[bzoj4852][Jsoi2016]炸弹攻击【随机化】

【题目链接】
　　https://www.lydsy.com/JudgeOnline/problem.php?id=4852
【题解】
　　在平面中随机选取一些点作为初始点，然后模拟退火。
　　tip：在模拟退火时，由于答案比较小，但是温度比较高，所以在算exp$exp$时最好把相差的点数乘以一个常数让选取更差的的概率降低。
　　

/* --------------
    user Vanisher
    problem bzoj-4852 
----------------*/
# include <bits/stdc++.h>
# define    ll      long long
# define    inf     0x3f3f3f3f
# define    N       11
# define    M       1010
using namespace std;
int read(){
    int tmp=0, fh=1; char ch=getchar();
    while (ch<'0'||ch>'9'){if (ch=='-') fh=-1; ch=getchar();}
    while (ch>='0'&&ch<='9'){tmp=tmp*10+ch-'0'; ch=getchar();}
    return tmp*fh;
}
struct Point{
    double x,y;
}p[M];
Point operator +(Point x, Point y){return (Point){x.x+y.x,x.y+y.y};}
struct Circle{
    Point p;
    double r;
}b[N];
int n,m,ans;
double mr;
double sqr(double x){return x*x;}
double dis(Point x, Point y){
    return sqrt(sqr(x.x-y.x)+sqr(x.y-y.y));
}
double rand_0_1(){return (rand() % 32767) / 32767.0;}
double solve(Point x){
    double r=mr; double cnt=0;
    for (int i=1; i<=n; i++)
        r=min(r,dis(b[i].p,x)-b[i].r);
    if (r<0) return 0;
    for (int i=1; i<=m; i++)
        if (dis(x,p[i])<=r) cnt++;
    return cnt;
}
int Simulate_Anneal(Point ths, double S, double P, double Lim){
    double mx=solve(ths), now=mx, tmp;
    Point nex;
    for (double t=S; t>=Lim; t=t*P){
        double step = t * mr / S + 0.1;
        nex.x=ths.x+(2*step)*rand_0_1()-step;
        nex.y=ths.y+(2*step)*rand_0_1()-step;
        tmp=solve(nex);
        if (tmp>now) ths=nex, now=tmp;
            else if (exp(1e4*(tmp-now)/t)>rand_0_1())
                ths=nex, now=tmp;
        mx=max(now,mx);
    }
    return mx;
}
int main(){
    n=read(), m=read(), mr=read();
    for (int i=1; i<=n; i++)
        b[i].p.x=read(), b[i].p.y=read(), b[i].r=read();
    for (int i=1; i<=m; i++)
        p[i].x=read(), p[i].y=read();
    for (int i=1; i<=20; i++)
        ans=max(ans,Simulate_Anneal((Point){2*mr*rand_0_1()-mr,2*mr*rand_0_1()-mr},mr,0.998,0.01));
    printf("%d\n",ans);
    return 0;
}