M Zipline(勾股定理+三分)

链接：https://ac.nowcoder.com/acm/contest/13168/M
来源：牛客网

题目描述
A zipline is a very fun and fast method of travel. It uses a very strong steel cable, connected to two poles. A rider (which could be a person or some cargo) attaches to a pulley which travels on the cable. Starting from a high point on the cable, gravity pulls the rider along the cable.

Your friend has started a company which designs and installs ziplines, both for fun and for utility. However, there’s one key problem: determining how long the cable should be between the two connection points. The cable must be long enough to reach between the two poles, but short enough that the rider is guaranteed to stay a safe distance above the ground. Help your friend determine these bounds on the length.

The cable connects to two vertical poles that are ww meters apart, at heights gg and hh meters, respectively. You may assume that the cable is inelastic and has negligible weight compared to the rider, so that there is no sag or slack in the cable. That is, at all times the cable forms two straight line segments connecting the rider to the two poles, with the sum of the segments lengths equal to the total length of the cable. The lowest part of the rider hangs rr meters below the cable; therefore the cable must stay at least rr meters above the ground at all times during the ride. The ground is flat between the two poles. Please refer to the diagram in Figure M.1 for more information.

Figure M.1: A zipline, annotated with the four variables used to describe it.

输入描述:
The input starts with a line containing an integer nn, where 1 \leq n \leq 1 0001≤n≤1000. The next nn lines each describe a zipline configuration with four integers: ww, gg, hh, and rr. These correspond to the variables described above. The limits on their values are: 1 \leq w, g, h \leq 1 000 0001≤w,g,h≤1000000, and 1 \leq r \leq min(g, h)1≤r≤min(g,h).
输出描述:
For each zipline, print a line of output with two lengths (in meters): the minimum and maximum length the cable can be while obeying the above constraints. Both lengths should have an absolute error of at most 10^{−6}10
−6
.
示例1
输入
复制
2
1000 100 100 20
100 20 30 2
输出
复制
1000.00000000 1012.71911209
100.49875621 110.07270325

最短的绳子自然就是直接一条线连在两个柱子上了
最长的要分析一下，就以题目给定这个图来看

设左边三角形底长为x,那么绳子的公式就是sqrt(xx+(g-r)(g-r))+sqrt((w-x)(w-x)+(h-r)(h-r))
可以发现这大概是一个单峰函数，直接三分去试x的值

三分详解

#include <bits/stdc++.h>
using namespace std;
double w, g, h, r;

double cal(double x) {
    return sqrt(x*x+(g-r)*(g-r))+sqrt((w-x)*(w-x)+(h-r)*(h-r));
}

int main() {
    int T;
    scanf("%d", &T);
    while (T--) {
        cin >> w >> g >> h >> r;
        double l = 0, r = w;
        while ((r-l) > 1e-9) {
            double lmid = l+(r-l)/3;
            double rmid = r-(r-l)/3;
            if (cal(lmid) < cal(rmid)) r = rmid;
            else l = lmid;
        }
        printf("%.8lf %.8lf\n", sqrt(w*w+(g-h)*(g-h)), cal(l));
    }
    return 0;
}