Triangle POJ

Triangle

 POJ - 2954

题意：给你一个三角形三个点的坐标，问你三角形内部有多少点

思路：先利用多边形面积公式求出三角形面积，再gcd(detax,detay)之和求出边上有多少点，最后利用皮克定理求出内部有多少点，s=in+1+on/2;

// 
// Created by HJYL on 2020/2/4.
//
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cstring>
#include<math.h>
#include<algorithm>
using namespace std;
const double eps=1e-8;
const int maxn=1e6+5;
int gcd(int a,int b) {
    while (b) {
        int r = b;
        b = a % b;
        a = r;
    }
    return a;
}
struct Point{
    int x,y;
    Point(int x=0,int y=0):x(x),y(y){}
    Point operator - (Point const &b)const
    {
        return Point(x-b.x ,y-b.y);
    }
    bool operator < (Point const &c)const{
        if(x==c.x)
            return y<c.y;
        return x<c.x;
    }
};
double Cross(Point A,Point B)
{
    return (A.x*B.y)-(A.y*B.x);
}
long long PolygonArea(Point* p, int n) {//p为端点集合，n为端点个数
    long long s = 0;
    for (int i = 1; i < n - 1; ++i)
        s += Cross(p[i] - p[0], p[i + 1] - p[0]);
    return s<0?-s:s;
}
int main()
{
    Point p[3];
    while(~scanf("%d%d%d%d%d%d",&p[0].x,&p[0].y,&p[1].x,&p[1].y,&p[2].x,&p[2].y))
    {
        if(p[0].x==0&&p[1].x==0&&p[2].x==0&&p[0].y==0&&p[1].y==0&&p[2].y==0)
            break;
        long long s=PolygonArea(p,3);//s=on/2+in-1
        int on=0;
        for(int i=1;i<3;i++)
        {
            on+=gcd(abs(p[i].x-p[i-1].x),abs(p[i].y-p[i-1].y));
        }
        on+=gcd(abs(p[2].x-p[0].x),abs(p[2].y-p[0].y));
        int in=(s+2-on)/2;
        printf("%d
",in);

    }
    return 0;
}