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：

 

 1 #include<iostream>

 2 #include<stdio.h>

 3 #include<algorithm>

 4 #include<iomanip>

 5 #include<cmath>

 6 #define in(x) scanf("%d",&x)

 7 using namespace std;

 8 int main(){

 9     int  n,t,ans,k;

10     in(t);

11     while(t--){

12         in(n);

13         ans=0;

14         for(int i=0;i<n;i++){

15             in(k);

16             if(k%4==0) ans^=k-1;

17             else if(k%4==3) ans^=k+1;

18             else ans^=k;

19         }

20         puts(ans?"Alice":"Bob");

21     }

22     return 0;

23 }

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