poj2954Triangle

传送门

Pick定理

定点坐标为整点的三角形，面积为S，边上的整点个数为L，三角形内部整点个数为N

S=N+L/2-1

 //Achen
 #include<algorithm>
 #include<iostream>
 #include<cstring>
 #include<cstdlib>
 #include<vector>
 #include<cstdio>
 #include<queue>
 #include<cmath>
 #include<set>
 #include<map>
 #define Formylove return 0
 #define For(i,a,b) for(int i=(a);i<=(b);i++)
 #define Rep(i,a,b) for(int i=(a);i>=(b);i--)
 typedef long long LL;
 typedef double db;
 using namespace std;
 LL x[],y[];

 template<typename T>void read(T &x)  {
     char ch=getchar(); x=; T f=;
     while(ch!='-'&&(ch<''||ch>'')) ch=getchar();
     if(ch=='-') f=-,ch=getchar();
     for(;ch>=''&&ch<='';ch=getchar()) x=x*+ch-''; x*=f;
 }

 db get_S(int x,int y,int xx,int yy) {
     return abs(x*yy-xx*y)/2.0;
 }

 LL gcd(LL a,LL b) { return !b?a:gcd(b,a%b); }

 db get_L(int x,int y,int xx,int yy) {
     if(xx-x==&&yy-y==) return ;
     if(xx-x==) return abs(yy-y)-;
     if(yy-y==) return abs(xx-x)-;
     return gcd(abs(x-xx),abs(y-yy))-;
 }

 int main() {
 #ifdef ANS
     freopen(".in","r",stdin);
     freopen(".out","w",stdout);
 #endif
     for(;;) {
         read(x[]); read(y[]);
         read(x[]); read(y[]);
         read(x[]); read(y[]);
         if(x[]==&&y[]==&&x[]==&&y[]==&&x[]==&&y[]==) break;
         db S=get_S(x[]-x[],y[]-y[],x[]-x[],y[]-y[]);
         db L=+get_L(x[],y[],x[],y[])+get_L(x[],y[],x[],y[])+get_L(x[],y[],x[],y[]);
         db n=S-L/2.0+;
         printf("%d\n",(int)n);
     }
     Formylove;
 }