Zipline（ 牛客2021年度训练联盟热身训练赛第三场 ）

链接：https://ac.nowcoder.com/acm/contest/16303/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≤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: 1 000 0001≤w,g,h≤1000000, and 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 .

示例1
输入

2
1000 100 100 20
100 20 30 2

输出

1000.00000000 1012.71911209
100.49875621 110.07270325

题意：

求Cable的最小和最大长度

题上其实已经描述了什么时候为最长？什么时候为最短？
下面这个英语句子就是：
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.

思路：
那么如何直白的表达这个题并可以成功的做对呢？
直接上图！

此时为最短 红色线即为所求

此时为最长，绿色线即为所求

代码：

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
using namespace std;
typedef long long ll;
int main()
{
	int t;
	scanf("%d",&t);
	while(t--)
	{
		double  w,g,h,r,tt;
		scanf("%lf %lf %lf %lf",&w,&g,&h,&r);
		if(g<h)
		swap(g,h);
		double rr=g-h;
		double ww=sqrt(w*w+rr*rr);
		double wq=sqrt(w*w+(g+h-2*r)*(g+h-2*r));
		printf("%.8lf %.8lf\n",ww,wq);
	}
	return 0;
}