POJ 3348 Cows 凸包 + 多边形面积公式

一定要注意 总的点数 n<= 2 时 graham不适用。

还要注意 graham找到凸包后 注意 top <=2 时面积为0。

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
using namespace std;

struct point
{
    double x, y;

}p[10003];

double det(double x1, double y1, double x2, double y2)
{
    return x1 * y2 - x2 * y1;
}

double cross(point o, point a, point b)
{
     return det(a.x - o.x, a.y - o.y, b.x - o.x, b.y - o.y);
}

bool cmp(point a, point b)
{
    if(a.y == b.y) return a.x < b.x;
    return a.y < b.y;
}

int n;
int top;
point res[10003<<1];

void graham()
{
    sort(p, p + n, cmp);
    int i;
    top = -1;
    if(n <= 2 ) return;
    res[++top] = p[0];
    res[++top] = p[1];
    for(i = 2; i < n; i++)
    {
        while(top >= 1 && cross(res[top-1], res[top], p[i]) <= 0 )
            top--;
        res[++top] = p[i];
    }
    res[++top] = p[n-2];
    int t = top;
    for(i = n - 3; i >= 0; i--)
    {
        while(top >= t && cross(res[top-1], res[top], p[i]) <= 0)
            top--;
        res[++top] = p[i];
    }
}

double cal_area(int n, point* p){
    double s = 0;
    int i;
    p[n] = p[0];
    for (i = 0; i < n; i++)
        s += p[i].x * p[i+1].y - p[i].y * p[i+1].x;
    return fabs(s)/2;
}

int main()
{
    int i, j;
    while( ~scanf("%d", &n) )
    {
        for(i = 0; i < n; i++)
            scanf("%lf%lf", &p[i].x, &p[i].y);
        graham();
        if(top <= 2) { printf("0\n"); continue; }
        double ans = cal_area(top, res);
        printf("%d\n", (int) (ans/50));
    }
    return 0;
}