简单几何(直线求交点) POJ 2074 Line of Sight

 

题目传送门

题意：从一条马路(线段)看对面的房子(线段)，问连续的能看到房子全部的最长区间

分析：自己的思路WA了：先对障碍物根据坐标排序，然后在相邻的障碍物的间隔找到区间，这样还要判断是否被其他障碍物遮挡住(哇

　　　　网上有很好的思路，先对每条线段找到阴影的端点，然后根据坐标排序，求和左端点的距离的最大值，这样省去线段相交的判断。

　　　　trick点应该就是障碍物的位置随意，可能在房子和马路的外面。

 

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/************************************************ * Author        :Running_Time * Created Time  :2015/11/2 星期一 20:33:38 * File Name     :POJ_2074.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)  {       //三态函数，减少精度问题     if (fabs (x) < EPS) return 0;     else    return x < 0 ? -1 : 1; } struct Point    {       //点的定义     double x, y;     Point () {}     Point (double x, double y) : x (x), y (y) {}     Point operator + (const Point &r) const {       //向量加法         return Point (x + r.x, y + r.y);     }     Point operator - (const Point &r) const {       //向量减法         return Point (x - r.x, y - r.y);     }     Point operator * (double p) const {       //向量乘以标量         return Point (x * p, y * p);     }     Point operator / (double p) const {       //向量除以标量         return Point (x / p, y / p);     }     bool operator < (const Point &r) const {       //点的坐标排序         return x < r.x || (x == r.x && y < r.y);     }     bool operator == (const Point &r) const {       //判断同一个点         return dcmp (x - r.x) == 0 && dcmp (y - r.y) == 0;     } }; typedef Point Vector;       //向量的定义 Point read_point(void)   {      //点的读入     double x, y;     scanf ("%lf%lf", &x, &y);     return Point (x, y); } double dot(Vector A, Vector B)  {       //向量点积     return A.x * B.x + A.y * B.y; } double cross(Vector A, Vector B)    {       //向量叉积     return A.x * B.y - A.y * B.x; } double polar_angle(Vector A)  {     //向量极角     return atan2 (A.y, A.x); } double length(Vector A) {       //向量长度，点积     return sqrt (dot (A, A)); } double angle(Vector A, Vector B)    {       //向量转角，逆时针，点积     return acos (dot (A, B) / length (A) / length (B)); } Vector rotate(Vector A, double rad) {       //向量旋转，逆时针     return Vector (A.x * cos (rad) - A.y * sin (rad), A.x * sin (rad) + A.y * cos (rad)); } Vector nomal(Vector A)  {       //向量的单位法向量     double len = length (A);     return Vector (-A.y / len, A.x / len); } Point line_line_inter(Point p, Vector V, Point q, Vector W)    {        //两直线交点，参数方程     Vector U = p - q;     double t = cross (W, U) / cross (V, W);     return p + V * t; } double point_to_line(Point p, Point a, Point b)   {       //点到直线的距离，两点式     Vector V1 = b - a, V2 = p - a;     return fabs (cross (V1, V2)) / length (V1); } double point_to_seg(Point p, Point a, Point b)    {       //点到线段的距离，两点式     if (a == b) return length (p - a);     Vector V1 = b - a, V2 = p - a, V3 = p - b;     if (dcmp (dot (V1, V2)) < 0)    return length (V2);     else if (dcmp (dot (V1, V3)) > 0)   return length (V3);     else    return fabs (cross (V1, V2)) / length (V1); } Point point_line_proj(Point p, Point a, Point b)   {     //点在直线上的投影，两点式     Vector V = b - a;     return a + V * (dot (V, p - a) / dot (V, V)); } bool can_seg_seg_inter(Point a1, Point a2, Point b1, Point b2)  {       //判断线段相交，两点式     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) * dcmp (c4) < 0; } bool can_line_seg_inter(Point a1, Point a2, Point b1, Point b2)    {        //判断直线与线段相交，两点式     double c1 = cross (a2 - a1, b1 - a1), c2 = cross (a2 - a1, b2 - a1);     return dcmp (c1 * c2) <= 0; } bool on_seg(Point p, Point a1, Point a2)    {       //判断点在线段上，两点式     return dcmp (cross (a1 - p, a2 - p)) == 0 && dcmp (dot (a1 - p, a2 - p)) < 0; }   struct Line2 {     double x1, x2;     Line2 () {}     Line2 (double x1, double x2) : x1 (x1), x2 (x2)  {}     bool operator < (const Line2 &r) const   {         return x1 < r.x1;     } };   struct Line    {     Point a, b;     Line () {}     Line (Point a, Point b) : a (a), b (b) {} };   int main(void)    {     Line h, p;     double x1, x2, y;     while (scanf ("%lf%lf%lf", &x1, &x2, &y) == 3) {         if (dcmp (x1) == 0 && dcmp (x2) == 0 && dcmp (y) == 0)    break;         h.a = Point (x1, y);    h.b = Point (x2, y);         scanf ("%lf%lf%lf", &x1, &x2, &y);         p.a = Point (x1, y);    p.b = Point (x2, y);         int n;  scanf ("%d", &n);         vector<Line2> xs;         for (int i=0; i<n; ++i) {             scanf ("%lf%lf%lf", &x1, &x2, &y);             if (dcmp (y - h.a.y) >= 0 || dcmp (y - p.a.y) <= 0) continue;             Point p1 = Point (x1, y), p2 = Point (x2, y);             x1 = line_line_inter (h.b, h.b - p1, p.b, p.b - p.a).x;             x2 = line_line_inter (h.a, h.a - p2, p.b, p.b - p.a).x;             if (dcmp (x1 - x2) >= 0)    continue;             xs.push_back (Line2 (x1, x2));         }         xs.push_back (Line2 (p.b.x, p.b.x));         sort (xs.begin (), xs.end ());         double left = p.a.x, ans = 0;         for (int i=0; i<xs.size (); ++i)    {             x1 = xs[i].x1;  x2 = xs[i].x2;             if (x1 - left > ans)   ans = x1 - left;             if (dcmp (x2 - left) > 0)   {                 left = x2;                 if (dcmp (left - p.b.x) > 0)   break;             }         }         if (dcmp (ans) == 0)    puts ("No View");         else    printf ("%.2f\n", ans);     }          //cout << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";       return 0; }