HDU 5033 Building(类凸包+向量叉积的应用)

Building

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 1138    Accepted Submission(s): 321
Special Judge

Problem Description

Once upon a time Matt went to a small town. The town was so small and narrow that he can regard the town as a pivot. There were some skyscrapers in the town, each located at position x _i with its height h _i. All skyscrapers located in different place. The skyscrapers had no width, to make it simple. As the skyscrapers were so high, Matt could hardly see the sky.Given the position Matt was at, he wanted to know how large the angle range was where he could see the sky. Assume that Matt's height is 0. It's guaranteed that for each query, there is at least one building on both Matt's left and right, and no building locate at his position.

 

Input

The first line of the input contains an integer T, denoting the number of testcases. Then T test cases follow.

Each test case begins with a number N(1<=N<=10^5), the number of buildings.

In the following N lines, each line contains two numbers, x _i(1<=x _i<=10^7) and h _i(1<=h _i<=10^7).

After that, there's a number Q(1<=Q<=10^5) for the number of queries.

In the following Q lines, each line contains one number q _i, which is the position Matt was at.

 

Output

For each test case, first output one line "Case #x:", where x is the case number (starting from 1).

Then for each query, you should output the angle range Matt could see the sky in degrees. The relative error of the answer should be no more than 10^(-4).

 

Sample Input

3 3 1 2 2 1 5 1 1 4 3 1 3 2 2 5 1 1 4 3 1 4 2 3 5 1 1 4

 

Sample Output

Case #1: 101.3099324740 Case #2: 90.0000000000 Case #3: 78.6900675260

 

题意：n块木板，q组询问，木板的描述为xi和hi，询问的是位于x时，仰角为多少？

思路：离线处理，将询问点也视为木板，然后类似与求凸包的方法，通过维护向量的“单调性”来保证当前队列的第一个点即为目标点（即仰角的边界）。

用一张图来解释该过程：

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