Transmitters
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 4955 | Accepted: 2624 |
Description
In a wireless network with multiple transmitters sending on the same frequencies, it is often a requirement that signals don‘t overlap, or at least that they don‘t conflict. One way of accomplishing this is to restrict a transmitter‘s coverage area. This problem uses a shielded transmitter that only broadcasts in a semicircle.
A transmitter T is located somewhere on a 1,000 square meter grid.
It broadcasts in a semicircular area of radius r. The transmitter may be
rotated any amount, but not moved. Given N points anywhere on the grid,
compute the maximum number of points that can be simultaneously reached
by the transmitter‘s signal. Figure 1 shows the same data points with
two different transmitter rotations.
All input coordinates are integers (0-1000). The radius is a
positive real number greater than 0. Points on the boundary of a
semicircle are considered within that semicircle. There are 1-150 unique
points to examine per transmitter. No points are at the same location
as the transmitter.
Input
Input
consists of information for one or more independent transmitter
problems. Each problem begins with one line containing the (x,y)
coordinates of the transmitter followed by the broadcast radius, r. The
next line contains the number of points N on the grid, followed by N
sets of (x,y) coordinates, one set per line. The end of the input is
signalled by a line with a negative radius; the (x,y) values will be
present but indeterminate. Figures 1 and 2 represent the data in the
first two example data sets below, though they are on different scales.
Figures 1a and 2 show transmitter rotations that result in maximal
coverage.
Output
For
each transmitter, the output contains a single line with the maximum
number of points that can be contained in some semicircle.
Sample Input
25 25 3.5 7 25 28 23 27 27 27 24 23 26 23 24 29 26 29 350 200 2.0 5 350 202 350 199 350 198 348 200 352 200 995 995 10.0 4 1000 1000 999 998 990 992 1000 999 100 100 -2.5
Sample Output
3 4 4 题意：半圆围绕圆心旋转能够覆盖平面内最多的点题解：先去掉所有和圆心距离大于r的点,然后我们以每一点和圆心组成的线段为边界来计算线段两边的点,比较出最大值就好了.记得赋值最大值的时候要赋值为0，因为它有可能不会进循环。
#include<stdio.h>
#include<iostream>
#include<string.h>
#include <stdlib.h>
#include<math.h>
#include<algorithm>
using namespace std;
const int N = 160;
const double eps = 1e-8;
struct Point{
double x,y;
}p[N],circle;
struct Line{
Point a,b;
}line;
double r;
int n;
int cross(Point a,Point b,Point c){
double ans = (a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y);
if(fabs(ans)<eps) return 0;
if(ans<0) return 1;
return -1;
}
int main(){
while(true){
scanf("%lf%lf%lf",&circle.x,&circle.y,&r);
if(r<=0) break;
scanf("%d",&n);
int k = 0;
for(int i=0;i<n;i++){
double x,y;
scanf("%lf%lf",&x,&y);
if((x-circle.x)*(x-circle.x)+(y-circle.y)*(y-circle.y)>r*r) continue;
p[k].x = x;
p[k++].y = y;
}
int temp1 ,temp2,mx = 0; ///mx要赋值为0，因为有可能一个点都没有,习惯赋值成-1被坑了一把
for(int i=0;i<k;i++){
line.a = p[i];
line.b = circle;
temp1=temp2 =0;
for(int j=0;j<k;j++){
if(cross(p[j],line.a,line.b)==0) {
temp1++;
temp2++;
}else if(cross(p[j],line.a,line.b)==1){
temp1++;
}else temp2++;
}
int ans = max(temp1,temp2);
mx = max(ans,mx);
}
printf("%d\n",mx);
}
return 0;
}