Sothan

转自：http://blog.youkuaiyun.com/luomingjun12315/article/details/45555495在介绍SG函数和SG定理之前我们先介绍介绍必胜点与必败点吧.必胜点和必败点的概念：       P点：必败点，换而言之，就是谁处于此位置，则在双方操作正确的情况下必败。       N点：必胜点，处于此情况下，双方操作均正确的情况下必胜

POJ 1740 A New Stone Game Alice and Bob decide to play a new stone game.At the beginning of the game they pick n(1<=n<=10) piles of stones in a line. Alice and Bob move the stones in turn. At each step of the game,the player choose a pile,remove at least

POJ 3710 Christmas Game 树上删边博弈 压缩环 Fusion Principle

参考自：《组合游戏略述——浅谈SG游戏的若干拓展及变形》无向图删边游戏：树的删边游戏 规则如下：* 给出一个有N个点的树，有一个点作为树的根节点。* 游戏者轮流从树中删去边，删去一条边后，不与根节点相连的部分将被移走。* 谁无路可走谁输。定理：叶子结点的SG值为0，中间节点的SG值为它的所有子节点的SG值加一后的异或和。Fusion

HDU 5299 L - Circles Game 树上删边博弈 There are n circles on a infinitely large table.With every two circle, either one contains another or isolates from the other.They are never crossed nor tangent.Alice and Bob are playing a game concerning these circles.Th

POJ 1704 Georgia and Bob 阶梯尼姆博弈 Georgia and Bob decide to play a self-invented game. They draw a row of grids on paper, number the grids from left to right by 1, 2, 3, ..., and place N chessmen on different grids, as shown in the following figure for examp

转自:http://blog.youkuaiyun.com/luomingjun12315/article/details/45479073我国民间有个古老的游戏：就是有物品若干堆，（物品可以是火柴，围棋都可以）。两个人轮流从堆中取若干件，规定取光物体者为胜。这个就是我们今天要研究的组合游戏。组合游戏定义：       1、有且仅有两个玩家    2、游戏双方轮流操作    3、游戏操作状态是

重点结论：对于一个Nim游戏的局面(a1,a2,...,an)，它是P-position当且仅当a1^a2^...^an=0，其中^表示位异或(xor)运算。Nim游戏是博弈论中最经典的模型（之一？），它又有着十分简单的规则和无比优美的结论，由这个游戏开始了解博弈论恐怕是最合适不过了。Nim游戏是组合游戏(Combinatorial Games)的一种，准确来说，属于“Impa

HDU 5754 Life Winner Bo 博弈 Bo is a "Life Winner".He likes playing chessboard games with his girlfriend G.The size of the chessboard is N×M.The top left corner is numbered(1,1) and the lower right corner is numberd (N,M).For each game,Bo and G take turn