Triangle POJ - 2954 

题意：求一个三角形内包含多少个整数点

思路：求S，求on,in=(2S-on+2)/2;

#include<cstdio>
#include<vector>
#include<cmath>
#include<string>
#include<string.h>
#include<iostream>
#include<algorithm>
#define PI acos(-1.0)
#define pb push_back
#define F first
#define S second
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int N=3e5+5;
const int MOD=1e9+7;
template <class T>
bool sf(T &ret){ //Faster Input
    char c; int sgn; T bit=0.1;
    if(c=getchar(),c==EOF) return 0;
    while(c!='-'&&c!='.'&&(c<'0'||c>'9')) c=getchar();
    sgn=(c=='-')?-1:1;
    ret=(c=='-')?0:(c-'0');
    while(c=getchar(),c>='0'&&c<='9') ret=ret*10+(c-'0');
    if(c==' '||c=='\n'){ ret*=sgn; return 1; }
    while(c=getchar(),c>='0'&&c<='9') ret+=(c-'0')*bit,bit/=10;
    ret*=sgn;
    return 1;
}
struct Point{
    int x,y;
    Point(ll x=0, ll y=0) : x(x), y(y) {}
    Point operator - (const Point &rhs) const{
        return Point(x-rhs.x,y-rhs.y);
    }
}p[4];
typedef Point Vector;
ll cross(Vector A,Vector B){
    return A.x*B.y-A.y*B.x;
}

int main(void){
    while(1){
        int cnt=0;
        for(int i=1;i<=3;i++){
            sf(p[i].x),sf(p[i].y);
            if(p[i].x==0)   cnt++;
            if(p[i].y==0)   cnt++;
        }
        if(cnt==6)  break;
        ll ds=cross(p[1],p[2])+cross(p[2],p[3])+cross(p[3],p[1]);
//        ll ds=cross(p[1]-p[2],p[1]-p[3]);
        if(ds<0)    ds=-ds;
//        cout <<ds<<endl;
        ll on=1ll*abs(__gcd(p[1].x-p[2].x,p[1].y-p[2].y))+abs(__gcd(p[3].x-p[2].x,p[3].y-p[2].y))+
        abs(__gcd(p[3].x-p[1].x,p[3].y-p[1].y));
        ll in=1ll*(ds+2-on)/2;

        printf("%lld\n",in);
    }


    return 0;
}