Electric Fence（皮克定理）

In this problem, `lattice points' in the plane are points with integer coordinates.

In order to contain his cows, Farmer John constructs a triangular electric fence by stringing a "hot" wire from the origin (0,0) to a lattice point [n,m] (0<=;n<32,000, 0<m<32,000), then to a lattice point on the positive x axis [p,0] (0<p<32,000), and then back to the origin (0,0).

A cow can be placed at each lattice point within the fence without touching the fence (very thin cows). Cows can not be placed on lattice points that the fence touches. How many cows can a given fence hold?

翻译 ：（0,0）（m,n）,(p,0) 形成的三角形内的点有几个？

皮克定理：一个计算点阵中顶点在格点上的多边形面积公式，该公式可以表示为2S=2a+b-2。

其中a表示多边形内部的点数，b表示多边形边界上的点数，S表示多边形的面积。

线段的两个顶点：（x1，y1） ( x2 , y2 );

另一问题：一条线段上的点有几个？gcd(|x1-x2|,|y1-y2|)+1;

 

#include<iostream>
#include<cmath>
using namespace std;
int gcd(int a,int b)
{
    return b==0?a:gcd(b,a%b);
}
int main()
{
    int n,m,p;
    cin>>n>>m>>p;
    double s,b;
    s=0.5*m*p;
    b=p+gcd(m,n)+gcd(fabs(n-p),m);
    printf("%d
",(int)(s+1-b/2));
}