[URAL][1520][Empire Strikes Back][模拟退火]

/*
题目：Empire Strikes Back
题目来源：URAL 1520
题目难度：中等偏难
题目内容或思路：
    模拟退火
    08年顾研论文例题。一开始没看论文只用模拟退火一直WA，后来看了
    论文才发现，如果所找的点在圆的边上的话，很难调整到该点。所以
    还要加上O(n^3)的特判
做题日期：2011.3.8
*/
#include <cstdio>
#include <cstdlib>
#include <climits>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <queue>
#include <map>
#include <vector>
#include <bitset>
#include <cmath>
#include <set>
#include <utility>
#include <ctime>
#define sqr(x) ((x)*(x)) 
using namespace std;

const int N = 310, g = 20, L = 30;
const double pi = acos(-1.0);
const double inf = 1e10;
const double eps = 1e-9;
int n;
double r, delta;
struct cpoint {
    double x, y, d;
}cp[N], test[N], o;

int dcmp(double x) {
    if (x < -eps) return -1; else return x > eps;
}

double dissqr(cpoint a, cpoint b) {
    return sqr(a.x - b.x) + sqr(a.y - b.y);
}

void calc(cpoint &p) {
    p.d = inf;
    if (dcmp(sqr(p.x) + sqr(p.y) - r * r) > 0) {
        p.d = 0; return;
    }
    for (int i = 0; i < n; ++i) {
        p.d = min(p.d, dissqr(p, cp[i]));
    }
}

void updata(int id) {
    cpoint t;
    double angle = rand();
    angle -= (int)(angle / pi / 2) * pi * 2;
    t.x = test[id].x + delta * cos(angle);
    t.y = test[id].y + delta * sin(angle);
    calc(t);
    if (t.d > test[id].d) test[id] = t;
}

int CirCrossLine(cpoint p0, double r, 
    double a, double b, double c, cpoint &cp1, cpoint &cp2) {
    double aa = a * a, bb = b * b, s = aa + bb;
    double d = r * r * s - sqr(a * p0.x + b * p0.y + c);
    if (d + eps < 0) return 0;
    if (d < eps) d = 0; else d = sqrt(d);
    double ab = a * b, bd = b * d, ad = a * d;
    double xx = bb * p0.x - ab * p0.y - a * c;
    double yy = aa * p0.y - ab * p0.x - b * c;
    cp2.x = (xx + bd) / s; cp2.y = (yy - ad) / s;
    cp1.x = (xx - bd) / s; cp1.y = (yy + ad) / s;
    if (d > eps) return 2; else return 1;
}

void solve() {
//    srand(time(0));
    for (int i = 0; i < n; ++i) {
        scanf("%lf%lf", &cp[i].x, &cp[i].y);
    }
    for (int i = 0; i < g; ++i) {
        double len = rand();
        len -= (int)(len / r) * r;
        double angle = rand();
        angle -= (int)(angle / pi / 2) * pi * 2;
        test[i].x = len * cos(angle);
        test[i].y = len * sin(angle);
        calc(test[i]);
    }
    delta = r * 2 / sqrt((double)g);
    for (; delta > 1e-7; delta *= 0.8)
        for (int i = 0; i < g; ++i)
            for (int j = 0; j < L; ++j)
                updata(i);
    double res = 0;
    for (int i = 0; i < g; ++i)
        res = max(res, test[i].d);
    for (int i = 0; i < n; ++i) {
        for (int j = i + 1; j < n; ++j) {
            cpoint p1, p2;
            CirCrossLine(o, r, 2 * (cp[i].x - cp[j].x), 2 * (cp[i].y - cp[j].y),
                dissqr(cp[j], o) - dissqr(cp[i], o), p1, p2);
            calc(p1);
            res = max(res, p1.d);
            calc(p2);
            res = max(res, p2.d);
        }
    }
    for (int i = 0; i < n; ++i) {
        double d = sqrt(dissqr(cp[i], o));
        if (dcmp(d) <= 0) continue;
        cpoint p;
        p.x = cp[i].x * r / d;
        p.y = cp[i].y * r / d;
        calc(p);
        res = max(res, p.d);
        p.x = -p.x; p.y = -p.y;
        calc(p);
        res = max(res, p.d);
    }
    printf("%lf\n", sqrt(res));
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("D:\\in.txt", "r", stdin);
#endif
    o.x = o.y = 0;
    while (scanf("%d%lf", &n, &r) != EOF) {
        solve();
    }
    return 0;
}