BallBouncing | Topcoder Archive

Problem Statement

A ball is moving diagonally on a rectangular board composed of unit squares in rows rows and columns columns. Each square is identified by its row and column number. The lowermost row is marked row 0 and the leftmost column is column 0.

The ball is initially located in the middle of a starting square given by two integers, startrow and startcol, and is moving diagonally up-right at an angle of 45 degrees. Whenever it reaches a wall, it bounces off it at a right angle (an angle of 90 degrees) and continues moving. If the ball runs into a corner, it bounces back in the opposite direction from which it came..

A number of holes have been drilled in the board and the ball will fall in upon reaching a square with a hole. Given the board size, starting location and locations of holes, return the number of times the ball will bounce off a wall before falling into a hole, or -1 if the ball will continue bouncing indefinitely.

Definition

Class:: BallBouncing
Method:: bounces
Parameters:: int, int, int, int, String[]
Returns:: int
Method signature:: int bounces(int rows, int columns, int startrow, int startcol, String[] holes)
(be sure your method is public)

Notes

Bouncing back from a corner counts as only one bounce.

Constraints

rows and columns will be between 1 and 1000000, inclusive.
startrow will be between 0 and rows-1, inclusive.
startcol will be between 0 and columns-1, inclusive.
holes will contain between 0 and 50 elements, inclusive.
Each element of holes will be formatted as "row column" (quotes for clarity), where row and column will be integers with no leading zeros representing a square inside the board.
There will be no holes at the starting position of the ball.
No two holes will occupy the same position on the board.

Examples

```
8
```
```
11
```
```
2
```
```
1
```
```
{ "1 5", "5 3", "4 4" }
```
```
Returns: 3
```
This example corresponds to the image in the problem statement.
```
6
```
```
5
```
```
5
```
```
3
```
```
{ "1 3" }
```
```
Returns: 7
```
Bouncing back from a corner counts as only one bounce.
```
6
```
```
7
```
```
4
```
```
4
```
```
{ }
```
```
Returns: -1
```
With no holes, the ball is bound to bounce around for quite a while.
```
3
```
```
3
```
```
1
```
```
1
```
```
{ "2 2" }
```
```
Returns: 0
```

{ "4 1", "3 2", "4 3", "2 1", "3 0", "5 2" }

Returns: -1

{ "854350 4982" }

Returns: 1662562

```
5
```
```
7
```
```
3
```
```
4
```
```
{ "0 6", "2 3" }
```
```
Returns: 5
```
```
1
```
```
5
```
```
0
```
```
1
```
```
{ "0 3" }
```
```
Returns: 2
```

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