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 th…

http://codeforces.com/problemset/problem/662/A 题目大意: 给定n(n <= 500000)张卡片,每张卡片的两个面都写有数字,每个面都有0.5的概率是在正面,各个卡牌独立.求把所有卡牌来玩Nim游戏,先手必胜的概率. (⊙o⊙)-由于本人只会在word文档里写公式,所以本博客是图片格式的. Code #include <cstdio> #include <cstring> #include <algorithm> u…

A Simple Nim Problem Description   Two players take turns picking candies from n heaps,the player who picks the last one will win the game.On each turn they can pick any number of candies which come from the same heap(picking no candy is not allowed)…

Problem: You are playing the following Nim Game with your friend: There to 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 t…

题意 \(K(1 \le K \le 10^9)\)堆石子,每堆石子个数不超过\(L(2 \le 50000)\),问Nim游戏中先手必败局面的数量,答案对\(10^9+7\)取模. 分析 容易得到\(f(i, k) = \sum_{j=0}^{n-1} f(i-1, j) f(i-1, k^j), f(1, i(2 \le i \le L))=1\),其中\(n=min(2^i, 2^i > L)\).发现其实这就是操作为\(xor\)的卷积.于是用鬼畜的fwt做就行了. 题解 然后fwt+快…

1.HDU 2509  2.题意:n堆苹果,两个人轮流,每次从一堆中取连续的多个,至少取一个,最后取光者败. 3.总结:Nim博弈的变形,还是不知道怎么分析,,,,看了大牛的博客. 传送门 首先给出结论:先手胜当且仅当(1)所有堆石子数都为1且游戏的SG值为0,(2)存在某堆石子数大于1且游戏的SG值不为0.证明:(1)若所有堆石子数都为1且SG值为0,则共有偶数堆石子,故先手胜.(2) i)只有一堆石子数大于1时,我们总可以对该堆石子操作,使操作后石子堆数为奇数且所有堆得石子数均为1 ii)有…

1.HDU 1907 2.题意:n堆糖,两人轮流,每次从任意一堆中至少取一个,最后取光者输. 3.总结:有点变形的Nim,还是不太明白,盗用一下学长的分析吧 传送门 分析:经典的Nim博弈的一点变形.设糖果数为1的叫孤独堆,糖果数大于1的叫充裕堆,设状态S0:a1^a2^..an!=0&&充裕堆=0,则先手必败(奇数个为1的堆,先手必败).S1:充裕堆=1,则先手必胜(若剩下的n-1个孤独堆个数为奇数个,那么将那个充裕堆全部拿掉,否则将那个充裕堆拿得只剩一个,这样的话先手必胜).T0:a1…

目前有3堆石子,每堆石子个数也是任意的,双方轮流从中取出石子,规则如下:1)每一步应取走至少一枚石子:每一步只能从某一堆中取走部分或全部石子:2)如果谁不能取谁就失败. Bouton定理: 必败状态当且仅当x1^x2^x3==0 SG函数和SG定理: 对于任意状态x,SG(x)=mex(S),S是x后继状态中SG函数值集合,mex(S)表示不在S内的最小非负整数  SG(x)=0当且仅当x为P 有这样一个游戏,是多个游戏共同进行,每个游戏都执行到底时才算整个游戏结束,每次一个选手可以把一个游戏进…

加强版的NIM游戏,多了一个操作,可以将一堆石子分成两堆非空的. 数据范围太大,打出sg表后找规律. # include <cstdio> # include <cstring> # include <cstdlib> # include <iostream> # include <vector> # include <queue> # include <stack> # include <map> # inc…

292. Nim Game 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 tur…