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：
1 // #pragma comment(linker, "/STACK:102c000000,102c000000") 2 #include <iostream> 3 #include <cstdio> 4 #include <cstring> 5 #include <sstream> 6 #include <string> 7 #include <algorithm> 8 #include <list> 9 #include <map> 10 #include <vector> 11 #include <queue> 12 #include <stack> 13 #include <cmath> 14 #include <cstdlib> 15 // #include <conio.h> 16 using namespace std; 17 #define clc(a,b) memset(a,b,sizeof(a)) 18 #define inf 0x3f3f3f3f 19 #define lson l,mid,rt<<1 20 // #define rson mid+1,r,rt<<1|1 21 const int N = 1e5+10; 22 const int M = 1e6+10; 23 const int MOD = 1e9+7; 24 #define LL long long 25 #define LB long double 26 // #define mi() (l+r)>>1 27 double const pi = acos(-1); 28 const double eps = 1e-8; 29 void fre(){freopen("in.txt","r",stdin);} 30 inline int read(){int x=0,f=1;char ch=getchar();while(ch>'9'||ch<'0') {if(ch=='-') f=-1;ch=getchar();}while(ch>='0'&&ch<='9') { x=x*10+ch-'0';ch=getchar();}return x*f;} 31 32 int g[1010]; 33 bool vis[1010]; 34 int sg(int x){ 35 if(g[x] != -1) return g[x]; 36 if(x == 0) return 0; 37 if(x == 1) return 1; 38 if(x == 2) return 2; 39 if(x == 3) return 3; 40 clc(vis,0); 41 vis[0]=1; 42 for(int i = 1; i < x; i++){ 43 for(int j=1; i+j<x; j++){ 44 int t = 0; 45 int a = sg(i), b = sg(j),c=sg(x-i-j); 46 t ^= a; 47 t ^= b; 48 t^=c; 49 vis[a] = vis[b] =vis[c]=1; 50 vis[t] = 1; 51 } 52 vis[g[i]]=1; 53 } 54 for(int i = 0;; i++) if(!vis[i]) 55 return i; 56 } 57 int main(){ 58 int n; 59 clc(g,-1); 60 for(int i = 1; i <= 100; i++){ 61 g[i] = sg(i); 62 printf("%d %d\n", i, g[i]); 63 } 64 return 0; 65 }
代码：
1 // #pragma comment(linker, "/STACK:102c000000,102c000000") 2 #include <iostream> 3 #include <cstdio> 4 #include <cstring> 5 #include <sstream> 6 #include <string> 7 #include <algorithm> 8 #include <list> 9 #include <map> 10 #include <vector> 11 #include <queue> 12 #include <stack> 13 #include <cmath> 14 #include <cstdlib> 15 // #include <conio.h> 16 using namespace std; 17 #define clc(a,b) memset(a,b,sizeof(a)) 18 #define inf 0x3f3f3f3f 19 #define lson l,mid,rt<<1 20 // #define rson mid+1,r,rt<<1|1 21 const int N = 1e6+10; 22 const int M = 1e6+10; 23 const int MOD = 1e9+7; 24 #define LL long long 25 #define LB long double 26 // #define mi() (l+r)>>1 27 double const pi = acos(-1); 28 const double eps = 1e-8; 29 void fre(){freopen("in.txt","r",stdin);} 30 inline int read(){int x=0,f=1;char ch=getchar();while(ch>'9'||ch<'0') {if(ch=='-') f=-1;ch=getchar();}while(ch>='0'&&ch<='9') { x=x*10+ch-'0';ch=getchar();}return x*f;} 31 32 int sg(int x){ 33 if(x%8==0) return x-1; 34 if(x%8==7) return x+1; 35 return x; 36 } 37 int main(){ 38 int T,n; 39 scanf("%d",&T); 40 while(T--){ 41 int sum=0; 42 scanf("%d",&n); 43 for(int i=1;i<=n;i++){ 44 int x; 45 scanf("%d",&x); 46 sum^=sg(x); 47 } 48 printf("%s\n",sum?"First player wins.":"Second player wins."); 49 } 50 return 0; 51 }
