poj 2315 Football Game nimk 博弈

Football Game

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 332 Accepted: 118

Description

Alice and Bob both love football very much, and both of them are vanguards. They are both good at football control. One day after a football match, they play an interesting game, in which they shoot footballs forward the goal directly. There are N footballs in front of the goal, and they play this game in turn. For example, if it is Alice's turn, Alice can choice some footballs (the number of footballs mush equal or less than M) and shoot them forward. Because the footballs' quality is not very good, footballs are not a complete sphere and can only roll integer times of its girth. And because of restriction of the friction and strength of them, they cannot shoot a football farther then L centimeters. Of course, they know the radius of a football is R centimeters. Alice and Bob love this game very much. If both of them have unlimited IQ and precision shooting skill, can you guess who can win the football game? By the way, though Alice is as strong as Bob, Alice is a girl, so she will shoot first.

Input

The input consists of several cases, each of which contains two lines. 

For each test case, the first line contains 4 integers N, M, L and R (1 <= M <= N <= 30, 0 < L < 100000000, 0 < R < 10000), separated by a single space. N is the number of the footballs, M is the maximum number of footballs one player can shot in one turn, L is the maximum distance that a player can shoot, and R is the radius of footballs. 

The next line contains N numbers, S(1), S(2), ..., S(N) (0 < S(i) < 100000000), which describe the distance between footballs and the goal.

Output

For each case output contains one line describing the name of the winner.

Sample Input

2 1 30 18 142 1 30 18 122 1 30 18 102 1 30 140 200

Sample Output

AliceBobBobBob

题意：给你 n 个球 某个人最多一次踢球的个数 能踢的最远的距离 l 和半径r  

接下来一行是n个球  距离球门的距离。 

两个人轮流踢  知道有一个人把最后一个球踢进去为赢  。

注意 踢的最远距离为l  但是不一定踢l  每一踢球必须为周长的整数倍并且小等于l

思路：  其实转换一下就可以发现  是一种nim 博弈 问题  对于每一个球距离球门

的距离我们可以转换成至少要踢多少下才可以踢到 球门里边 而能踢的最长距离为l

也可以转换成 最多 踢几次 那么就转化成了 一种 nim  游戏

给你n堆石子 每堆有x个 每一次可以从m 堆中取出 k 个  （每一堆都可以取出k个）

最后取完的为胜者。  问谁胜。

nimk  博弈 ： nimk  博弈的博客

代码：

#include<stdio.h>#include<string.h>#include<math.h>#include<iostream>#include<algorithm>#define PI acos(-1)#define N 35using namespace std;int s[N];int xorr[205];int n,m,l,r;double dis;int k;int solve(){memset(xorr,0,sizeof(xorr));int maxcnt=-1;for(int i=1;i<=n;i++){int num=s[i];int cnt=0;for(int j=0;num;j++,num>>=1){xorr[j]+=num&1;cnt++;maxcnt=max(cnt,maxcnt);}}for(int i=0;i<maxcnt;i++){if(xorr[i]%(m+1)) return 1;}return 0;}int main(){while(cin>>n>>m>>l>>r){for(int i=1;i<=n;i++) cin>>s[i];dis=2*PI*r;k=floor(l*1.0/dis)+1;for(int i=1;i<=n;i++){s[i]=floor(s[i]*1.0/dis);s[i]++;s[i]%=k;}int f=solve();if(f) printf("Alice\n");else printf("Bob\n");}return 0;}