POJ 1379 （随机算法）模拟退火

 题目大意：

给定一堆点，找到一个点的位置使这个点到所有点中的最小距离最大

这里数据范围很小，精度要求也不高，我们这里可以利用模拟退火的方法，随机找到下一个点，如果下一个点比当前点优秀就更新当前点

参考：http://www.cnblogs.com/heaad/archive/2010/12/20/1911614.html

http://wenku.baidu.com/view/0c6b5df5f61fb7360b4c65a9.html

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <climits>
#include <cmath>
#include <queue>
#include <cstdlib>
#include <ctime>
using namespace std;
#define random(x) ((rand()%x)+1)
#define N 1005
#define ll long long
#define eps 1e-4
const double PI = acos(-1.0);
const int INF = INT_MAX;
const int P = 20;
const int L = 30;

double x,y;
int n;
double dist[N];

struct Point{
    double x,y;
    Point(double x=0 , double y=0):x(x),y(y){}
}p[N] , tmp[N];

double dis(Point a , Point b)
{
    double x = a.x-b.x , y = a.y - b.y;
    return sqrt(x*x+y*y);
}

double min_dis(Point t)
{
    double minn = 1e20;
    for(int i=0 ; i<n ; i++) minn=min(minn , dis(t , p[i]));
    return minn;
}

bool ok(Point t)
{
    return t.x>=0 && t.x<=x && t.y>=0 && t.y<=y;
}

int main()
{
    #ifndef ONLINE_JUDGE
        freopen("a.in" , "r" , stdin);
    #endif // ONLINE_JUDGE
    srand(time(0));
    int T;
    scanf("%d" , &T);
    while(T--)
    {
        Point ans;
        double ret=0;

        scanf("%lf%lf%d" , &x , &y , &n);
        for(int i=0 ; i<n ; i++){
            scanf("%lf%lf" , &p[i].x , &p[i].y);
        }

        for(int i=0 ; i<P ; i++){
            tmp[i].x = random(1000)/1000.0*x;
            tmp[i].y = random(1000)/1000.0*y;
            dist[i] = min_dis(tmp[i]);
        }
        double step = sqrt(x*x+y*y)/2;
        while(step>eps){

            for(int i=0 ; i<P ; i++){
                Point cur;
                for(int j=0 ; j<L ; j++){
                    double ang = random(1000)/1000.0*2*PI;
                    cur.x = tmp[i].x+cos(ang)*step;
                    cur.y = tmp[i].y+sin(ang)*step;
                    if(!ok(cur)) continue;
                    double val = min_dis(cur);
                    if(val>dist[i]){
                        tmp[i]=cur;
                        dist[i] = val;
                    }
                }
            }
            step *= 0.85;
        }

        for(int i=0 ; i<P ; i++){
            if(dist[i]>ret){
                ret = dist[i];
                ans = tmp[i];
            }
        }
        printf("The safest point is (%.1f, %.1f).
" , ans.x , ans.y);
    }
    return 0;
}