Simple geometry (circle and Polygon public area) uvalive 7072 Signal Interference (14 Guangzhou D)

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Test instructions: A polygon, a point and a B point, meet the PB <= K * PA p range and the polygon's public area.

Analysis: This is a Apollonius circle. Since it is a circle, then the general equation of the Circle: (x + d/2) ^ 2 + (y + e/2) ^ 2 = (D ^ 2 + E ^ 2-4 * F)/4, the center and radius are solved by the PB = = PA * k solution equation. Then is a set of templates, Shanghai Jiaotong University's Red Book.

/************************************************* author:running_time* Created TIME:2015/11/9 Monday 11:51:27* Fil E Name:D. cpp ************************************************/#include <bits/stdc++.h>using namespace std;# Define Lson L, Mid, RT << 1#define Rson mid + 1, R, RT << 1 | 1typedef long ll;const int N = 5e2 + 10;const int INF = 0x3f3f3f3f;const int MOD = 1e9 + 7;const Double EPS = 1e-10;c    Onst 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) {}-operator + (const point &r) const {//vector    addition 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 {//vector multiplied by a scalar return point (x * p, Y * p);    } point operator/(double p) Const {   The vector is divided by a scalar return point (x/p, y/p); } BOOL operator < (const point &r) const {return x < r.x | |    (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 Polar_angle (Vector V) {return atan2 (v.y, v.x);} Double Dot (point A, point B) {return a.x * b.x + a.y * B.Y;} Double Cross (Point A, point B) {return a.x * b.y-a.y * b.x;} Double Length (Vector v) {return sqrt (dot (v, v));} Double my_sqrt (double x) {return sqrt (max (0.0, x));} Point Ps[n];d ouble R, k;double x1, y1, x2, Y2;int n;double Sqr (double x) {return x * x;}    struct line {point P;    Vector v;    Double R;    Line () {} line (const point &p, const Vector &v): P (P), V (v) {r = Polar_angle (v); } PoiNT point (Double A) {return P + v * A;    }};struct Circle {point C;    Double R; Circle () {} circle (point C, Double R): C (c), R (r) {}-point-point (double a) {return-point (c.x + cos (    A) * R, C.y + sin (a) * R); }};int Line_cir_inter (line L, Circle C, double &t1, double &t2, vector<point> &p) {Double A = L.V    . x, B = l.p.x-c.c.x, C = l.v.y, d = l.p.y-c.c.y;    Double E = A * a + c * C, F = 2 * (A * b + c * d), G = b * B + d * D-C.R * C.R;    Double delta = f * f-4 * e * g;    if (dcmp (delta) < 0) return 0; if (dcmp (delta) = = 0) {T1 = t2 =-F/(2 * e);        P.push_back (L.point (t1));    return 1;    } T1 = (-f-sqrt (delta))/(2 * e);    T2 = (-f + sqrt (delta))/(2 * e);    if (T1 > T2) swap (t1, T2);    if (dcmp (T1) > 0 && dcmp (t1-1) < 0) P.push_back (l.point (t1));    if (dcmp (T2) > 0 && dcmp (t2-1) < 0) P.push_back (l.point (T2)); return (int) P.size ();}    Double Sector_area (Point A, point B) {Double theta = Polar_angle (a)-polar_angle (b);    while (dcmp (theta) <= 0) Theta + = 2 * PI;    while (Theta > 2 * pi) theta-= 2 * PI;    theta = min (theta, 2 * pi-theta); Return R * R * THETA/2;}    Double Cal (Point A, point B) {double T1, T2;    BOOL ina = dcmp (Length (a)-R) < 0;    BOOL INB = dcmp (length (b)-R) < 0;    if (Ina && inb) return Fabs (Cross (A, B))/2.0;    Vector<point> p;    int num = Line_cir_inter (line (A, b-a), Circle (point (0, 0), R), T1, T2, p);    if (INA) return Sector_area (b, p[0]) + fabs (cross (A, p[0]))/2.0;    if (INB) return Sector_area (P[0], a) + Fabs (cross (p[0], B))/2.0;    if (num = = 2) return Sector_area (A, p[0]) + Sector_area (p[1], b) + fabs (cross (p[0], p[1])/2.0; Return Sector_area (A, b);}    Double Cir_poly_area () {double ret = 0;  for (int i=0; i<n; ++i) {int sgn = dcmp (Cross (Ps[i], ps[i+1]));      if (sgn! = 0) {ret = SGN * CALs * CAL (Ps[i], ps[i+1]); }} return ret;}    void init (void) {Double D = (2 * x2-2 * SQR (k) * x1)/(1-SQR (k));    Double E = (2 * y2-2 * SQR (k) * y1)/(1-SQR (k));    Double F = (Sqr (k*x1) +sqr (k*y1)-sqr (x2)-sqr (y2))/(1-SQR (k));    Double x0 = d/2, y0 = E/2;    R = sqrt (F + SQR (D)/4 + SQR (E)/4);  for (int i=0; i<n; ++i) {ps[i].x-= x0;    PS[I].Y-= y0; } Ps[n] = Ps[0];}    int main (void) {int cas = 0;        while (scanf ("%d%lf", &n, &k) = = 2) {for (int i=0; i<n; ++i) {Ps[i] = Read_point ();        } scanf ("%lf%lf", &x1, &y1);        scanf ("%lf%lf", &x2, &y2);        Init ();    printf ("Case%d:%.10f\n", ++cas, Fabs (Cir_poly_area ()));    }//cout << "time Elapsed:" << 1.0 * Clock ()/clocks_per_sec << "s.\n"; return 0;}

　　

Simple geometry (circle and Polygon public area) uvalive 7072 Signal Interference (14 Guangzhou D)