hdu 4717 The Moving Points(三分)

题目连接：hdu 4717 The Moving Points

题目大意：给出n个点，每个点有初始的位置(x,y),以及单位时间内移动的距离，向量形式给出。且在哪一个时刻中，n个点之间两两距离的最大值最小，最小值为多少。

解题思路：类似与二分算法的三分，因为如果将时间t和所要求的两两之间距离的最大值d做成一个函数曲线，单调性应该是先递减后递增的，所以用三分法求极值。

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>

using namespace std;
const int N = 305;
const double eps = 1e-6;
struct point {
    double x;
    double y;
}s[N], p[N];

int n;

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

inline double dis (double x, double y) {
    return sqrt(x*x+y*y);
}

double cat (double k) {
    double ans = 0;
    for (int i = 0; i < n; i++) {
        double xi = s[i].x + p[i].x * k;
        double yi = s[i].y + p[i].y * k;

        for (int j = i + 1; j < n; j++) {
            double pi = s[j].x + p[j].x * k;
            double qi = s[j].y + p[j].y * k;
            ans = max(ans, dis(xi-pi, yi-qi));
        }
    }
    return ans;
}

void solve () {
    double l = 0;
    double r = 0xffffff;

    while (fabs(r-l) > eps) {
        double tmp = (r-l)/3;
        double midl = l + tmp;
        double midr = r - tmp;
        if (cat(midl) < cat(midr))
            r = midr;
        else
            l = midl;
    }
    printf("%.2lf %.2lf\n", l, cat(l));
}

int main () {
    int cas;
    scanf("%d", &cas);
    for (int i = 1; i <= cas; i++) {
        init ();
        printf("Case #%d: ", i);
        solve();
    }
    return 0;
}