TopCoder Statistics - Problem Statement

Problem Statement

You are playing a strategy game on a rectangular board. The board is divided into a grid of unit square cells. Some of the cells are occupied by enemies. It is now your turn and you want to eliminate as many enemies as possible.

Some of the cells that are not occupied by enemy units contain your laser towers. Each laser tower is pointed in one of the four cardinal directions. The tower can target any single cell in its direction and eliminate all enemies in that cell. Note that the tower is tall and can target any cell in its direction, even if there are some enemies in cells that are closer than the target cell.

For each tower, you have to decide whether it is going to shoot or not. Then, you have to choose a valid target cell for each of the towers that is going to shoot. Finally, all selected towers shoot their lasers at the same time and they eliminate all enemies in their target cells.

You are also given two important pieces of information about the laser towers:

For safety purposes, the towers were designed in such a way that no tower can target another tower. (You may assume that this is true in all test cases.)
When you fire your laser towers, their laser beams are not allowed to cross, not even at their endpoints. That is, for each cell on the board there can be at most one laser tower that is shooting at or over that cell.

You are given a String[] board that represents the board at the beginning of your turn, using the following format:

Empty cells are represented by the character '.' (period).
Characters '1' through '9' represent cells that contain 1 through 9 enemy units.
Characters 'A', 'V', '<', and '>' represent laser towers pointed north, south, west, and east, respectively.

Return the maximal total number of eliminated enemies.

Definition

Class:: LaserTowersDiv1
Method:: countMaxEnemies
Parameters:: String[]
Returns:: int
Method signature:: int countMaxEnemies(String[] board)
(be sure your method is public)

Constraints

board contains between 1 and 50 elements, inclusive.
Each element of board contains between 1 and 50 characters, inclusive.
All elements of board are of the same size.
No tower is directed towards another one.
Each character of the board is 'A', 'V', '<', '>', '.', or a digit between '1' and '9', inclusive.

Examples

{ ".9", ">3", ".A" }

Returns: 9

The lasers shouldn't cross (Even at their endpoints)
{ ".......................9<>9.......................", "......................99<>99......................", ".....................998<>899.....................", "....................9988<>8899....................", "...................99888<>88899...................", "..................998887<>788899..................", ".................9988877<>7788899.................", "................99888777<>77788899................", "...............998887776<>677788899...............", "..............9988877766<>6677788899..............", ".............99888777665<>56677788899.............", "............998887776655<>556677788899............", "...........9988877766555<>5556677788899...........", "..........99888777665554<>45556677788899..........", ".........998887776655544<>445556677788899.........", "........9988877766555444<>4445556677788899........", ".......99888777665554443<>34445556677788899.......", "......998887776655544433<>334445556677788899......", ".....9988877766555444332<>2334445556677788899.....", "....99888777665554443322<>22334445556677788899....", "...998887776655544433222<>222334445556677788899...", "..9988877766555444332221<>1222334445556677788899..", ".99888777665554443322211<>11222334445556677788899.", "998887776655544433222111<>111222334445556677788899", "AAAAAAAAAAAAAAAAAAAAAAAA..AAAAAAAAAAAAAAAAAAAAAAAA", "VVVVVVVVVVVVVVVVVVVVVVVV..VVVVVVVVVVVVVVVVVVVVVVVV", "998887776655544433222111<>111222334445556677788899", ".99888777665554443322211<>11222334445556677788899.", "..9988877766555444332221<>1222334445556677788899..", "...998887776655544433222<>222334445556677788899...", "....99888777665554443322<>22334445556677788899....", ".....9988877766555444332<>2334445556677788899.....", "......998887776655544433<>334445556677788899......", ".......99888777665554443<>34445556677788899.......", "........9988877766555444<>4445556677788899........", ".........998887776655544<>445556677788899.........", "..........99888777665554<>45556677788899..........", "...........9988877766555<>5556677788899...........", "............998887776655<>556677788899............", ".............99888777665<>56677788899.............", "..............9988877766<>6677788899..............", "...............998887776<>677788899...............", "................99888777<>77788899................", ".................9988877<>7788899.................", "..................998887<>788899..................", "...................99888<>88899...................", "....................9988<>8899....................", ".....................998<>899.....................", "......................99<>99......................", ".......................9<>9......................." }

Returns: 1296

One of the biggest maxflow inputs.
{ "..V..", ">.54.", ".>3.6", "9..A." }

Returns: 12
{ ".9V.", ">..7", ".A1." }

Returns: 10
{"."}

Returns: 0
{">2"}

Returns: 2
{".8<"}

Returns: 8
{".6.<"}

Returns: 6
{"7<>.6"}

Returns: 13
{".>.5.."}

Returns: 5
{"7","A"}

Returns: 7
{">5",">3"}

Returns: 8
{">61","..A"}

Returns: 7
{".>75","9
Returns: 16
{"57>6.","AA>5."}

Returns: 23
{".>...7",">...5."}

Returns: 12
{"2","A","."}

Returns: 2
{"V8","7A",".."}

Returns: 15
{"V5V","7..",".A4"}

Returns: 16
{">8..",".>64",".5
Returns: 23
{">6.3.",".AV.V","7.7<5"}

Returns: 18
{"..6..<",".6..<.",">....7"}

Returns: 19
{"2","A","V","6"}

Returns: 8
{">5",".3",">7",".A"}

Returns: 12
{">2.","V.7","3
Returns: 15
{"887<","6A.V","A.A6","..>7"}

Returns: 36
{"68","5<.>6",">.85.",".>.7."}

Returns: 40
{"V...V.","5....<",".V>.67","67.>.6"}

Returns: 26
{"7","A","V","7","."}

Returns: 14
{".3","VA","7<","3V",".7"}

Returns: 17
{">4.","25<",".7<",".A.",".5<"}

Returns: 21
{"7.<5",".VVA",">71.",".96<",".2.<"}

Returns: 31
{"15<..","6..7<","9777"}

Returns: 49
{".95<.V",".A>.59","5..6.","5..7>5"}

Returns: 50
{"7","A","V",".","6","."}

Returns: 13
{"V.","78","..",".A","7<","9<"}

Returns: 31
{"3.7","6<.","AV.",">6.",">.4",".3A"}

Returns: 19
{".V66",".5A.","5.>5","A.VA",">.5.",">51."}

Returns: 32
{"7.>67",".VVA2","A5.VA",".6..<","6..9<",">.36."}

Returns: 46
{ ">...5.", "VV7V.6", "...7<.", "24..
Returns: 41
{ "........7..7......4...<...V9.5.", ">.........2.........5..46......", ".6...........9..<..>...5.......", ".6...................<..A>...5.", ".V>....................6.......", ".....57.............<...>....7.", "..............6.......................61..", "..V.......V..A.....>.....5.....", "......7....V....>.........7....", "1...........<>..............6..", "............5...........<......", ".........6..V.......V...V..A...", ".2...........<....A..>....7....", "5..........................<...", ".............V...5...>.....6...", "........5.......V.V....A...>.8.", ".....A.........7.....>......5..", "96.........................<...", "....AV..............7V.....VA.A", "..............5....6........<.V", "..6................<........V..", "....V..............>.......5..6", "8.6................<...>....6..", ".........A.............V.....A.", ".....6A........A.A.>.....6.....", "69....<.A>.............3.......", "...2.....<....A.......>...2.6..", "...76..5.....7..7..5........7<.", "...8.......6..<..V5>.....9..7..", "....7.....5.5.<>.4...7.556.4..."}

Returns: 328
{"..2..6..3..7...3..........4..<.V",".VA.....A.>.................5.7.","5.....6..7<...>.............5...","9..6....7..66...","1...7.........2",".8<.....VV................A..V..","..>...5.....6....1..........6...","A......7........6..5..7...V.....",">.........................7.....","..V...........V..........>.....2",".........................V......",">..........................2....",".7...........A..............A...","V............>..........1.......","....A......A.>................3.","..1..........<.....AA.......>..4",".......5..........7<.6......V...","....V...............V...A.......","3.............7.........<....6..","...1............9.",".......A..6....5A.......V..A...7",".....A.....>............5.6.....","...A.........>........6..5......",".6.........5.....","5.......5...<>.........7........","6.............6....<..........A.",".............5.............<..>1","...........7..........<....>5..8",".6.......6............6..","....55..............53...4.13.3.5..25.5."}

Returns: 335
{"6.....6......4.....<...8..8...V..","1..6....<....A..>...1.....7....6.","....6.........6..........3..<....","3<...>.........5.............5...","2....<.>..................7......","..68.<.>............7............",".....5.....................<>.4..","A.......V..6.V5..7V..5.A.AAV>...2",".V...V..........V..>....5.....6..",">.....6.........................9",".......V..7.6..6....A....V..V...6","...................V......V....A.",".........5.......A..>..........1.","V................V..V..>........3","..4............................<.","..........A...........6>........6","..........V..................A.>1","..............A........V.....>.3.","....A................A.......>..9","..AA>..................9.........","8.<.........A.>...........7......",".52",".3..<...5A.A............A.......A","1...<.A..>..............5........","..>6......6...............7......",".5<.>.........6...5.7......6.....","..>..........5.........5.....7...",".7.......5....<..5...>...7..7.5.9","......7.......2",".....5...............4.........<.","5...........9.........6.3.......<"}

Returns: 344
{"........75....7........<..5.>...97","...7......<>.................75..5",".7.........6.....6....9..2......3..............5","5..7..........5....9............<.","..5.6.........6.................<.","......5....................<...V.A","............5....5..8............<",".....5...5....5.........1","...........................5.....<","..6.......<..>.....5..............","A.A.A.VVA.....A.>................7","V.......V....>..............5.....",".................7...........<...V","..VA.A...A...V>...............5...","..............7...............5","...V.V........V>.............7....",".1..<...........>..........6......",".................5...........4",".A.......V..A..V.AAAA.>.....5.....","...67....................<...V..>9","..............7.................<.","...6.......................2..<.V.",".V..>.................5...........","..5.....6.................7","5....6.5......8..........7..",".....5...........<>..........6....",".........7......<>..............7.",".6........<>...................4.7","....6.7...<>...7.......2...7.9....",".7....5925..<4..>.....6.51.....548"}

Returns: 361
{".>.6....................6....8.....",">.....................6.........556","8<.A>........................6.....","..6.............8...........9.","..............7.............<.6...V","........6.................<>.6.....","....7.....................1","7<.>..............7...7............","..6.......<>..................7....",".................7...........<>..6.",">..............7...................",".>...................8.........6...",".7..<>......................7......","6.........<>.............6.........","..6..............5............<>.5.","V....>.....................6.......","5 ...........................5...",".>..............................5.6","...............7.................<.","5..................7............",".>..........................7......","..5..................6..........",".....7..................6......","...6<>......................5......",".............5................<.>.5","4<.>............6..................","7.3.........5.............<.>.5....","..5........................86.",".>............7..............527..."}

Returns: 358
{"6.5..2..<......V......5V7..>9..","........7.....5...<>.6..6....6.",".>.1...3.......5....9.........7","5........3.......<..A....7V>.4.",".........7.......<..V......>..8",".....5.............<.......>.8.","6..6..............<>.........8.",".......6..........................5........7..",".5................2","9<..>..........6...............","8<....>......5.................","2...............5...7.......",".6.................<..V......A.",".>.................77..........","A.AA..VAVA>.............7......",".6.....<.>............5........",".>............7...........7....","5<>...................6.......6","...............5.........<.7AV.","......7....<>.............5....","V.V.>...........6..............",".5.....<.VVVVV>1.8.........5...","1<..>........................95",".>....................5........",".5..............1....<...V..>.3","5<..V>............5............","8<.>.....................5.....","......7.69.3......1...4.<...V..","7>3.4.2...5.66..5........3..1.."}

Returns: 374
{".........135...1..........<>8.3.","..8.6..............4..9....<..AV","..58.6<>...9........7.......7...","......6..............<.>....75..","6............................5..","7..<.>.......................7..","..>.........5...............5...","6.<>................7...........","............5....4.....<.....V..",".7.............7...........<....","....1.....5.............5....","........6...........<..>.5.....6","..6................<...V..>....7","6.<>................6...........","..>.....................6.......","....5..........<.AA>..5.........","..........5........<.....A>....6",".........5.................6....","........5.................<.V...","......7...<..>............5....5",".......7.............<>...5.....","A...AV...A.A.V>...........7..6..","V.V......>................7.5...","...>........3..........77.......","...6............3...<>........5.","3................7......","4....5...<>.................5...",".A.......VV>...........7........","2.6<68>..2..................6...",".......6253..5.....4...9.9.<...."}

Returns: 357
{"9..........8.....6..1...989<>..4.","A.75>.6...4....9.4...3..6.....54.","..9.<.A..>..................6....",".2..<.>....................5....7","....7.......................<.AAA",".....6...<...>..................5","V.........AA.V...A67AA..A....7VVV","35..<..5...V5..A.....V.7...>....7","2.........<....V.V..V...>.......4","....V.....V...........6.V.AV>...4","..1...<..V..A.6.6........A>.....3","......V...........A.........V....","............V.....V...A..>......9",".....68.7.............<..>......1","..........8...........<..VV......","......................V..........","................A................","...A............>.........9......",".2.<.......7....V7.....A.........","4..<...A..6............>7.....77.","6......<......A....A...>.......9.",".A...........................A...","2.7.......8...",".>.....................8.........","5>....7...............1..........",".9....................5<..5..V...","2.......7..7.66..5.......7......","1.<>..........6.5...5........6.5.",".......6...........<.............","6<>...........5........5...5....6",".>......................56......."}

Returns: 390
{"161<>.............3.....7.........","VAA>..................6........4..","..5..............................<","....6......<>..................6..",".>......................5.........","..7.............................<.","..............7.................<.",".7<..>...................6........","..5.........................5..","............7...............7.","...7.....<>....................5..",".5...........<>..1........5.......","8<>.............................7.","..........5..................<>5..",".................5............6","8..<.>.......................5....","...5...........................<>9","...............7............<.>..6","9.........................7...","6...VV>..............5............","..557...........5...........<>..5.","..7..............................<","7..........................5..","..........5................<.>...5","6..........................<>....5","...6..<>...........5.....9........","...............5...............<>6","...7....................5......<.V",".....6....................<.>.7...",".>.................7.............5",".....7....................<>...5..","7....6..........................<."}

Returns: 356
{"...5......1.68......4.<>.....8...6.","655.2.<>.................61...3....","..A>.......................6.......",".7.<.>..........................5..",".........1.....6..................<","......5....5......<>...........5.5.","...........5............................6.5...","A.>.............6..................","........7.................5.....",".6......7.....................<..A.",".1<>....................7.......5..","V...AVV.>...................6......",".....6.......................<.A.V.","..>........................5.......","......6.....................................7....6","..7...........................7",".AV>............5..................",".5..............................<..","3<.>.............................7.","...5.3.....................<>.....6","....5....................<..>...7..",".7..<....>...........6.............","..5.........................6.",".7.....<.>........4...............5","7>...........................5.....",".6...........................5..",".............6.....9....<.A..V>...5","5...................<>...8.......5.","3<9V>..................65....7.....","...5..8.2......7...........<>..6.96"}

Returns: 358
{"..7.......945......8.4.....4<..","....65...8..4.....<..A>...87...","...............7............<.V","......3.....7.........<>...7...","..8..<.VV..AAV>.....9....6.....","........5..<>..........5.......","...6.......6............<.AA>.8","............5..............<>.9","1<..A>...............6.........",".V.......AA.>............5.....","....>.................6........","6........6..................<5.",".......6..............5...",".....5..........<...>....15....",".....5....<...>..........7.....","7......................5..","..A.......V....>...........5...","1...<>..........6..............","7........................5.6","........7..<...>.........7.....","...............5...........<>.3","...............5..........<>..9","......7.....................<..","65 ......................7...","A.>..........7............7....","V.VV>.................6........","....7..4....................<..","5.........6...................7......","........7.................<..A.","5...5....<.VV.VVV>............5",".....6..7...8.6..<5AV>2.3.....7","...1.......2..731...5..2.<.>5.5"}

Returns: 374
{"57495...8","6.........3.<..>8.7.7.....7...3.","7...................3..","..AAA>...........6......6.......",".A.>..........5........2.......4","..6.............<>.5........5..7","......7..........<.A..5......V5A",".>............7.................","..5.........................7",".>...........7..................","6..................<....A.A...A.","..5...................6","65.................2..","3<>...............6.............","...........5..............<.....","...6......<9.5.>....7....6......","......7...............<>.......9","..........7........8.<....V.A...","8<.V>...9...........5......7....","2.<.VV>................6.....7..",".......7......5<.....V.>.......9",".>...........6..................","A......>..........6............7","V.>.............5...............",".....6......<..V......V.V...>.2.","5<....>.......5..8............5.","....3..7............<..>.......6",".4<...>............7......7.....",".>..............7..6............","1<>..4.........27...............","2..9....7.........3.<77.7A..>8.."}

Returns: 398
{".5.1<8..3...>....4..9..7....4....","...6......9...<>..4....1........7","................5.....3...<.....7",".>8..........5...................","1.......................6....","1<>.....................5........","1..5<.>......................77..","..5.....................<.>....2.",".........6.............1.","A..>.............7.......5...6...",".7............<..A.....A..V.A....","...........5..........<.......A7.",">...........6..............5.....","67.","2...6....3......",".V....V......6..5.......7.....V..","4.....................<......V...","......6..5<.V.>.................8","9......................2","....6..............6..<....A...>2","4.............<......A>.........4","5....<6..A..6A>...7..........7..3",".7.6.....<.A....A........A.>...2.","5...<..A7V.V.VV5V7.......V......A",".65.V>.........5....7..7..7.5.5..",".....7.........................<.",".....6...............<.....>...7.","64...<.V..>..................7...",".....6.....................<...VV",".4...<....>...........6.........4","....6>...2.9....2...5............","..7....9.....83.......<..6.>..13."}

Returns: 382
{"6V.......67..5.....V..V>..67.75.5.","..1...5....7...<.......V6......>36","A.V....5....>...6....5...7.3....7.","........6A...A.>................5.",">....5......................5..5..","V..5.....V...V...6.......A.....>.3","..7............................<..","........A..AV........A.........V..","...55...<..V........5V...>.......6","7.......<......V..7......V........","4.......<.................A.A.....","8.......<.................V.V.....","........>...............3.........","..5.....V..................A......","......3.......5............<......",".....A.......6....A........>.....1","8....<...........AV.............AA","8....6","...........7...............<....V.","6....5.........5...........<.....V","....A......5...............V.V....","....V..............6.5.7......A6..",".6...VV.......................V...","..................................","..................................",".........5..........A...A7........","....................V...>.....7.6.","..1.........7...........<..7.7..6.","....5.........A.A6......>.....9...","........5.A...V.V.......>.......96",".......A..>...........6...4.......","...A..6...>....5..........6.......","..5<.6.>......965.6.7.......5....."}

Returns: 372
{"..V>....39.2.8...97.........5.3....","..2<.V5.AA.AVA44VA>9........6......","..............7............<.>..6..",".7.<...7>..........5...............","..........6......................<.","9..<..AA.>......................5..",".3.<..>...........................5","6........6................<..>..7.7","......5..<.>...................57..","4..<..>.......................6....",".7..6........6.............<.>....4",".........6...<.A.>.............7...","......7......................<.6.V.","..........6...6...............4.","................6...........<.AA...","9.................7...","..65......................<..V.V...","....5.............7.........","..............6............<>..5..3","..6.....................<>.5.6.....","AA.....>......................5....",".............5..............<.>...6",".....6..............<>........6....","..............5............<>.....7","7...............7.............<....","6.......<.V..>.................5...","7..<..>........5.......7...........","............5.............1..................6......","VV.>......1...................6....","2.....4...6..............<3.>.....5",".2........686....72........3..1...<"}

Returns: 405
{"V.>........1.5.....6.....66....","..5............<...A.>.....6...","........7..............<....>8.",".6.7..7.....................<..",".....5.............<..5.6A..V..","4........5..........",".2<..V.....A.............V.....","..........6........<.>........6",".......7...........<6>.......9.","............7...7..<.V..A..6...",".A........7........V...>.....67",".V.........V.....6......V......","2.<..........V.>.........1...7.","..>.............7.......1.5....","7.>.7...6.........7........2...","..>...........6...............4","9...............3","3........7.....<.......V...A...","........1......<...........V...","..V>..7.......................1","...>.........................2.","...>.......6..................8","...>..................2.....7..","7..<......A......A.............","7...........7.....","1..............<.V..A..........","37.<.....A..A7.......7A........","8...<..AA.V.V...A7A...>..5....8","...6..........................5.....","...6..........<>.........5.....","..........7.......2.<.....A5.AV","...>...39...3...6.....7........",".6..<....>4.....8..........6..5"}

Returns: 383
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Returns: 383
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Returns: 403
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Returns: 386
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Returns: 399
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Returns: 411
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Returns: 432
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Returns: 447
{"7.....8..67.......9.....1........<......VV.9V2...","....V..V....VVV.....>.7..1.....1..2642....4..7...","...1.......4...6.....7....9.9.................5<.","...................6V>.....9....................6","...7............61...........................5.","....................5................<...........","........>.................6......................","..........................6................<.....","........V>........................5..............","..>.............................6................","..V..>...............5...........................","....................6.....................<...A..",".............6.....................................................6...","......A............>.........................6...",".>...............5...............................","......>.........................7.....7..........","...................6.......................................5..............","........5......................<....>...........2",".>..................5..................6.........",".7.....................<.......V....>..........7.",".>............................7..................","..7............<>................7..........3....",".....7....................<.A................A...","............5...............<......A>..........2.",">..............................6.................","..........5..9......6..............<>..........2.","...>....................7........................",".>...............7...............................","...>..........8..............5...................",".......6.............................6",".............7......................<...........A",".........6....................<.....V.....>....8.","...V......V....V>...................7............","......>......................5.............6.....","..6......9....................<.......AA.........","...6....................................9.<......","............6..........................<..V...7..",".>......8...6......7.................6.........7.","....6............<>....................7.........",".....................7.......................<...",".......6...A....VVV...A..>........6.............7","...........>...6.....9....................7......","..6.....6.............<...V>....2..2......86.....",".6..4............7....<.A>..1.......7....2....6..","...2.>....8.....2.9.......1.54.4.7...8..........."}

Returns: 432
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Returns: 433

Statistics

Problem Statement for "LaserTowersDiv1"

Problem Statement

Definition

Constraints

Examples