多校6 1003 HDU5795 A Simple Nim (sg函数)

思路：直接打表找sg函数的值，找规律，没有什么技巧

还想了很久的，把数当二进制看，再类讨二进制中1的个数是必胜或者必败状态。。。。

打表：

 // #pragma comment(linker, "/STACK:102c000000,102c000000")
 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <sstream>
 #include <string>
 #include <algorithm>
 #include <list>
 #include <map>
 #include <vector>
 #include <queue>
 #include <stack>
 #include <cmath>
 #include <cstdlib>
 // #include <conio.h>
 using namespace std;
 #define clc(a,b) memset(a,b,sizeof(a))
 #define inf 0x3f3f3f3f
 #define lson l,mid,rt<<1
 // #define rson mid+1,r,rt<<1|1
 const int N = 1e5+;
 const int M = 1e6+;
 const int MOD = 1e9+;
 #define LL long long
 #define LB long double
 // #define mi() (l+r)>>1
 double const pi = acos(-);
 const double eps = 1e-;
 void fre(){freopen("in.txt","r",stdin);}
 inline int read(){int x=,f=;char ch=getchar();while(ch>''||ch<'') {if(ch=='-') f=-;ch=getchar();}while(ch>=''&&ch<='') { x=x*+ch-'';ch=getchar();}return x*f;}

 int g[];
 bool vis[];
 int sg(int x){
     if(g[x] != -) return g[x];
     if(x == ) return ;
     if(x == ) return ;
     if(x == ) return ;
     if(x == ) return ;
     clc(vis,);
     vis[]=;
     for(int i = ; i < x; i++){
         for(int j=; i+j<x; j++){
             int t = ;
             int a = sg(i), b = sg(j),c=sg(x-i-j);
             t ^= a;
             t ^= b;
             t^=c;
             vis[a] = vis[b] =vis[c]=;
             vis[t] = ;
         }
         vis[g[i]]=;
     }
     for(int i = ;; i++) if(!vis[i])
             return i;
 }
 int main(){
     int n;
     clc(g,-);
     for(int i = ; i <= ; i++){
         g[i] = sg(i);
         printf("%d %d\n", i, g[i]);
     }
     return ;
 }

代码：

 // #pragma comment(linker, "/STACK:102c000000,102c000000")
 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <sstream>
 #include <string>
 #include <algorithm>
 #include <list>
 #include <map>
 #include <vector>
 #include <queue>
 #include <stack>
 #include <cmath>
 #include <cstdlib>
 // #include <conio.h>
 using namespace std;
 #define clc(a,b) memset(a,b,sizeof(a))
 #define inf 0x3f3f3f3f
 #define lson l,mid,rt<<1
 // #define rson mid+1,r,rt<<1|1
 const int N = 1e6+;
 const int M = 1e6+;
 const int MOD = 1e9+;
 #define LL long long
 #define LB long double
 // #define mi() (l+r)>>1
 double const pi = acos(-);
 const double eps = 1e-;
 void fre(){freopen("in.txt","r",stdin);}
 inline int read(){int x=,f=;char ch=getchar();while(ch>''||ch<'') {if(ch=='-') f=-;ch=getchar();}while(ch>=''&&ch<='') { x=x*+ch-'';ch=getchar();}return x*f;}

 int sg(int x){
     if(x%==) return x-;
     if(x%==) return x+;
     return x;
 }
 int main(){
     int T,n;
     scanf("%d",&T);
     while(T--){
         int sum=;
         scanf("%d",&n);
         for(int i=;i<=n;i++){
             int x;
             scanf("%d",&x);
             sum^=sg(x);
         }
         printf("%s\n",sum?"First player wins.":"Second player wins.");
     }
     return ;
 }