Chris and Road

题意翻译

人在 $(0,0)$ 沿着 $y$ 轴竖直向上跑，一个 $n$ 顶点凸包形状的汽车水平向左开，人的最大速度为 $u$，汽车的速度为 $v$。问人最少需要多长时间才能跑到 $(0,w)$ 处（记为 $t$）。 输入第一行 $4$ 个整数，分别为 $n,w,v,u$。 接下来 $n$ 行，每行 $2$ 个整数，分别为 $x_i,y_i$，表示汽车凸包的顶点坐标。 输出一个浮点数 $t$，表示过马路的最少时间。 $3\le n\le 10000，1\le w\le 10^9，1\le v,u\le 1000，-10^9\le x_i\le 10^9，0\le y_i\le w$。输出与标准答案之差小于 $10^{-6}$ 即为正确。

题目描述

And while Mishka is enjoying her trip... Chris is a little brown bear. No one knows, where and when he met Mishka, but for a long time they are together (excluding her current trip). However, best friends are important too. John is Chris' best friend. Once walking with his friend, John gave Chris the following problem: At the infinite horizontal road of width $ w $ , bounded by lines $ y=0 $ and $ y=w $ , there is a bus moving, presented as a convex polygon of $ n $ vertices. The bus moves continuously with a constant speed of $ v $ in a straight $ Ox $ line in direction of decreasing $ x $ coordinates, thus in time only $ x $ coordinates of its points are changing. Formally, after time $ t $ each of $ x $ coordinates of its points will be decreased by $ vt $ . There is a pedestrian in the point $ (0,0) $ , who can move only by a vertical pedestrian crossing, presented as a segment connecting points $ (0,0) $ and $ (0,w) $ with any speed not exceeding $ u $ . Thus the pedestrian can move only in a straight line $ Oy $ in any direction with any speed not exceeding $ u $ and not leaving the road borders. The pedestrian can instantly change his speed, thus, for example, he can stop instantly. Please look at the sample note picture for better understanding. We consider the pedestrian is hit by the bus, if at any moment the point he is located in lies strictly inside the bus polygon (this means that if the point lies on the polygon vertex or on its edge, the pedestrian is not hit by the bus). You are given the bus position at the moment $ 0 $ . Please help Chris determine minimum amount of time the pedestrian needs to cross the road and reach the point $ (0,w) $ and not to be hit by the bus.

输入输出格式

输入格式

The first line of the input contains four integers $ n $ , $ w $ , $ v $ , $ u $ ( $ 3<=n<=10000 $ , $ 1<=w<=10^{9} $ , $ 1<=v,u<=1000 $ ) — the number of the bus polygon vertices, road width, bus speed and pedestrian speed respectively. The next $ n $ lines describes polygon vertices in counter-clockwise order. $ i $ -th of them contains pair of integers $ x_{i} $ and $ y_{i} $ ( $ -10^{9}<=x_{i}<=10^{9} $ , $ 0<=y_{i}<=w $ ) — coordinates of $ i $ -th polygon point. It is guaranteed that the polygon is non-degenerate.

输出格式

Print the single real $ t $ — the time the pedestrian needs to croos the road and not to be hit by the bus. The answer is considered correct if its relative or absolute error doesn't exceed $ 10^{-6} $ .

输入输出样例

输入样例 #1

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

输出样例 #1

5.0000000000

说明

Following image describes initial position in the first sample case: