题意:对于n堆石子,每堆若干个,两人轮流操作,每次操作分两步,第一步从某堆中去掉至少一个,第二步(可省略)把该堆剩余石子的一部分分给其它的某些堆. 真是好♂题,代码不长就是好♂题. 首先考虑两堆相同的石子,先手一定必输,因为若是我操作第一堆,则后手也可以对第二堆做对称决策. 其实,其他情况,一定是先手必胜. 第一种情况:奇数堆. 我们可以将最大堆的石子分配给其他堆让他们两两配对,如下图所示: 显然,红色部分绝壁不会超过第五个 石子的高度. 第二种情况:偶数情况 我们可以把最大堆和最小堆先配对,剩…

有若干堆石子,每一次需要从一堆石子中拿走一些,然后如果愿意的话,再从这堆石子中拿一些(揣度题意应该是不能拿出全部)分给其它任意不为空的堆.不能操作的人为负. 一直不会博弈啊..感觉完全就是个智商题,虽然本质还是差不多的寻找策略,根据性质从简单的模型入手,尝试拓展结论,在尝试寻找一种稳定的策略转化为该模型.翻了这位的题解,orzorz.侵删. 补充一下,偶数堆的话如果最多的一堆与最矮的一堆看齐,砍掉的全补上了呢,这是就是一对一对相等的情况,与当前情况矛盾,所以不可能. #include<iostr…

博弈论(一):Nim游戏 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“Impartial Combinatorial Games”(以下简称ICG).满足以下条件的游戏…

基础博弈的小结:http://blog.csdn.net/acm_cxlove/article/details/7854530 经典翻硬币游戏小结:http://blog.csdn.net/acm_cxlove/article/details/7854534 经典的删边游戏小结:http://blog.csdn.net/acm_cxlove/article/details/7854532 五篇国家集训队论文: 张一飞: <由感性认识到理性认识——透析一类搏弈游戏的解答过程 > 王晓珂:<…

转载请注明出处,谢谢http://blog.csdn.net/ACM_cxlove?viewmode=contents    by---cxlove 首先当然要献上一些非常好的学习资料: 基础博弈的小结:http://blog.csdn.net/acm_cxlove/article/details/7854530 经典翻硬币游戏小结:http://blog.csdn.net/acm_cxlove/article/details/7854534 经典的删边游戏小结:http://blog.csdn…

http://poj.org/problem?id=1740 (题目链接) 男人八题之一 题意 对于n堆石子,每堆若干个,两人轮流操作,每次操作分两步,第一步从某堆中去掉至少一个,第二步(可省略)把该堆剩余石子的一部分分给其它的某些堆.最后谁无子可取即输. Solution 首先我们考虑两堆相等的情况,一定是谁取谁输,因为对方永远可以做对称的操作.对于四堆,1.2堆相等,3.4堆相等的情况,一定也是先手输,后手也只需要做对称的操作(在先手取石子的对称堆中取相同多的石子,并把和先手等量的石子分给先…

A New Stone Game Time Limit: 1000MS   Memory Limit: 30000K Total Submissions: 5769   Accepted: 3158 Description 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…

1.题目: 1180. Stone Game Time limit: 1.0 secondMemory limit: 64 MB Two Nikifors play a funny game. There is a heap of N stones in front of them. Both Nikifors in turns take some stones from the heap. One may take any number of stones with the only cond…

Zhuge Liang's Stone Sentinel Maze Time Limit: 10000/4000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 385    Accepted Submission(s): 106 Problem Description Zhuge Liang was a chancellor of the state of Shu Han dur…

A New Stone Game Time Limit: 1000MS   Memory Limit: 30000K Total Submissions: 5453   Accepted: 2989 Description 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…

F - Again Stone Game Time Limit:2000MS     Memory Limit:32768KB     64bit IO Format:%lld & %llu Submit Status Description Alice and Bob are playing a stone game. Initially there are n piles of stones and each pile contains some stone. Alice stars the…

Lifting the Stone Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u Submit Status Practice HDU 1115 Description There are many secret openings in the floor which are covered by a big heavy stone. When the stone is lifted up…

http://poj.org/problem?id=1740 题目大意就是,对于n堆石子,每堆若干个,两人轮流操作,每次操作分两步,第一步从某堆中去掉至少一个,第二步(可省略)把该堆剩余石子的一部分分给其它的某些堆.最后谁无子可取即输. 看了题解感觉太神了. 首先我们来分析: 当只有一堆时,先手必胜,直接一次取完即可 当有两堆时,分两种情况,一是两堆相同时,先手必输,因为无论先手怎样取,后手总有办法再次平衡两堆:而是两堆不同时,先手必胜,因为先手总有办法先平衡两堆,然后就像一的情况. 当有三堆时…

A simple stone game                                                                                                       Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)                                             …

A New Stone Game 题意: 对于n堆石子,每堆若干个,两人轮流操作,每次操作分两步,第一步从某堆中去掉至少一个,第二步(可省略)把该堆剩余石子的一部分分给其它的某些堆.最后谁无子可取即输. 题解: 首先我们考虑两堆相等的情况,一定是谁取谁输,因为对方永远可以做对称的操作.对于四堆,1.2堆相等,3.4堆相等的情况,一定也是先手输,后手也只需要做对称的操作(在先手取石子的对称堆中取相同多的石子,并把和先手等量的石子分给先手分配给的堆的对称堆.(若先手在3堆取,并分给1堆,那后手就在4…

题目链接 A Sample Stone Game 题目大意:给定n,k,表示最初时有n个石头,两个人玩取石子游戏,第一个人第一次可以取1~n-1个石头,后面每个人最多可以拿走前面一个人拿走的个数的K倍,当有一个人可以一次性全部拿走时获胜.问两人都在不失误的情况下,先拿着有没有必胜局势.有的话求他第一次最少该取多少个. 思考过程: 首先讨论k=1的情况,我们可以把一个数n(石子的个数),写为二进制下的表示,那先者取走最后一个1,那后者必然不能取走比它高一位的1,那么先拿者一定会赢,当然如果n本来就…

题目: E - A simple stone game Time Limit:1000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u Submit Status Practice POJ 3922 Description After he has learned how to play Nim game, Mike begins to try another stone game which seems much eas…

[题目] Description The funny stone game is coming. There are n piles of stones, numbered with 0, 1, 2, ..., n − 1. Twopersons pick stones in turn. In every turn, each person selects three piles of stones numbered i, j, k(i < j, j ≤ k and at least one s…

A New Stone Game Time Limit: 1000MS   Memory Limit: 30000K Total Submissions: 5694   Accepted: 3119 Description 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…

A New Stone Game Time Limit: 1000MS   Memory Limit: 30000K Total Submissions: 5338   Accepted: 2926 Description 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…

Lifting the Stone Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 6104    Accepted Submission(s): 2546 Problem Description There are many secret openings in the floor which are covered by a big…

1180. Stone Game Time limit: 1.0 second Memory limit: 64 MB Two Nikifors play a funny game. There is a heap of N stones in front of them. Both Nikifors in turns take some stones from the heap. One may take any number of stones with the only condition…

UVA 10165 - Stone Game 题目链接 题意:给定n堆石子,每次能在一堆取1到多个.取到最后一个赢,问谁赢 思路:就裸的的Nim游戏,利用定理求解 代码: #include <stdio.h> #include <string.h> int n, num; int main() { while (~scanf("%d", &n) && n) { int sum = 0; for (int i = 0; i < n;…

外语学习强烈推荐Rosetta Stone 外语学习强烈推荐Rosetta Stone…

题目: Lifting the Stone Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 168 Accepted Submission(s): 98   Problem Description There are many secret openings in the floor which are covered by a big he…

DP: dp[i][j]前i堆放j序列长度有多少行法, dp[i][j]=dp[i-1][j] (不用第i堆), dp[i][j]+=dp[i-1][j-k]*C[j][k] (用第i堆的k个石头) A Famous Stone Collector Time Limit: 30000/15000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 845    Accepted Su…

题目链接:hdu 5996 dingyeye loves stone 题意: 给你一棵树,树的每一个节点有a[i]个石子,每个人可以将这个节点的石子移向它的父亲,如果没有合法操作,那么就算输,现在给你当前的局面,问你能否赢 题解: 设根节点的深度为0,将所有深度为奇数的节点的石子数目xor起来,则先手必胜当且仅当这个xor和不为0. 证明同阶梯博弈.对于偶深度的点上的石子,若对手移动它们,则可模仿操作:对于奇深度上的石子,移动一次即进入偶深度的点. 时空复杂度O(n). #include<bit…

Problem Description There are many secret openings in the floor which are covered by a big heavy stone. When the stone is lifted up, a special mechanism detects this and activates poisoned arrows that are shot near the opening. The only possibility i…

Alice and Bob are playing a stone game. Initially there are n piles of stones and each pile contains some stone. Alice stars the game and they alternate moves. In each move, a player has to select any pile and should remove at least one and no more t…

Lifting the Stone Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 230 Accepted Submission(s): 130   Problem Description There are many secret openings in the floor which are covered by a big heavy…