LaserShooting | Topcoder Archive

Problem Statement

There is a laser cannon at coordinates (0, 0) on the cartesian plane. There are also several targets on the plane. Each target is a vertical line segment, and the endpoints of the i-th target are at coordinates (x[i], y1[i]) and (x[i], y2[i]). A random angle between -Pi/2 and Pi/2, inclusive, is chosen, and a single shot is fired. The angle -Pi/2 is straight down vertically, 0 is straight to the right horizontally, and Pi/2 is straight up vertically. A shot is a straight ray of infinite length starting from the point (0, 0). A shot hits a target if there is a common point between them. Return the expected number of targets that will be hit by the single shot. Hitting a target doesn't change the direction of the laser shot.

Definition

Class:: LaserShooting
Method:: numberOfHits
Parameters:: int[], int[], int[]
Returns:: double
Method signature:: double numberOfHits(int[] x, int[] y1, int[] y2)
(be sure your method is public)

Notes

A return value with either an absolute or relative error of less than 1.0e-9 is considered correct.

Constraints

x will contain between 1 and 50 elements, inclusive.
All elements of x will be distinct.
x, y1 and y2 will contain the same number of elements.
Each element of x will be between 1 and 1,000, inclusive.
Each element of y1 and y2 will be between -1,000 and 1,000, inclusive.
All targets will have positive lengths.

Examples

```
{1}
```
```
{-1}
```
```
{1}
```
```
Returns: 0.5
```
The only one target will be hit with probability 1/2.
```
{1,2}
```
```
{-1,-2}
```
```
{1,2}
```
```
Returns: 1.0
```
Both targets will be hit with probability 1/2.

{3,4,7,1}

{1,2,3,4}

{4,3,2,1}

Returns: 0.4623163952488826

{134,298,151,942}

{-753,-76,19,568}

{440,689,-39,672}

Returns: 1.444210260641501

This problem statement is the exclusive and proprietary property of Topcoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of Topcoder, Inc. is strictly prohibited. (c)2024, Topcoder, Inc. All rights reserved.