阐述...博弈在一列阶梯上进行...每个阶梯上放着自然数个点..两个人进行阶梯博弈...每一步则是将一个集体上的若干个点( >=1 )移到前面去..最后没有点可以移动的人输.. 如这就是一个阶梯博弈的初始状态 2 1 3 2 4 ... 只能把后面的点往前面放...如何来分析…

A Chess Game Time Limit: 3000MS   Memory Limit: 65536K Total Submissions: 3791   Accepted: 1549 Description Let's design a new chess game. There are N positions to hold M chesses in this game. Multiple chesses can be located in the same position. The…

Nim or not Nim? Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u Submit Status Practice HDU 3032 Description Nim is a two-player mathematic game of strategy in which players take turns removing objects from distinct heaps.…

Nim or not Nim? Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 613    Accepted Submission(s): 282 Problem Description Nim is a two-player mathematic game of strategy in which players take turns…

Nim or not Nim? Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 623    Accepted Submission(s): 288 Problem Description Nim is a two-player mathematic game of strategy in which players take turns…

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Nim or not Nim? Problem Description Nim is a two-player mathematic game of strategy in which players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object, and may remove any number of objects provide…