Poj1981circle and points (points with the largest unit circle coverage)

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O (N ^ 3) practices:

Enumerate any two points as the circle of the string, and then enumerate whether other points are in the circle.

Two functions are used.

Atan2 returns the arc tangent function. It is said that it can avoid some special situations.

 1 #include <iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 #include<stdlib.h> 6 #include<vector> 7 #include<cmath> 8 #include<queue> 9 #include<set>10 using namespace std;11 #define N 31012 #define LL long long13 #define INF 0xfffffff14 const double eps = 1e-8;15 const double pi = acos(-1.0);16 const double inf = ~0u>>2;17 struct point18 {19     double x,y;20     point(double x = 0,double y =0 ):x(x),y(y){}21 }p[N];22 double dis(point a,point b)23 {24     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));25 }26 point getcircle(point p1,point p2)27 {28     point mid = point((p1.x+p2.x)/2,(p2.y+p1.y)/2);29     double angle = atan2(p2.y-p1.y,p2.x-p1.x);30     double d = sqrt(1.0-dis(p1,mid)*dis(p1,mid));31     return point(mid.x+d*sin(angle),mid.y-d*cos(angle));32 }33 int dcmp(double x)34 {35     if(fabs(x)<eps)return 0;36     else return x<0?-1:1;37 }38 int main()39 {40     int i,j,n;41     while(scanf("%d",&n)&&n)42     {43         for(i = 1 ;i <= n; i++)44         scanf("%lf%lf",&p[i].x,&p[i].y);45         int maxz = 1;46         for(i = 1; i <= n; i++)47             for(j = i+1 ; j <= n ;j++)48             {49                 if(dis(p[i],p[j])>2.0) continue;50                 int tmax = 0;51                 point cir = getcircle(p[i],p[j]);52                 for(int g =  1; g <= n ;g++)53                 {54                     if(dcmp(dis(cir,p[g])-1.0)>0)55                     continue;56                     tmax++;57                 }58                 maxz = max(maxz,tmax);59             }60         printf("%d\n",maxz);61     }62     return 0;63 }

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O (N ^ 2log (n ))

This is similar to the scanning line practice. The circle is centered on each point, and the circle is obtained by enumeration. the intersection point and angle are saved, sorted by angle, and scanned.

 

1 # include <iostream> 2 # include <cstdio> 3 # include <cstring> 4 # include <algorithm> 5 # include <stdlib. h> 6 # include <vector> 7 # include <cmath> 8 # include <queue> 9 # include <set> 10 using namespace STD; 11 # define n 31012 # define ll long long13 # define INF 0xfffffff14 const double EPS = 1e-8; 15 const double Pi = ACOs (-1.0); 16 const double INF = ~ 0u> 2; 17 struct point18 {19 Double X, Y; 20 point (double x = 0, Double Y = 0): x (x), y (y) {} 21} p [N]; 22 struct node23 {24 Double Ang; 25 int in; 26} arc [N * n]; 27 double DIS (point a, point B) 28 {29 return SQRT (. x-b.x) * (. x-b.x) +. y-b.y) * (. y-b.y); 30} 31 int DCMP (Double X) 32 {33 If (FABS (x) <EPS) return 0; 34 else return x <0? -1:1; 35} 36 bool CMP (node A, Node B) 37 {38 If (DCMP (. ang-b.ang) = 0) 39 return. in> B. in; 40 return DCMP (. ang-b.ang) <0; 41} 42 int main () 43 {44 int I, j, N; 45 while (scanf ("% d", & N) 46 {47 for (I = 1; I <= N; I ++) 48 scanf ("% lf", & P [I]. x, & P [I]. y); 49 int G = 0; 50 int ans = 0, maxz = 1; 51 for (I = 1; I <= N; I ++) 52 {53 ans = 0; 54g = 0; 55 for (j = 1; j <= N; j ++) 56 {57 if (DIS (P [I], P [J])> 2.0) continue; 58 double ang1 = atan2 (P [J]. y-P [I]. y, P [J]. x-P [I]. x); 59 double ang2 = ACOs (DIS (P [I], p [J])/2); 60 arc [++ g]. ang = ang1-ang2; // here the angle algorithm is cleverly 61 arc [g]. in = 1; 62 arc [++ g]. ang = ang1 + ang2; 63 arc [g]. in =-1; 64} 65 sort (ARC + 1, arc + G + 1, CMP); 66 67 // cout <G <Endl; 68 for (j = 1; j <= g; j ++) 69 {70 ans + = arc [J]. in; 71 maxz = max (maxz, ANS); 72} 73} 74 printf ("% d \ n", maxz); 75} 76 return 0; 77}

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