poj 1265 计算几何

题意：多边形的顶点坐标为整数，问多边形内部的整点数，边上的整点数，面积。

分析：向量(0,0)->(x,y)上的整点数为gcd(x, y)，

pick定理：面积 = 内部整点数 + 边上整点数/2 - 1.

 

 

const int M = 105;
int m, in, on;
double s;
int x[M], y[M];

int gcd(int i, int j){
    int t;
    for( ; i; t=i, i=j%i, j=t){}
    return abs(j);
}

double S(int x1, int y1, int x2, int y2){
    return (x1*y2 - x2*y1)/2.0;
}

int main(){
    #ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
    #endif

    int T; scanf("%d", &T);
    FOE(t, 1, T){
        in = on = 0; s = 0.0;
        scanf("%d", &m);
        FOE(i, 1, m) {
            scanf("%d%d", &x[i], &y[i]);
            on += gcd(x[i], y[i]);

            x[i] += x[i-1];
            y[i] += y[i-1];

            if(i>1 && i<m)
                s += S(x[i], y[i], x[i-1], y[i-1]);
        }

        if(s<0) s = -s;
        in = s+1-on/2;

        cout<<"Scenario #"<<t<<":"<<endl;
        cout<<in<<' '<<on<<' '<<fixed<<setprecision(1)<<s<<endl<<endl;
    }

    return 0;
}