简单几何(线段相交) POJ 2826 An Easy Problem?!

 

题目传送门

题意：两条线段看成两块木板，雨水从上方往下垂直落下，问能接受到的水的体积

分析：恶心的分类讨论题，考虑各种情况，尤其是入口被堵住的情况，我的方法是先判断最高的两个点是否在交点的同一侧，然后看看是否高的点覆盖了低的点，用叉积判断方向，其他的情况见网上的解释。貌似没有什么卡精度的数据。最后膜拜楼教主，难以望其项背。。。

 

/************************************************
* Author        :Running_Time
* Created Time  :2015/10/30 星期五 18:36:27
* File Name     :POJ_2826.cpp
 ************************************************/

#include <cstdio>
#include <algorithm>
#include <iostream>
#include <sstream>
#include <cstring>
#include <cmath>
#include <string>
#include <vector>
#include <queue>
#include <deque>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <bitset>
#include <cstdlib>
#include <ctime>
using namespace std;

#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
typedef long long ll;
const int N = 1e5 + 10;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
const double EPS = 1e-10;
const double PI = acos (-1.0);
int dcmp(double x)  {
    if (fabs (x) < EPS) return 0;
    else    return x < 0 ? -1 : 1;
}
struct  Point   {
    double x, y;
    Point () {}
    Point (double x, double y) : x (x), y (y) {}
    Point operator + (const Point &r) const {
        return Point (x + r.x, y + r.y);
    }
    Point operator - (const Point &r) const {
        return Point (x - r.x, y - r.y);
    }
    Point operator * (double p) const {
        return Point (x * p, y * p);
    }
    Point operator / (double p) const {
        return Point (x / p, y / p);
    }
    bool operator < (const Point &r) const {
        return x < r.x || (!dcmp (x - r.x) && y < r.y);
    }
    bool operator == (const Point &r) const {
        return dcmp (x - r.x) == 0 && dcmp (y - r.y) == 0;
    }
};
typedef Point Vector;
Point read_point(void)  {
    double x, y;
    scanf ("%lf%lf", &x, &y);
    return Point (x, y);
}
double dot(Vector A, Vector B)  {
    return A.x * B.x + A.y * B.y;
}
double cross(Vector A, Vector B)    {
    return A.x * B.y - A.y * B.x;
}
Point line_line_inter(Point p, Vector V, Point q, Vector W) {
    Vector U = p - q;
    double t = cross (W, U) / cross (V, W);
    return p + V * t;
}
bool can_inter(Point a1, Point a2, Point b1, Point b2)  {
    double c1 = cross (a2 - a1, b1 - a1), c2 = cross (a2 - a1, b2 - a1),
           c3 = cross (b2 - b1, a1 - b1), c4 = cross (b2 - b1, a2 - b1);
    return dcmp (c1) * dcmp (c2) <= 0 && dcmp (c3 * c4) <= 0;
}
double area_triangle(Point a, Point b, Point c) {
    return fabs (cross (b - a, c - a)) / 2.0;
}

int main(void)    {
    int T;  scanf ("%d", &T);
    Point a1, a2, b1, b2;
    while (T--) {
        a1 = read_point ();
        a2 = read_point ();
        b1 = read_point ();
        b2 = read_point ();     //a1，b1是纵坐标较高的点
        if (dcmp (a1.y - a2.y) < 0 || (dcmp (a1.y - a2.y) == 0 && dcmp (a1.x - a2.x) > 0))    swap (a1, a2);
        if (dcmp (b1.y - b2.y) < 0 || (dcmp (b1.y - b2.y) == 0 && dcmp (b1.x - b2.x) > 0))    swap (b1, b2);
        if (dcmp (a1.x - a2.x) == 0 && dcmp (b1.x - b2.x) == 0)  {      //竖直平行
            puts ("0.00");  continue;
        }
        if (dcmp (a1.y - a2.y) == 0 || dcmp (b1.y - b2.y) == 0)  {      //水平平行
            puts ("0.00");  continue;
        }
        if (dcmp (cross (a1 - a2, b1 - b2)) == 0)   {                   //共线
            puts ("0.00");  continue;
        }
        if (!can_inter (a1, a2, b1, b2))    {                           //不能相交
            puts ("0.00");  continue;
        }
        Point p = line_line_inter (a1, a2 - a1, b1, b2 - b1), q;
        if (dcmp (a1.y - p.y) <= 0 || dcmp (b1.y - p.y) <= 0)   {       //有一个点纵坐标低于交点
            puts ("0.00");  continue;
        }
        double ans = 0.0;
        if (dcmp (a1.y - b1.y) == 0)    {
            ans = area_triangle (a1, b1, p);
        }
        else if (dcmp (a1.y - b1.y) < 0)   {
            if (dcmp (a1.x - p.x) > 0 && dcmp (b1.x - p.x) > 0)   {
                if (dcmp (b1.x - a1.x) >= 0 && cross (a1 - p, b1 - p) >= 0)    {    //入口被覆盖，以下同
                    puts ("0.00");  continue;
                }
            }
            else if (dcmp (a1.x - p.x) < 0 && dcmp (b1.x - p.x) < 0)  {
                if (dcmp (b1.x - a1.x) <= 0 && cross (b1 - p, a1 - p) >= 0)    {
                    puts ("0.00");  continue;
                }
            }
            q = line_line_inter (a1, Vector (1, 0), b1, b2 - b1);
            ans = area_triangle (a1, q, p);
        }
        else    {
            if (dcmp (a1.x - p.x) > 0 && dcmp (b1.x - p.x) > 0)   {
                if (dcmp (a1.x - b1.x) >= 0 && cross (b1 - p, a1 - p) >= 0)    {
                    puts ("0.00");  continue;
                }
            }
            else if (dcmp (a1.x - p.x) < 0 && dcmp (b1.x - p.x) < 0)  {
                if (dcmp (a1.x - b1.x) <= 0 && cross (a1 - p, b1 - p) >= 0)    {
                    puts ("0.00");  continue;
                }
            }
            q = line_line_inter (a1, a2 - a1, b1, Vector (1, 0));
            ans = area_triangle (b1, q, p);
        }
        double eps = 1e-8;
        printf ("%.2f\n", ans + eps);
    }

   //cout << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";

    return 0;
}