HNUOJ_10046

最新推荐文章于 2021-08-09 18:19:24 发布

原创

最新推荐文章于 2021-08-09 18:19:24 发布 · 1k 阅读

2 ·

CC 4.0 BY-SA版权

文章标签：

#算法

本文详细介绍了自适应Simpson积分法，包括原理、公式推导及C语言实现。通过将积分区间不断细分，利用二次曲线逼近原函数，确保在设定精度下求得准确的积分结果。同时，强调了积分函数连续性和预处理图形的重要性。

Bridge

Time Limit: 1000ms, Special Time Limit:2500ms,Memory Limit:32768KB

Total submit users: 153, Accepted users:110

Problem 10046 : No special judgement

Problem description

A suspension bridge suspends the roadway from huge main cables, which extend from one end of the bridge to the other. These cables rest on top of high towers and are secured at each end by anchorages. The towers enable the main cables to be draped over long distances.

Suppose that the maximum distance between two neighboring towers is D, and that the distance from the top of a tower to the roadway is H. Also suppose that the shape of a cable between any two neighboring towers is the same symmetric parabola (as shown in the figure). Now given B, the length of the bridge and L, the total length of the cables, you are asked to calculate the distance between the roadway and the lowest point of the cable, with minimum number of towers built (Assume that there are always two towers built at the two ends of a bridge).

Input

Standard input will contain multiple test cases. The first line of the input is a single integer T (1 <= T <= 10) which is the number of test cases. T test cases follow, each preceded by a single blank line.

For each test case, 4 positive integers are given on a single line.
D - the maximum distance between two neighboring towers;
H - the distance from the top of a tower to the roadway;
B - the length of the bridge; and
L - the total length of the cables.

It is guaranteed that B <= L. The cable will always be above the roadway.

Output

Results should be directed to standard output. Start each case with "Case #:" on a single line, where # is the case number starting from 1. Two consecutive cases should be separated by a single blank line.

For each test case, print the distance between the roadway and the lowest point of the cable, as is described in the problem. The value must be accurate up to two decimal places.

Sample Input