TopCoder problem "MirrorPath" used in SRM 237 (Division II Level Three)



Problem Statement

     NOTE: This problem statement contains an image that may not display properly if viewed outside of the applet.

You will be given the map of a maze containing mirrors. There will be exactly two openings on the boundary of the maze. A laser shined through one opening will reflect off the mirrors and exit through the other opening. You are to write a method that outputs the map of the maze with the laser's path drawn in it.

Mirrors are always at a 45-degree angle to the axis of the maze, and deflect the laser at a right angle. The maze will consist of walls ('#'), open spaces ('.'), and mirrors ('/' and '`') arranged on a regular grid. Your method should replace some or all of the '.' characters in the map with '|', '-', and '+' characters, indicating the open spaces where the laser travels vertically, travels horizontally, and crosses its own path, respectively.

For example, given the following three mazes:


    #######    #######    #######
    ##....#    ##/..`#    ##/..`#
    ##.##.#    ##.##.#    ##.##.#
    ##.##.#    ##.##.#    ##.##.#
    ..`...#    ...../#    ../../#
    ##.####    ##.####    ##.####
    ##.####    ##.####    ##.####

the laser would be reflected as shown in the following figure:

and the solutions for each of these three examples are as follows:


    #######    #######    #######
    ##....#    ##/--`#    ##/--`#
    ##.##.#    ##|##|#    ##|##|#
    ##.##.#    ##|##|#    ##|##|#
    --`...#    --+--/#    --/--/#
    ##|####    ##|####    ##|####
    ##|####    ##|####    ##|####

Note that the laser can bounce of both sides of the same mirror.

 

Definition

    
Class:MirrorPath
Method:path
Parameters:String[]
Returns:String[]
Method signature:String[] path(String[] map)
(be sure your method is public)
    
 

Notes

-Since '\' is a special character, we will use the '/' (forward slash) and '`' (back quote) characters to indicate mirrors in the input.
 

Constraints

-map will contain between 3 and 50 elements, inclusive.
-The length of each element of map will be the same, and be between 3 and 50, inclusive.
-map will contain only the characters '#', '.', '/', and '`'.
-Exactly 2 characters on the boundary of map will be '.'. All other characters on the boundary will be '#'.
-The characters in the four corners of map will be '#'.
-The map will be such that if a laser is shined through one opening on the boundary, it will exit through the other opening.
 

Examples

0)
    
{ "#.#",
  "#.#",
  "#.#" }
Returns: {"#|#", "#|#", "#|#" }
1)
    
{ "############",
  "#######/....",
  "######//####",
  "#####//#####",
  "####//######",
  "..../#######",
  "############" }
Returns: 
{"############",
"#######/----",
"######//####",
"#####//#####",
"####//######",
"----/#######",
"############" }
2)
    
{ "#######",
  "##/..`#",
  "##.##.#",
  "##.##.#",
  "...../#",
  "##.####",
  "##.####" }
Returns: {"#######", "##/--`#", "##|##|#", "##|##|#", "--+--/#", "##|####", "##|####" }
This is the second example in the problem statement.
3)
    
{ "###########.#",
  "#/........./.",
  "#.#########.#",
  "#`........./#",
  "#############" }
Returns: 
{"###########|#",
"#/---------/-",
"#|#########|#",
"#`---------/#",
"#############" }
This is similar to the third example in the problem statement.
4)
    
{ "########.##",
  "#./......`#",
  "#../.`....#",
  "#.`...../.#",
  "#....`.../#",
  "###.#######" }
Returns: 
{"########|##",
"#./-----+`#",
"#.|/-`..||#",
"#.`+-+--/|#",
"#..|.`---/#",
"###|#######" }
5)
    
{ "##.########",
  "#.........#",
  "..`.`.....#",
  "#..`......#",
  "#.`.`.`...#",
  "#....`....#",
  "#...`.`.`.#",
  "#.........#",
  "#.....`./.#",
  "#.........#",
  "###########" }
Returns: 
{"##|########",
"#.|.......#",
"--`-`.....#",
"#.|`|.....#",
"#.`-`-`...#",
"#...|`|...#",
"#...`-`-`.#",
"#.....|.|.#",
"#.....`-/.#",
"#.........#",
"###########" }

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4462

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=6536&pm=4462

Writer:

legakis

Testers:

PabloGilberto , lbackstrom , brett1479

Problem categories:

Geometry, Simple Math, Simple Search, Iteration