CGL_2_B——Intersection（线段几何---判断线段是否相交）

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本文介绍了一种用于判断两线段是否相交的算法，适用于计算机图形学和游戏开发中碰撞检测等场景。通过计算复数形式的点积和叉积，结合向量方向判断，实现线段相交性的高效检测。

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Intersection

For given two segments s1 and s2, print "1" if they are intersect, "0" otherwise.

s1 is formed by end points p0 and p1, and s2 is formed by end points p2 and p3.

Input

The entire input looks like:

q (the number of queries)
1st query
2nd query
...
qth query

Each query consists of integer coordinates of end points of s1 and s2 in the following format:

xp0 yp0 xp1 yp1 xp2 yp2 xp3 yp3

Output

For each query, print "1" or "0".

Constraints

1 ≤ q ≤ 1000
-10000 ≤ xpi, ypi ≤ 10000
p0≠p1 and p2≠p3.

Sample Input 1

3
0 0 3 0 1 1 2 -1
0 0 3 0 3 1 3 -1
0 0 3 0 3 -2 5 0

Sample Output 1

1
1
0

题目链接：http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B

#include<bits/stdc++.h>
using namespace std;
typedef complex<double> qua;
const double epx=1e-7;
int ccw(qua a,qua b,qua c)
{
    b-=a,c-=a,a=c*conj(b);
    if(a.imag()>epx) return 1;
    if(a.imag()<-epx) return -1;
    if(a.real()<-epx) return 2;
    if(abs(b)+epx<abs(c)) return -2;
    return 0;
}
int isintersect(qua a,qua b,qua c,qua d)
{
    return (ccw(a,b,c)*ccw(a,b,d)<=0)&&(ccw(c,d,a)*ccw(c,d,b)<=0);
}
int main()
{
    int t;
    for(scanf("%d",&t); t; --t)
    {
        double x1,x2,x3,x4,y1,y2,y3,y4;
        scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&x1,&y1,&x2,&y2,&x3,&y3,&x4,&y4);
        printf("%d\n",isintersect(qua(x1,y1),qua(x2,y2),qua(x3,y3),qua(x4,y4)));
    }
}