hdu2108和hdu2036 叉乘的运用

题目地址：

http://acm.hdu.edu.cn/showproblem.php?pid=2108

http://acm.hdu.edu.cn/showproblem.php?pid=2036

这两道题目分别是判断一个多边形是否是凸多边形，求一个多边形的面积

题意很简单，题目也不难，算是最基础的计算几何了

参考资料：计算几何基础

参考代码：

hdu2108 by ACShiryu

#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
struct ac {
    int x ;
    int y ;
}po[555555];
int cross(ac a , ac b ,ac c)
{
    return (b.x-a.x)*(c.y-b.y)-(b.y-a.y)*(c.x-b.x);
}
bool convex(int n)
{
    for(int i = 0 ; i < n ; i ++)
        if(cross(po[i],po[(i+1)%n],po[(i+2)%n])<0)
            return false;
    return true;
}
int main()
{
    int n ;
    while (cin >> n , n)
    {
        for (int i=0;i < n ; i ++ )
            cin >> po[i].x >> po[i].y;
        if (convex(n))
            cout<<"convex"<<endl;
        else
            cout<<"concave"<<endl;
    }
    return 0;
}

　　hdu2036 by ACShiryu

#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
struct ac {
    int x ;
    int y ;
}po[100];
int cross (ac a , ac b)
{
    return a.x*b.y-a.y*b.x;
}
int main()
{
    int n ;
    while ( scanf("%d",&n) , n)
    {
        int i ;
        for ( i = 0 ; i < n ; i ++ )
        {
            scanf("%d%d",&po[i].x,&po[i].y);
        }
        double sum = 0 ;
        for ( i = 0 ; i < n ; i ++ )
            sum += cross(po[i],po[(i+1)%n])/2.0;
        printf("%.1lf\n",sum);
    }
    return 0;
}