poj 2826

vjudge链接：https://vjudge.net/problem/POJ-2826

题意很简单，天上下雨，用两根线段接水，问能接住多少面积的水。

看起来很简单，然后WA了5发。。。
首先判断两根线段是否相交，若不相交则显然不能接到水。
然后求交点p。分别求出两条线段的端点中较上面的端点p1, p2。然后以交点为新的原点，p1 -= p, p2 -= p。这样就映射到了以p为原点的坐标系中。问题转化为p1、原点、p2形成的碗能不能接到水。

注意雨是从天下下的，因此需要特判一下较高的线段会不会把较低的线段挡住。
y = min(p1.y, p2.y)，显然y>=0
如果y=0，那么显然不能接到水。
y>0时，安排p1和p2的顺序，使得p1.y <= p2.y。然后看一下p1.x和p2.x是否在同一侧，如果不在则一定不会挡住。如果都在左侧，则看一下p1O是不是在p2O左侧以及fabs(p1.x)是否小于等于fabs(p2.x)，若是，则说明p1被p2挡住了。右侧同理。
没有被挡住的情况就正常求了。不赘述。

赠送一波数据：
100
0 1 1 0
1 0 2 1

0 1 2 1
1 0 1 2

0 0 1 1
2 0 0 2

0 1 1 0
2 0 3 1

2 0 0 2
1 1 2 2

-10000 10000 0 -10000
0 -10000 10000 10000

0 0 3 3
0 2 2 0

0 3 3 0
1 0 3 2

0 3 3 0
1 1 3 0

0 0 2 1
0 0 3 3

0 0 3 3
0 0 3 3

0 2 2 0
0 1 2 0

0 0 2 1
0 0 2 2

0 0 3 3
0 0 1 2

>>
1.00
0.00
0.00
0.00
1.00
200000000.00
1.00
1.00
0.00
0.00
0.00
0.00
0.00
1.00

代码：

#include <cstdio>
#include <cmath>
#include <algorithm>

using namespace std;

#define MAXN 100011

template <typename T>
T sq(T x) {
    return x * x;
}

const double eps = 1e-8, pi = acos(-1.0);
int sgn(double x) {
    return x < -eps ? -1 : (x > eps ? 1 : 0);
}

struct VEC {
    double x, y;
    bool operator == (const VEC& b) const {
        return sgn(x - b.x) == 0 && sgn(y - b.y) == 0;
    }
    bool operator < (const VEC& b) const {
        return sgn(y - b.y) == 0 ? sgn(x - b.x) < 0 : y < b.y;
    }

    VEC operator - (const VEC& b) const {
        return VEC{x - b.x, y - b.y};
    }
    VEC operator + (const VEC& b) const {
        return VEC{x + b.x, y + b.y};
    }

    double len() const {
        return hypot(x, y);
    }
    double dist(const VEC& b) const {
        return (*this - b).len();
    }

    double len2() const {
        return sq(x) + sq(y);
    }
    double dist2(const VEC& b) const {
        return (*this - b).len2();
    }

    VEC operator * (double k) const {
        return VEC{x * k, y * k};
    }
    VEC trunc(double l) const {
        double ori = len();
        if (!sgn(ori)) return *this;
        return *this * (l / ori);
    }

    VEC operator / (double k) const {
        return VEC{x / k, y / k};
    }
    VEC norm() const {
        return *this / len();
    }

    double operator ^ (const VEC& b) const {
        return x * b.y - y * b.x;
    }
    double operator * (const VEC& b) const {
        return x * b.x + y * b.y;
    }
    // The angle between *this and b
    //anticlockwise is plus
    double rad_di(const VEC& b) const {
        return atan2(*this ^ b, *this * b);
    }
    double rad(const VEC& b) const {
        return fabs(rad_di(b));
        //return asin(fabs(*this ^ b) / (len() * b.len()));
    }

    VEC rotleft() const {
        return VEC{-y, x};
    }
    VEC rotright() const {
        return VEC{y, -x};
    }
    VEC rot(double a) const {
        double c = cos(a), s = sin(a);
        return VEC{x * c - y * s, x * s + y * c};
    }

    //Independent
    //0 <= slope < pi
    double slope() const {
        double ans = atan2(y, x);
        if (sgn(ans) < 0) ans += pi;
        else if (sgn(ans - pi) == 0) ans -= pi;
        return ans;
    }

    double cross(const VEC& p1, const VEC& p2) const {
        return (p1 - *this) ^ (p2 - *this);
    }

    //-1: left
    //0: parallel
    //1: right
    int relation(const VEC& b) const {
        return sgn(b ^ *this);
    }

    VEC operator - () const {
        return VEC{-x, -y};
    }
    bool SameDi(const VEC& b) const {
        return sgn(x) == sgn(b.x) && sgn(y) == sgn(b.y);
    }

    void input() {
        scanf("%lf%lf", &x, &y);
    }
};

struct LINE {
    VEC s, v;
    LINE() {}
    LINE(const VEC& _s, const VEC& _v) : s(_s), v(_v) {}
    void set(const VEC& _s, double a) {
        s = _s;
        v = {cos(a), sin(a)};
    }
    //ax + by + c = 0
    void set(double a, double b, double c) {
        v = {b, -a};
        s = fabs(a) > fabs(b) ? VEC{-c / a, 0} : VEC{0, -c / b};
    }

    //-1: left
    //0: on it
    //1: right
    int relation(const VEC& p) const {
        return sgn((p - s) ^ v);
    }
    //0: parallel
    //1: coincide
    //2: intersect
    int relation(const LINE& b) const {
        if (v.relation(b.v) == 0)
            return b.relation(s) == 0;
        return 2;
    }

    //Assume that they intersect
    VEC CrossPoint(const LINE& b) const {
        double t = ((b.s - s) ^ b.v) / (v ^ b.v);
        return s + v * t;
    }

    //left is plus
    double dist_di(const VEC& p) const {
        return (v ^ (p - s)) / v.len();
    }
    double dist(const VEC& p) const {
        return fabs(dist_di(p));
    }

    VEC projection(const VEC& p) const {
        VEC v1 = v.norm();
        return v1 * ((p - s) * v1) + s;
    }
    VEC symmetry(const VEC& p) const {
        VEC p0 = projection(p);
        return p0 * 2 - p;
    }

    void SetAngularBisector(const VEC& a, const VEC& b, const VEC& c) {
        set(a, (atan2(b.y - a.y, b.x - a.x) + atan2(c.y - a.y, c.x - a.x)) / 2);
    }
};

struct SEG : LINE {
    VEC e;
    SEG() {}
    SEG(const VEC& _s, const VEC& _e) : e(_e), LINE(_s, _e - _s) {}

    bool exclusive_between(const VEC& p) const {
        return sgn((p - s) * (p - e)) < 0;
    }

    bool between(const VEC& p) const {
        return sgn((p - s) * (p - e)) <= 0;
    }
    bool OnSeg(const VEC& p) const {
        return sgn((p - s) ^ v) == 0 && between(p);
    }
    //0: Not cross
    //1: Just cross (unnorm cross 非规范相交)
    //2: Cross inner (norm cross 规范相交)
    int relation(const SEG& b) const {
        int d1 = sgn(v ^ (b.s - s));
        int d2 = sgn(v ^ (b.e - s));
        int d3 = sgn(b.v ^ (s - b.s));
        int d4 = sgn(b.v ^ (e - b.s));
        if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 2;
        else return (d1 == 0 && between(b.s)) || (d2 == 0 && between(b.e)) ||
                    (d3 == 0 && b.between(s)) || (d4 == 0 && b.between(e));
    }
    int relation(const LINE& b) const {
        int d1 = sgn(b.v ^ (s - b.s));
        int d2 = sgn(b.v ^ (e - b.s));
        if ((d1 ^ d2) == -2) return 2;
        else return d1 == 0 || d2 == 0;
    }
    double dist(const VEC& p) const {
        if (sgn((p - s) * v) < 0 || sgn((p - e) * v) > 0)
            return min(p.dist(s), p.dist(e));
        return LINE::dist(p);
    }
    double dist(const SEG& b) const {
        return relation(b) ? 0 : min(min(dist(b.s), dist(b.e)), min(b.dist(s), b.dist(e)));
    }
};

double GetX(const VEC& v, double y) {
    return v.x / v.y * y;
}
int main() {
    int T;

    scanf("%d", &T);
    while (T--) {
        SEG a, b;
        a.s.input();
        a.e.input();
        a.v = a.e - a.s;
        b.s.input();
        b.e.input();
        b.v = b.e - b.s;
        bool fail = false;
        if (!a.relation(b)) {
            fail = true;
        } else {
            VEC p = a.CrossPoint(b);
            VEC p1 = a.s.y > a.e.y ? a.s : a.e;
            VEC p2 = b.s.y > b.e.y ? b.s : b.e;
            p1 = p1 - p;
            p2 = p2 - p;
            double y = min(p1.y, p2.y);
            if (sgn(y)) {
                if (p1.y > p2.y) {
                    swap(p1, p2);
                }
                int side = sgn(p1.x);
                if (0 == (side ^ sgn(p2.x)) && p2.relation(p1) == side && sgn(fabs(p1.x) - fabs(p2.x)) <= 0) {
                    fail = true;
                }
                if (!fail) {
                    double x1 = GetX(p1, y), x2 = GetX(p2, y);
                    if (x1 > x2) swap(x1, x2);
                    printf("%.2f\n", (x2 - x1) * y / 2 + eps);
                }
            } else {
                fail = true;
            }
        }
        if (fail) {
            puts("0.00");
        }
    }

    return 0;
}