hdu 3032 Nim or not Nim? 博弈论

 这题是Lasker’s Nim.

Clearly the Sprague-Grundy function for the one-pile game satisfies g(0) = 0 and g(1) = 1. The followers of 2 are 0, 1 and (1,1), with respective Sprague-Grundy values of 0, 1, and 1⊕1 = 0. Hence, g(2) = 2. The followers of 3 are 0, 1, 2, and (1,2), with Sprague-Grundy values 0, 1, 2, and 1⊕2 = 3. Hence, g(3) = 4.

Continuing in this manner, we see

x 0 1 2 3 4 5 6 7 8 9 10 11 12...

g(x) 0 1 2 4 3 5 6 8 7 9 10 12 11...

We therefore conjecture that g(4k + 1) = 4k + 1,g(4k + 2) = 4k + 2,g(4k + 3) = 4k +4 and g(4k + 4) = 4k + 3, for all k ≥ 0.

代码如下：

#include<iostream>
#include<stdio.h>
#include<algorithm>
#include<iomanip>
#include<cmath>
#define in(x) scanf("%d",&x)
using namespace std;
int main(){
    int  n,t,ans,k;
    in(t);
    while(t--){
        in(n);
        ans=0;
        for(int i=0;i<n;i++){
            in(k);
            if(k%4==0) ans^=k-1;
            else if(k%4==3) ans^=k+1;
            else ans^=k;
        }
        puts(ans?"Alice":"Bob");
    }
    return 0;
}