The Moving Points

题意

二维空间中有(n)个运动的点，每个点有一个初始坐标和速度向量。求出一个时间(T)，使得此时任意两点之间的最大距离最小。输出(T)和最大距离。

题解

模拟退火。

这个题告诉了我，初始步长要够大。这是很重要的。

//#include <bits/stdc++.h>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <algorithm>
#include <iostream>

#define FOPI freopen("in.txt", "r", stdin)
#define FOPO freopen("out.txt", "w", stdout)

using namespace std;
typedef long long LL;
const int maxn = 300 + 5;
const double eps = 1e-6;
const int inf = 0x3f3f3f3f;
const double start_T = 2000;

struct Point
{
    double x, y, z;
    Point() {}
    Point(double _x, double _y, double _z = 0):x(_x), y(_y), z(_z) {}
}a[maxn];
double vx[maxn], vy[maxn];

int n;

double dist(Point a, Point b)
{
    return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y) + 1e-10);
}

Point pos[maxn];
double getMax(double ti)
{
    for (int i = 1; i <= n; i++)
        pos[i] = Point(a[i].x + vx[i]*ti, a[i].y + vy[i]*ti);

    double res = 0;
    for (int i = 1; i <= n; i++)
        for (int j = i+1; j <= n; j++)
        res = max(res, dist(pos[i], pos[j]));
    return res;
}

double SA()
{
    double T = start_T, rate = 0.92;
    double ti = 0, ans = getMax(ti), to;

    while(T > eps)
    {
        double tmp = inf;
        for (int i = 1; i <= 5; i++)
        {
            double nextt = ti + T / start_T * (rand() % inf);
            double lastt = ti - T / start_T * (rand() % inf);
            double d1 = getMax(nextt), d2 = getMax(lastt);

            if (d1 < tmp) tmp = d1, to = nextt;
            if (d2 < tmp && lastt > eps) tmp = d2, to = lastt;
        }

        if (tmp < ans || (rand()%1000)/1000.0 < exp(-fabs(ans-tmp)/T*start_T))
        {
            ans = tmp;
            ti = to;
        }
        T *= rate;
    }
    printf("%.2f %.2f
", ti, ans);
    return ans;
}

int t;
int main()
{
//    FOPI;
    srand(time(NULL));
    scanf("%d", &t);
    for (int ca = 1; ca <= t; ca++)
    {
        scanf("%d", &n);
        for (int i = 1; i <= n; i++)
            scanf("%lf%lf%lf%lf", &a[i].x, &a[i].y, &vx[i], &vy[i]);

        printf("Case #%d: ", ca);
        SA();
    }
}