poj2954

Pick公式：平面上以格子点为顶点的简单多边形，如果边上的点数为on，内部的点数为in，则它的面积为area=on/2+in-1
利用gcd求每个边上的点数。

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

struct Point
{
    int x, y;
}point[3];

void input()
{
    for (int i = 0; i < 3; i++)
        scanf("%d%d", &point[i].x, &point[i].y);
    int ret = 0;
    for (int i = 0; i < 3; i++)
        ret |= point[i].x | point[i].y;
    if (!ret)
        exit(0);
}

int xmult(Point a, Point b, Point c)
{
    return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y);
}

int gcd(int x, int y)
{
    if (!x || !y)
        return x > y ? x : y;
    for (int t; t = x % y; x = y, y = t);
    return y;
}

void work()
{
    int area = abs(xmult(point[0], point[1], point[2]));
    int on = 0;
    for (int i = 0; i < 3; i++)
        on += gcd(abs(point[i % 3].x - point[(i + 1)%3].x), abs(point[i % 3].y - point[(i + 1)%3].y));
    int in = (area - on) / 2 + 1;
    printf("%d\n", in);
}

int main()
{
    //freopen("t.txt", "r", stdin);
    while (1)
    {
        input();
        work();
    }
    return 0;
}