[POJ][3285][Point of view in Flatland][模拟退火]

/*
题目：Point of view in Flatland
题目来源：POJ 3285
题目难度：中等偏难
题目内容或思路：
    模拟退火
    这题的难点在找到合适的评估函数
做题日期：2011.3.9
*/
#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 = 30, nt = 20, step = 30;
const double inf = 1e100;
const double eps = 1e-3;
const double pi = acos(-1.0);
double delta;

struct cpoint{
    double x, y, r;
}cp[N], test[N];

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

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

void calc(cpoint &p) {
    double t[3], ave = 0;
    int id = 0;
    for (int i = 0; i < 3; ++i) {
        t[i] = dis(p, cp[i]) / cp[i].r;
        ave += t[i];
    }
    ave /= 3;
    p.r = 0;
    for (int i = 0; i < 3; ++i) {
        p.r += sqr(t[i] - ave);
    }
}

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.r < test[id].r)
        test[id] = t;
}

bool solve() {
    double t = 0, maxx, minx, maxy, miny;
    maxx = maxy = -inf;
    minx = miny = inf;
    for (int i = 0; i < 3; ++i) {
        scanf("%lf%lf%lf", &cp[i].x, &cp[i].y, &cp[i].r);
        t += cp[i].r;
        maxx = max(maxx, cp[i].x);
        minx = min(minx, cp[i].x);
        maxy = max(maxy, cp[i].y);
        miny = min(miny, cp[i].y);
    }
    if (dcmp(t) == 0) return false;
    for (int i = 0; i < nt; ++i) {
        test[i].x = minx + (rand() % (int)(maxx * 10 - minx * 10 + 1)) / 10.0;
        test[i].y = miny + (rand() % (int)(maxy * 10 - miny * 10 + 1)) / 10.0;
        calc(test[i]);
    }
    delta = max(maxx - minx, maxy - miny);
    for (; delta > 1e-6; delta *= 0.9) {
        for (int i = 0; i < nt; ++i)
            for (int j = 0; j < step; ++j)
                updata(i);
    }
    int res = -1;
    for (int i = 0; i < nt; ++i) {
        if (dcmp(test[i].r) == 0) {
            double u = dis(test[i], cp[0]);
            double v = dis(test[res], cp[0]);
            if (res == -1 || dcmp(u - v) < 0)
                res = i;
        }
    }
    if (res == -1) puts("No solution");
    else {
        if (dcmp(test[res].x) == 0) test[res].x = 0;
        if (dcmp(test[res].y) == 0) test[res].y = 0;
        printf("%.2lf %.2lf\n", test[res].x, test[res].y);
    }
    return true;
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("D:\\in.txt", "r", stdin);
#endif
    while (solve());
    return 0;
}