【HDOJ】1086 You can Solve a Geometry Problem too

数学题，证明AB和CD。只需证明C、D在AB直线两侧，并且A、B在CD直线两侧。
公式为：（ABxAC）*（ABxAD）<= 0 and（CDxCA）*（CDxCB）<= 0

#include <stdio.h>

#define MAXNUM 105

typedef struct {
    double x1,  y1;
    double x2,  y2;
} line_st;

line_st lines[MAXNUM];

int cal(int i, int j) {
    double ab_x, ab_y, ac_x, ac_y, ad_x, ad_y;
    double a, b;

    ab_x = lines[i].x2 - lines[i].x1;
    ab_y = lines[i].y2 - lines[i].y1;
    ac_x = lines[j].x1 - lines[i].x1;
    ac_y = lines[j].y1 - lines[i].y1;
    ad_x = lines[j].x2 - lines[i].x1;
    ad_y = lines[j].y2 - lines[i].y1;
    a = ab_x*ac_y - ab_y*ac_x;
    b = ab_x*ad_y - ab_y*ad_x;
    if (a*b <= 0)
        return 1;
    else
        return 0;
}

int main() {
    int n;
    int i, j, k;

    while (scanf("%d", &n)!=EOF && n) {
        for (i=0; i<n; ++i)
            scanf("%lf%lf%lf%lf", &lines[i].x1,&lines[i].y1,&lines[i].x2,&lines[i].y2);
        k = 0;
        for (i=0; i<n; ++i)
            for (j=0; j<i; ++j)
                if (cal(i, j) && cal(j, i))
                    k++;
        printf("%d
", k);
    }

    return 0;
}