简单几何(线段相交)+模拟 POJ 3449 Geometric Shapes

 

题目传送门

题意：给了若干个图形，问每个图形与哪些图形相交

分析：题目说白了就是处理出每个图形的线段，然后判断是否相交。但是读入输出巨恶心，就是个模拟题加上线段相交的判断，我第一次WA不知道输出要按字母序输出，第二次WA是因为忘记多边形的最后一条线段，还好找到了，没有坚持的话就不会AC了。

 

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/************************************************ * Author        :Running_Time * Created Time  :2015/10/31 星期六 13:38:11 * File Name     :POJ_3449.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; } double area_triangle(Point a, Point b, Point c) {       //三角形面积，叉积     return fabs (cross (b - a, c - a)) / 2.0; } double area_poly(Point *p, int n)   {       //多边形面积，叉积     double ret = 0;     for (int i=1; i<n-1; ++i)   {         ret += fabs (cross (p[i] - p[0], p[i+1] - p[0]));     }     return ret / 2; } struct Seg  {     Point a, b;     Seg ()  {}     Seg (Point a, Point b) : a (a), b (b)   {} }; struct  Pic {     char ch;     int cnt;     vector<Seg> seg;     vector<int> ans;     bool operator < (const Pic &r) const    {         return ch < r.ch;     } }p[33], pp[33];   bool cmp(int i, int j)  {     return p[i].ch < p[j].ch; }   void run(int tot)  {     for (int i=0; i<tot; ++i)   {         p[i].cnt = 0;         for (int j=0; j<tot; ++j)   {             if (i == j) continue;             int sz1 = p[i].seg.size (), sz2 = p[j].seg.size ();             bool flag = false;             for (int ii=0; ii<sz1; ++ii)   {                 for (int jj=0; jj<sz2; ++jj)   {                     if (can_seg_seg_inter (p[i].seg[ii].a, p[i].seg[ii].b, p[j].seg[jj].a, p[j].seg[jj].b)) {                         flag = true;    p[i].cnt++; p[i].ans.push_back (j);                         break;                     }                 }                 if (flag)   break;             }         }         sort (p[i].ans.begin (), p[i].ans.end (), cmp);     } }   int main(void)    {     //freopen ("POJ_3449.in", "r", stdin);     //freopen ("POJ_3449.out", "w", stdout);     char str[22];     int x[22], y[22];     int tot = 0;     int x1, y1, x2, y2, x3, y3, x4, y4;     Point p1, p2, p3, p4;     while (scanf ("%s", &str) == 1) {         if (strcmp (str, ".") == 0)  break;         else if (strcmp (str, "-") == 0) {             run (tot);             for (int i=0; i<tot; ++i)   pp[i] = p[i];             sort (p, p+tot);             for (int i=0; i<tot; ++i)   {                 if (p[i].cnt == 0)  {                     printf ("%c has no intersections\n", p[i].ch);                 }                 else    {                     if (p[i].cnt == 1)  {                         printf ("%c intersects with %c\n", p[i].ch, pp[p[i].ans[0]].ch);                     }                     else if (p[i].cnt == 2) {                         printf ("%c intersects with %c and %c\n", p[i].ch, pp[p[i].ans[0]].ch, pp[p[i].ans[1]].ch);                     }                     else    {                         printf ("%c intersects with %c", p[i].ch, pp[p[i].ans[0]].ch);                         int sz = p[i].ans.size ();                         for (int j=1; j<sz-1; ++j)    {                             printf (", %c", pp[p[i].ans[j]].ch);                         }                         printf (", and %c\n", pp[p[i].ans[sz-1]].ch);                     }                 }                 p[i].ans.clear ();  p[i].seg.clear ();             }             puts ("");             tot = 0;    continue;         }           p[tot].ch = str[0];         scanf ("%s", &str);         if (str[0] == 's')  {             scanf (" (%d,%d) (%d,%d)", &x1, &y1, &x3, &y3);             //cal x2 x4             p1 = Point (x1, y1), p3 = Point (x3, y3), p2, p4;             Vector V = p3 - p1;             double len = length (V);             p2 = p1 + rotate (V, PI / 4) / sqrt (2.0);             p4 = p1 + rotate (V, -PI / 4) / sqrt (2.0);             p[tot].seg.push_back (Seg (p1, p2));             p[tot].seg.push_back (Seg (p2, p3));             p[tot].seg.push_back (Seg (p3, p4));             p[tot].seg.push_back (Seg (p4, p1));         }         else if (str[0] == 'l') {             scanf (" (%d,%d) (%d,%d)", &x1, &y1, &x2, &y2);             p[tot].seg.push_back (Seg (Point (x1, y1), Point (x2, y2)));         }         else if (str[0] == 't') {             scanf (" (%d,%d) (%d,%d) (%d,%d)", &x1, &y1, &x2, &y2, &x3, &y3);             p[tot].seg.push_back (Seg (Point (x1, y1), Point (x2, y2)));             p[tot].seg.push_back (Seg (Point (x2, y2), Point (x3, y3)));             p[tot].seg.push_back (Seg (Point (x3, y3), Point (x1, y1)));         }         else if (str[0] == 'p') {             int n;             scanf ("%d", &n);             for (int i=0; i<n; ++i) {                 scanf (" (%d,%d)", &x[i], &y[i]);             }             for (int i=0; i<n-1; ++i)   {                 p[tot].seg.push_back (Seg (Point (x[i], y[i]), Point (x[i+1], y[i+1])));                 p[tot].seg.push_back (Seg (Point (x[n-1], y[n-1]), Point (x[0], y[0])));        //忘记加了             }         }         else if (str[0] == 'r') {             scanf (" (%d,%d) (%d,%d) (%d,%d)", &x1, &y1, &x2, &y2, &x3, &y3);             //cal x4             p1 = Point (x1, y1), p3 = Point (x3, y3), p2 = Point (x2, y2), p4;             p4 = p1 + (p3 - p2);             p[tot].seg.push_back (Seg (p1, p2));             p[tot].seg.push_back (Seg (p2, p3));             p[tot].seg.push_back (Seg (p3, p4));             p[tot].seg.push_back (Seg (p4, p1));         }         tot++;     }       //cout << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";       return 0; }