# Simple Geometry (segment intersection + shortest path) POJ 1556 the Doors

Source: Internet
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Test instructions: From (0, 5) to (10, 5), there are some doors in the middle, the road is straight, ask the shortest distance

Analysis: The key is to build a map, you can save all the points, two-point connectivity is the condition is the line segment and the middle of the line is not intersected, the establishment of a directed graph, and then use Dijkstra to run the shortest way. Good question!

`/************************************************* author:running_time* Created time:2015/10/24 Saturday 09:48:49* Fi Le Name:P oj_1556.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 | 1typedef long ll;const int N = 300;const int E = n * n;const int INF = 0x3f3f3f3f;const int MOD = 1e9 + 7;const Doubl    E EPS = 1e-10;struct Point {//points defined by double x, y;       Point (Double x=0, double y=0): X (x), Y (y) {}};typedef point Vector; Vector definition point read_point (void) {//points read in Double X, Y    scanf ("%lf%lf", &x, &y); Return point (x, y);} Double Polar_angle (vector A) {//Vector polar return atan2 (A.Y, a.x);} Double dot (vector A, vector B) {//vector dot product return a.x * b.x + a.y * B.Y;} Double Cross (vector A, vector B) {//vector fork product return a.x * B.Y-A.Y * b.x;}    int dcmp (double x) {///three state function, reduced accuracy problem if (fabs (x) < EPS) return 0; else return x < 0? -1:1;} Vector operator + (vector A, vector B) {//vector addition return vector (a.x + b.x, A.Y + b.y);} Vector operator-(vector A, vector B) {//vector subtraction return vector (a.x-b.x, a.y-b.y);} Vector operator * (vector A, double p) {//vector multiplied by the scalar return vector (a.x * p, A.Y * p);} Vector operator/(vector A, double p) {//vector divided by scalar return vector (a.x/p, a.y/p);} BOOL operator < (const dot &a, const point &b) {//points ' coordinate sort return a.x < b.x | | (a.x = = b.x && a.y < B.Y);} BOOL operator = = (Const point &a, const point &b) {       Judge the same point return dcmp (a.x-b.x) = = 0 && dcmp (a.y-b.y) = = 0;} Double length (vector a) {//vector length, dot product return sqrt (dot (A, a));} Double angle (vector a, vector b) {//Vector corner, counterclockwise, dot product return ACOs (dot (A, b)/Length (a)/length (b));} Double Area_triangle (Point A, point B, point C) {//triangular area, fork product return Fabs (Cross (b-a, c-a))/2.0;} Vector Rotate (vector A, double rad) {//vector rotation, counter-clockwise return vector (a.x * cos (RAD)-A.y * sin (rad), a.x * sin (rad ) + a.y * cos (RAD));}    Vector Nomal (vector a) {//vector double len = length (a) of the unit method vectors; Return Vector (-a.y/len, A.x/len);}    Point Point_inter (point P, Vector V, point q, Vector W) {//two line intersection, parametric equation Vector U = p-q;    Double T = Cross (w, U)/Cross (V, W); return p + V * t;}    Double Dis_to_line the distance from {//points to a straight line, two-point Vector V1 = b-a, V2 = p-a; Return Fabs (Cross (V1, V2))/Length (V1);}    Double dis_to_seg (point P, point A, point B){//point-to-line distance, two-point 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_proj (point P, points a, dot b) {//dots are projected on a line, two points Vector V = b-a; Return a + v * (dot (v, p-a)/dot (V, v));} BOOL Inter (Points A1, point A2, Spot b1, dot b2) {//Judgment segment intersection, two-bit double C1 = Cross (A2-A1, b1-a1), C2 = Cro    SS (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 On_seg (point P, bit A1, points A2) {//Judgment dot on segment, two-point return dcmp (Cross (a1-p, a2-p)) = = 0 && DCMP (dot (a1-p, a2-p)) < 0;}    Double Area_poly (point *p, int n) {//polygon area DOUBLE ret = 0; for (int i=1; i<n-1; ++i) {ret + = Fabs (Cross (P[i]-p, p[i+1]-p)); } return RET/2;}    struct Edge {int V, NEX;    Double W;    Edge () {} edge (int V, double w, int nex): V (v), W (W), NEX (NEX) {} BOOL operator < (const Edge &AMP;R) const    {return w > R.W;    }}edge[e];d ouble d[n];int head[n];bool vis[n];int N, tot, e;void init (void) {memset (head,-1, sizeof (head)); e = 0;}    void Add_edge (int u, int v, double w) {Edge[e] = Edge (V, W, Head[u]); Head[u] = e++;}    void Dijkstra (int s) {memset (Vis, false, sizeof (VIS));    for (int i=0; i<tot; ++i) {d[i] = 1e9;    } D[s] = 0; Priority_queue<edge> Q;    Q.push (Edge (S, D[s], 0)); while (! Q.empty ()) {int u = q.top (). V;        Q.pop ();        if (Vis[u]) continue;        Vis[u] = true;            for (int i=head[u]; ~i; i=edge[i].nex) {int v = EDGE[I].V;            Double w = EDGE[I].W;        if (!vis[v] && d[v] > D[u] + W) {D[v] = D[u] + W;        Q.push (Edge (V, D[v], 0));        }}}}point P[n];int main (void) {while (scanf ("%d", &n) = = 1) {if (N = =-1) break;        Init ();    tot = 0;        Double x, y1, y2, y3, Y4;        p[tot++] = Point (0, 5);            for (int i=0; i<n; ++i) {scanf ("%lf%lf%lf%lf%lf", &x, &y1, &y2, &y3, &y4);            p[tot++] = point (x, y1);            p[tot++] = point (x, y2);            p[tot++] = point (x, y3);        p[tot++] = point (x, Y4);                } p[tot++] = Point (10, 5); for (int i=0, i<tot; ++i) {for (int j=i+1; j<tot; ++j) {if (p[i].x = = p[j].x) contin                Ue                BOOL flag = TRUE; for (int k=i+1; k<j; ++k) {if (p[k].x = = P[i].x | |                    p[k].x = = p[j].x) continue;                          if (k% 4 = = 1) {if (Inter (P[i], p[j], p[k], point (p[k].x, 0))) {  Flag = false;                        Break }} else if (k% 4 = = 0) {if (Inter (P[i], p[j], p[k], Po   Int (p[k].x))) {flag = false;                        Break }} else if (k% 4 = = 2) {if (Inter (P[i], p[j], p[k], p[   K+1]) {flag = false;                        Break }} else if (k% 4 = = 3) {if (Inter (P[i], p[j], p[k], p[   K-1]) {flag = false;                        Break }}} if (flag) {Add_edge (i, J, Length (P[j]-p[i                ]));        }}} Dijkstra (0);    printf ("%.2f\n", d[tot-1]); } return 0;}`

Simple Geometry (segment intersection + shortest path) POJ 1556 the Doors

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