计算几何初步——面积公式，GCD，PICK公式

这题主要用到PICK公式即：

area = I + E/2 - 1.（I为多边形内的格点数，E为边上的格点数，area为多边形面积）

用GCD可以算出一条边上的格点-1个，那么3×GCD即为3条边上的所有格点数（因为每个条边的顶点多算了一次）。。。

#include<iostream>
#include<cstdio>
using namespace std;

struct point {
    int x, y;    
};

int pick(int area, int num)
{
    return (area - num)/2 + 1;    
}

int cross(point &p, point &q)
{
    return q.y*p.x - p.y*q.x;    
}

int gcd(int x, int y)
{
    if (x == 0 || y == 0)return max(x,y);
    return gcd(y,x%y);
}

int main()
{
    point one, two, three;
    int x1, x2, x3, y1, y2, y3;
    while (scanf("%d%d%d%d%d%d",&x1,&y1,&x2,&y2,&x3,&y3) != EOF) {
        if (x1 == 0 && x2 == 0 && x3 == 0 && y1 == 0 && y2 == 0 && y3 == 0)break;
        one.x = x1;one.y = y1;
        two.x = x2;two.y = y2;
        three.x = x3;three.y = y3;
        int area = (cross(one,two) + cross(two,three) + cross(three,one));
        if (area < 0)area = -area;
        int num = gcd(abs(one.x - two.x),abs(one.y - two.y));
        num += gcd(abs(two.x - three.x),abs(two.y - three.y));
        num += gcd(abs(three.x - one.x),abs(three.y - one.y));
        cout<<pick(area,num)<<endl;        
    }
    return 0;    
}