模拟退火、爬山

https://www.luogu.org/problemnew/show/T30204
题意：给出平面上的n个圆，求没有被覆盖的点坐标。不存在输出GG。

此题的解空间比较平滑，使用爬山无大碍
但是要注意新随机出来的点坐标范围，不能太大也不能太小

1.爬山

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<ctime>
using namespace std;
const double r=0.8;
double R,RR;
double xx,yy;
struct node {
    double x,y;
} a[15];
int n,l;
inline double Ran(double x) {
    return rand()%10001/10000.0*x;
}
inline int calc(double xx,double yy) {
    int cnt=0;
    for (int i=1;i<=n;i++) {
        if ((a[i].x-xx)*(a[i].x-xx)+(a[i].y-yy)*(a[i].y-yy)<R*R+1e-6) cnt++;
    }
    return cnt;
}
inline void getnew(double &nx,double &ny) {
    double tmp=max((double)l,RR);
    do {
        nx=xx+Ran(2*tmp)-tmp;
    } while (nx<0||nx>l);
    do {
        ny=yy+Ran(2*tmp)-tmp;
    } while (ny<0||ny>l);
    RR*=r;
}
void ps() {
    xx=Ran(l),yy=Ran(l);
    for (int i=1;i<=1e3;i++) {
        if (calc(xx,yy)==0) return;
        double nx,ny;
        getnew(nx,ny);
        double dE=calc(nx,ny)-calc(xx,yy);
        if (dE<=0) xx=nx,yy=ny;
    }
}
int main() {
    scanf("%d%d",&n,&l);R=(double)l/n;RR=l;
    for (int i=1;i<=n;i++) scanf("%lf%lf",&a[i].x,&a[i].y);
    srand(time(0));
    for (int i=1;i<=100;i++) {
        ps();
        if (calc(xx,yy)==0) {
            printf("%lf %lf",xx,yy);
            return 0;
        }
    }
    printf("GG");
    return 0;
}

2.退火
此题接受劣解概率较小，注意调参

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<ctime>
using namespace std;
const double T_min=1e-8;
const double r=0.98;
double T=1,R,RR;
double xx,yy;
struct node {
    double x,y;
} a[15];
int n,l;
inline double Ran(double x) {
    return rand()%10001/10000.0*x;
}
inline int calc(double xx,double yy) {
    int cnt=0;
    for (int i=1;i<=n;i++) {
        if ((a[i].x-xx)*(a[i].x-xx)+(a[i].y-yy)*(a[i].y-yy)<R*R+1e-6) cnt++;
    }
    return cnt;
}
inline void getnew(double &nx,double &ny) {
    double tmp=max((double)l,RR);
    do {
        nx=xx+Ran(2*tmp)-tmp;
    } while (nx<0||nx>l);
    do {
        ny=yy+Ran(2*tmp)-tmp;
    } while (ny<0||ny>l);
    RR*=r;
}
void mnth() {
    xx=Ran(l),yy=Ran(l);
    while (T>T_min) {
        if (calc(xx,yy)==0) return;
        double nx,ny;
        getnew(nx,ny);
        double dE=calc(nx,ny)-calc(xx,yy);
        if (dE<=0) xx=nx,yy=ny;
        else if (exp(-dE/T)>Ran(1)) xx=nx,yy=ny;
        T=r*T;
    }
}
int main() {
    scanf("%d%d",&n,&l);R=(double)l/n;RR=l;
    for (int i=1;i<=n;i++) scanf("%lf%lf",&a[i].x,&a[i].y);
    srand(time(0));
    mnth();
    if (calc(xx,yy)==0) printf("%lf %lf",xx,yy);
    else printf("GG");
    return 0;
}