Statistics

Problem Statement for "Unjumpers"

Problem Statement

Unjumpers is a puzzle played on a board consisting of 100 squares in a straight line. Pawns are placed in a certain pattern on the board, and your goal is to see which other patterns can be created starting from that position. There are 3 legal moves in Unjumpers:

  1. Jump: A pawn jumps over an adjacent pawn and lands in the square immediately beyond the jumped pawn (in the same direction). The jumped pawn is removed from the board. To perform this move, there must be an adjacent pawn to jump, and the square in which the pawn lands must be unoccupied.
  2. Unjump: A pawn jumps over an adjacent empty space and lands in the square immediately beyond that space (in the same direction). A new pawn appears in the square that was jumped (between the starting and ending squares). To perform this move, both the middle and ending squares must be unoccupied.
  3. Superjump: A pawn moves 3 squares in one direction. To do this move, the target square must be empty. The two jumped squares may or may not have pawns - and they are not affected by the move.

Only one pawn can move at a time, and pawns may never move off of the board.

You are given a String start containing the initial layout of the board. Each character of the string describes one square, with the first character describing the leftmost square. In the string, '.' represents an empty space while '*' represents a pawn. You are also given a String[] targets, each element of which is a target layout formatted in the same way. The board is always 100 squares wide. The Strings given will specify up to 50 of the first (leftmost) squares of the layout. You must assume that the remaining squares are all empty, both when considering the the start position and when considering the various target positions.

For each target layout, evaluate whether that layout is reachable using any number of legal moves starting at the initial layout each time. Return the number of target layouts that can be reached.

Definition

Class:
Unjumpers
Method:
reachableTargets
Parameters:
String, String[]
Returns:
int
Method signature:
int reachableTargets(String start, String[] targets)
(be sure your method is public)

Constraints

  • start will contain between 1 and 50 characters, inclusive.
  • start will contain only '*' and '.' characters.
  • targets will contain between 1 and 50 elements, inclusive.
  • Each element of targets will contain between 1 and 50 characters, inclusive.
  • Each element of targets will contain only '*' and '.' characters.

Examples

  1. "**."

    { "..*", "*.**", ".*.*"}

    Returns: 3

    Each of the 3 target layouts can be reached in one move - the first is one jump, the second is one unjump, and the third is one superjump.

  2. "..***"

    { "..****..*", "..***....", "..****"}

    Returns: 2

    The first layout is reachable with a little ingenuity. The second layout doesn't require any moves (it's the same position, just with some extra blank spaces shown). The third is unreachable.

  3. "*..*"

    { "*..*......", "*.....*...", "...*.....*", "...*..*...", "*........*", "*...***..*"}

    Returns: 6

    All of these layouts can be reached.

  4. "...***"

    { "***...", "..****", "**....**", ".*.*.*"}

    Returns: 3

    Only the second layout shown is unreachable.

  5. ".................................................."

    {"."}

    Returns: 1

  6. ".*."

    {"*.*",".","***","*"}

    Returns: 1

  7. "*.."

    {"*","*...","*.....","*.........",".*.....",".*"}

    Returns: 4

    Position A

  8. "*..*"

    {"*..*","***", "************************************************", "**...*", "**....*", "**.....*", "...." }

    Returns: 4

    Position E (first 4 are reachable)

  9. "**************************************************"

    { "**********************************************.**.", "******************************************..*.***.", ".*****************************************..*.***.", ".**.**.**.**.**.**.**.**.**.**.**.**.**....******.", ".***..************************************..*.***.", ".***..********************************************", ".**.**.**.**.**.**.**.**.**.**.**.**.**.**.**.****", ".**.**.**.**.**.**.**.**.**.**.**.**.**....*******", ".**.**.**.**.**.**.**.*..**.**.**.**.**....*******", "**************************************************" }

    Returns: 7

    Unreachable: 2,3 and 8

  10. "****..........**.*..******..***..*"

    {"*..*.*.*...****.*", "**..**..*..****.*.*.**.....****.**", "****.*.**.***...*...*...*....*..**.****..", "..**..**.*.*****..*.*.**.***.*..*****...*...*", "*.", "..*.**.....****.*******.****", "***.**...*", "****....*.*.*.**......*..", "**..**..**..**..*..**.**.*****..****..**......**", "**.*..****......*.*", ".*..*.***.*..." }

    Returns: 4

    Random lengths...

  11. "*******.*******..*.**********.****.*.***.*"

    {"***************..**.****************.****", "***************.***...**.*****.**.*.***.***..**", "*.**.*******.*.****.*.***.**.****..****.*.*", "****.******.**.**..*.***..******.*.********.***", "***************.*****.*****.************..*.**.*", "***.*.***..***.*..***.**********************.***", "****.**********.*..****.*****.*..**.**..", ".***.**..*.**************..************.****.***", "*****.***.*.**.***.*.**.*********.*...********", "..*.****.********.*******.********.*********", "*************.**..******..*.*********..******", "**.***.*********.**************.********.**", ".***.********.*********..******..******.****", "**.****.*****.*.*.**.****..******.*....*******", "*.****.*.*.****.*****.*******.***************.****", "***.*************.*******.*.***.*..********", "***.*...********..****************.*****..*****", "****.******.*********.**.***********.***..*...***", "***********.*.******.*****.***.******.**.", "*.***.******.*****.**.******.****.****.*.**", "******.*.****.*******.******..**********.**..", "*.***.***********.*******.********..**************", ".*****.****************.*********************", "**..**.**.**..*.***.**.*******.****.******", "**.*.*.******.*.**********.*.***********.**.*****", ".**.**.**..***....**********.*******.****.*.***.", "*.******.**********************.*.******.*.*", "**.**.***.****.**.*******.***.*.*********.***..**", ".******..****.***..*****.**.************.", "..****.********.**.*.**.*.*.*********.*********", "*.****************.*****************.***.", ".****..**.**.**.***..******.****.*****.*.******.*.", "***.***.***..************.****.**.*****.*.*", ".****.***********.***.***.*.**********.*******", "**.***.**..**.***.*******.****.**********.", "********.**.***.******.****.****.*******.", "********.*.**********.**.******.**.*************", "*.****.**.**.*.**.****.*****.*******.*.*******..", "*.*******.*********.***.*************..**.", "**.********.***.*..************.*************..*", "****...**.***.**********.*..*..*****.****", ".*******.**.*.**.************.*****...***.****", "******.**..****.****.*..*.*..****************", "**.*************************.***.********.", "**.******.****.*.***..*.***********..***.****.*..*", "**..*******.*.**.******.***********.******.**.", ".**********.*.********.*******.************..**", "*.**.*****.***.**.**********.****.**.****.****", "*****.*********.*.**.**.**.*..**.****.*.****", ".**.**.****.*..*.******.**.***.*****.******.**"}

    Returns: 8

    Dense

  12. "......*.....*..........................*......"

    {"...*......................................*..", ".....*..*........*...................*.......*.", ".........****..............................*.", ".....*...........................................", "..........*..........................*.......*....", ".....................*........................", ".............*....*.*........*................", "...*.........*........*....................", "..*..***.....................................", "....*...................*..*.............", ".......................*............*...", "............................*........*....*", "............*..............................", ".............*.*...........................", "*.*..*...*.*..........*..................", "...........................................*..", "....................*.......*.....*...........", "....*............*..........................", ".......*..*...*.........*....................*...", "......................*.......................", "*..................*.....*.....................", ".....................*.........*...............", "....................................*...*..", ".................*...........*....................", "..........................................", "...............*..................*...........", ".*...................*......................", ".....................................*....", "...............................*...............", "..*...................*.....***....*............", "..............*.............................", "........*.*..........*.*...........*......", "............................*.......*........", "..............................*.................", ".......*.*...................................", "..*............................................", ".................*...............*........", ".......*...................*......*........", "....*............................*...........*..", ".........*.......*.......................", "..*..........................................", "..................*.*........................", "..........*........................*......", "...............................................", ".................................*........", "...........................................*.", ".............*..............*....**....*.....", "...*....................*................**....", "....*..............*........*.................", ".*....................................*.*....."}

    Returns: 12

    Sparse

  13. "*******.****.******************..******.**********"

    {"*********.*..******************.**.*****..********", "*****.**..**.****************.******************.*", "*****.************.**************.******.****.**.*", "****.***********..********************************", "****.*****************.********.**.***************", "******************.**.****************************", ".**.************.*****..******.*****************.*", "***************.*****.**.*************************", "*.**.*********.**********.***********************.", "**********.**.**********.******.*******.*.*****.**", "**************.*.**********.**.*******.***.*.*****", "**.******.************.*********.*****************", "*******************.*********.****.****.**********", "****.**********************************.*********.", "*****.**.*****.**.************.*.**********.******", "*****..***.*********.*******.*******.*************", "***.**************..****************************.*", "**..************.*.********.*****.**.*.***********", "*********************.**..********..*..***********", "****..*************.******.***************.*******", "**************************.***********.****.******", "***********.***********.****************..********", "******.*************.**********.*.***.*****.******", "****************.***..*.*******************.******", "**.**.***.******************.***.**.**.**********.", "************************************************.*", "****.*****.*.*********************************.***", "****.***********.**********..**.****************.*", "*************************.******.***.*************", "********.**.****.*****************..**.*.*********", "**.****************************.**.***********.***", "***.***********.*.*******.*.************.*********", "******.******************************.************", "*******.*********.********************.***********", "*********.********.****.*******.**********.*******", "****.************.*******.*.***.**.***.***********", "*****.*.**.*.*****.**********.*.************.**.**", "*.**********.****.*********.********.****.***.****", "******.*.***************.***********.*******.*****", "***********************.*******.*********.*.******", "************.***************..***************.***.", "*********.*.******.*******.*********.**********.**", "****************.***.********.********************", "********.***.*****************.******.*.***..***.*", "****.**************.***********.***.********.*****", "**********************************.*****.*********", "**************************************************", "***.***.*********.**********.********.************", "******.**.******..**************.*.***************", "************..*********.***.****************.**.**"}

    Returns: 9

  14. "*****.***************************...**************"

    {"**.***.******.*******.****************************", "***.*********.**.*.*********..********************", "**.*.*****.*******.****.************************.*", ".*********.************...****.**********.*****.**", "*****************.*.*****.************.***********", "***.**.***.**.****.********.*******.**************", "*******...**.******.*******************.******...*", "**.*********.**.***.*********.***.************.***", "**************.**.********************.***********", "****.***********************.****..*********.*****", "***********..*...****.***************.***.********", "**********.**********..*****.*********************", "********.*****************.***.**************.****", "*.***.*******.**.*********.***********************", "..**.********.************.*******.*********.*****", "****.**.****.**************.**************.*******", "****************************************.*********", "..*.*****.***.*******..*.*************************", "****************************.***********.*****..**", "***************************.**.************.******", ".***.*.**************.*************.*.**********.*", "**.*****************.***.******.*********.********", "**********..******.*.*.*******************.***.***", "***************..************************..*******", "**.************************.**********************", "*******.********.**.***..****.****************.***", "*********************************.************.**.", "************************.*******.*****************", "*****************.*********.***********.**********", "***********************************************.**", "**.****.*************.**********************.*.**.", "****.***********************.*************.***..**", "*******.**************.***************************", "***********.****.**********.***********.******.***", "*******.*************..*****..****************.***", "*************.***.****.***********.**.*.********..", "************.*******.***.***.****************...**", "************.***.*******************.*.***.*******", "*************************.********.********..*****", "******.*******.************.***.******************", "*****.***..************.****.****.*****.****.*.***", ".*****************.*********.*.**.********..******", "*.**.********************..**************.********", "**********.************************.******.*******", "*******.*.*************.*****.****..*******.**.***", "*.***********.****..*****.**.*******.***..*.******", "**********.**************..*********************.*", "***.***********.**********.********************..*", ".*******************..**.**********..*************", "******.*****.********.************..**************"}

    Returns: 9

  15. "."

    {"**..*.**", ".*.**", "*.*..*.**", "***.*...*.", "...**..."}

    Returns: 0

  16. "*"

    {"**..*.**", "..*.**", "*.*..*.**", "***....*.", "...**..."}

    Returns: 0

    Unlucky...

  17. ".*"

    {"**..*.**", "..*.**", "...*..*...*.***", "***....*.", "...*....*....."}

    Returns: 5

    All are "B"

  18. "*"

    {"*********.***.******", "***..***.*****.*.***", "****.**********..**.", "*****.********.*****", "****.*.*******.****.", "**.*******.*******.*", "****.**********..***", "..******.****.******", "*****.********..****", "********************"}

    Returns: 2

    Tests 17-20 are same targets, want to ensure all reachable. 2 "A"s

  19. ".*"

    {"*********.***.******", "***..***.*****.*.***", "****.**********..**.", "*****.********.*****", "****.*.*******.****.", "**.*******.*******.*", "****.**********..***", "..******.****.******", "*****.********..****", "********************"}

    Returns: 3

    3 "B"s

  20. "..*"

    {"*********.***.******", "***..***.*****.*.***", "****.**********..**.", "*****.********.*****", "****.*.*******.****.", "**.*******.*******.*", "****.**********..***", "..******.****.******", "*****.********..****", "********************"}

    Returns: 3

    3 "C"s

  21. "***"

    {"*********.***.******", "***..***.*****.*.***", "****.**********..**.", "*****.********.*****", "****.*.*******.****.", "**.*******.*******.*", "****.**********..***", "..******.****.******", "*****.********..****", "********************"}

    Returns: 2

    2 "E"s - total of 10. Good.

  22. "..*.."

    { "..*..", ".", "*", "..*", "..................................................", ".................................................*", "**.....................................*..*..*..*", "**..................................*..*..*..*..*" }

    Returns: 3

  23. "*................................................."

    {"*", "*.................................................", "...*.....*...**............*...**.*.*.****.*.*..**", "...*.....************.............*..............*", "...*.....******...***.............*..............*", "...*.....******...***......******.*.*.****.*.....*", "*..*..*..*...*****.......***......*.......*..*...*", "...**..*.***...***................*..*...*...*...*", "*..*..*..************....***......*..............*", "...**..*.***...******.............*..............*", "*..*..*..*********.......***......*.*..*..*..*...*", "...**..*.***...*...**.............*..*...*...*...*", "*..*..*..****...*****....******...*..............*", "...**..*.***...******.......***...*..............*", "*..............................................***", "...*.....*...**............*...**.*.*.****.*.*..**", "...*.....************.............*...........****", "...*.....******...***.............*...........****", "...*.....******...***......******.*.*.****.*..****", "*..*..*..*...*****.......***......*.......*..*****", "...**..*.***...***................*..*...*****...*", "*..*..*..************....***.........****.....****", "...**..*.***...******....***......*......***..****", "...**..*.***...******..***..***......*.....*******", "*.............***......***........*......***.....*", "*.*...............................................", "...*.....*...**...........**...**.*.*.****.*.*..**", "...*.....************....*........*..............*", "...*.....******...***.........*...*..............*", "...*.....******...***....*.******.*.*.****.*.....*", "*..*..*..*...*****........**......*.......*..*...*", "...**..*.***...*.*................*..*...*...*...*", "*..*..*..*******.**.*....***......*..............*", "...**..*.***...***.**.............*..............*", "*..*..*..******.**.......***......*.*..*..*..*...*", "...**..*.***...*...*..............*..*...*...*...*", "*..*..*..****...*****....***.**...*..............*", "...**..*.***...******.......***..................*", "*.............................*................***", "...*.....*...**............*...*..*.*.****.*.*..**", "...*.....************.........................****", "...*.....******...***.............*...........****", "...*.....******...***......***.**.*.*.****.*..****", "*..*..*..*...*****.......***......*.......*..*****", "...**..*.***...***................*..*...*****...*", "*..*..*..************....***.........****.....****", "...**..*.***...******....***......*......***..****", "...**..*.***...******..***..***......*......******", "*.............***......***........*......***.....*" }

    Returns: 32

  24. "***"

    {"*", "*.................................................", "...*.....*...**............*...**.*.*.****.*.*..**", "...*.....************.............*..............*", "...*.....******...***.............*..............*", "...*.....******...***......******.*.*.****.*.....*", "*..*..*..*...*****.......***......*.......*..*...*", "...**..*.***...***................*..*...*...*...*", "*..*..*..************....***......*..............*", "...**..*.***...******.............*..............*", "*..*..*..*********.......***......*.*..*..*..*...*", "...**..*.***...*...**.............*..*...*...*...*", "*..*..*..****...*****....******...*..............*", "...**..*.***...******.......***...*..............*", "*..............................................***", "...*.....*...**............*...**.*.*.****.*.*..**", "...*.....************.............*...........****", "...*.....******...***.............*...........****", "...*.....******...***......******.*.*.****.*..****", "*..*..*..*...*****.......***......*.......*..*****", "...**..*.***...***................*..*...*****...*", "*..*..*..************....***.........****.....****", "...**..*.***...******....***......*......***..****", "...**..*.***...******..***..***......*.....*******", "*.............***......***........*......***.....*", "*.*...............................................", "...*.....*...**...........**...**.*.*.****.*.*..**", "...*.....************....*........*..............*", "...*.....******...***.........*...*..............*", "...*.....******...***....*.******.*.*.****.*.....*", "*..*..*..*...*****........**......*.......*..*...*", "...**..*.***...*.*................*..*...*...*...*", "*..*..*..*******.**.*....***......*..............*", "...**..*.***...***.**.............*..............*", "*..*..*..******.**.......***......*.*..*..*..*...*", "...**..*.***...*...*..............*..*...*...*...*", "*..*..*..****...*****....***.**...*..............*", "...**..*.***...******.......***..................*", "*.............................*................***", "...*.....*....*............*...*..*.*.****.*.*..**", "...*.....**.*********.........................****", "...*.....**.***...***.............*...........****", "...*.....**.***...***......***.**.*.*.****.*..****", "*..*..*..*...*****.......***......*.......*..*****", "...**..*.**....***................*..*...*****...*", "*..*..*..**.*********....***.........****.....****", "...**..*.***...******....***......*......***..****", "...**..*.***...******..***..***......*......******", "*.............***......***........*......***.....*" }

    Returns: 6

  25. "*************************.********.********..*****"

    {"**.***.******.*******.****************************", "***.*********.**.*.*********..********************", "**.*.*****.*******.****.************************.*", ".*********.************...****.**********.*****.**", "*****************.*.*****.************.***********", "***.**.***.**.****.********.*******.**************", "*******...**.******.*******************.******...*", "**.*********.**.***.*********.***.************.***", "**************.**.********************.***********", "****.***********************.****..*********.*****", "***********..*...****.***************.***.********", "**********.**********..*****.*********************", "********.*****************.***.**************.****", "*.***.*******.**.*********.***********************", "..**.********.************.*******.*********.*****", "****.**.****.**************.**************.*******", "****************************************.*********", "..*.*****.***.*******..*.*************************", "****************************.***********.*****..**", "***************************.**.************.******", ".***.*.**************.*************.*.**********.*", "**.*****************.***.******.*********.********", "**********..******.*.*.*******************.***.***", "***************..************************..*******", "**.************************.**********************", "*******.********.**.***..****.****************.***", "*********************************.************.**.", "************************.*******.*****************", "*****************.*********.***********.**********", "***********************************************.**", "**.****.*************.**********************.*.**.", "****.***********************.*************.***..**", "*******.**************.***************************", "***********.****.**********.***********.******.***", "*******.*************..*****..****************.***", "*************.***.****.***********.**.*.********..", "************.*******.***.***.****************...**", "************.***.*******************.*.***.*******", "*************************.********.********..*****", "******.*******.************.***.******************", "*****.***..************.****.****.*****.****.*.***", ".*****************.*********.*.**.********..******", "*.**.********************..**************.********", "**********.************************.******.*******", "*******.*.*************.*****.****..*******.**.***", "*.***********.****..*****.**.*******.***..*.******", "**********.**************..*********************.*", "***.***********.**********.********************..*", ".*******************..**.**********..*************", "******.*****.********.************..**************"}

    Returns: 16

  26. "**************************************************"

    { "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "**************************************************", "***********************.**.***********************", "***********************************************...", "...***********************************************" }

    Returns: 50

    Perhaps solutions will find this mass of *s imposing or something.

  27. "*****"

    {"****************************", "*******", "*********************************", "*****.**************", "**************************************************", "*************************************", "*******************************", "**************", "**", "******************************", "**************************", "***************", "**************", "*******************", "************************************************", "**************************************", "***********", "*******************************************", "***********************************************", "*************************************", "**********************************************", "*", "*************.*****************************", "************************", "************************", "**************************", "***************************************", "***************************", ".*************************", "***************************", "**********************************", "*******************************************", "******", "******", "******.*****************", "********", "**********.****", "***********************************", "******************************", "*********", "*************************************************", "*", "*************.*********************", "*******************************************", "*****", "***********************************", "**", "*************************************************", "*********", "****************************************"}

    Returns: 15

  28. "****"

    {"**.**"}

    Returns: 0

  29. "*.*.****.****.*.*....*...*..******.**.*.****.***."

    {"*.*.****.****.*.*....*...*..******.**.*.****.***.", "*.****.***.**...**.***.****.***.**.", "*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*", "...*", "*.***.***.***************", "*****************", ".", "*.**.******.***...........*", "********...****...****", "*****.*****.*****.*****.*****.*****", "*.*.****.****.*.*....*...*..******.**.*.********", "*.*.*.*******.*.*....*...*..******.**.*.****.***.", "*.*.****.****.*.*....*...*..******.**.*.****.***.", "..*********.*.*.*..**....*..******.**.*.****.***.", ".................", "*.***.*****", "*....*****....****....****", "*.*.****.****.*.*....*...*..******.**.*.****.***.*", "*............*", "...*...*...*...", "**********.*************.********", "*.*.*.*.*.*.*.*.*.*", "........*.......*......*", "**************", "**************************", "..........*...*..****.***.***....*", "********", "*.*....*...*.*", "..........*...*..****.***.***....*", "..........*...*..****.***.***....*", "..........*...*..****.***.***....*", "*******.**********.*******.", "*.*.****.****.*.*....*...*..******.**.*.****.***.", "*.*.****.****.*.*....*...*..******.**.*.****.***.", "*.*.****.****.*.*....*...*..******.**.*.****.***." }

    Returns: 12

  30. "..."

    {"***" }

    Returns: 0

  31. "."

    {".", "*", ".*", "*.", "**", "..*", ".*.", ".**", "*..", "*.*", "**.", "***", "...*", "..*.", "..**", ".*..", ".*.*", ".**.", ".***", "*..*", "*.*.", "*.**", "**..", "**.*", "***.", "****", "....*", "...*.", "...**", "..*..", "..*.*", "..**.", "..***", ".*..*", ".*.*.", ".*.**", ".**..", ".**.*", ".***.", ".****", "*...*", "*..*.", "*..**", "*.*..", "*.*.*", "*.**.", "*.***", "**..*", "**.*.", "**.**" }

    Returns: 1

  32. "..*..*.*.*.**.**..**.*...*.**.*.*.*.**.*..*.*.*"

    {"..*..*.*.*.**.**..**.*...*.**.*.*.*.**.*..*.*.*", "..*..*.*.*.**.**..**.*..**.**.*.*.*.**.*..*.*.*", ".**.**..**.*.*..*.*.*..*.*.**.*.**.**...*.....*" }

    Returns: 1

  33. "***"

    {"..." }

    Returns: 0

  34. "...*..*..*.***.***..*.**...**"

    {"***...*.**", "**..*..**..***", "*.**..***...." }

    Returns: 1

  35. "."

    {"******" }

    Returns: 0

  36. "*"

    {".*" }

    Returns: 0

  37. "**************************************************"

    {".................................................*", "................................................*", "...............................................*", "..............................................*", ".............................................*", "............................................*", "*", "**", "***", "****", "*****", "**.*..**.*.*.*.*.*.*.**..*.*.*.*.*.*.*..*.*.*.*", ".**..*.*.*.*.*.*.*.*.*.*.****.*.**" }

    Returns: 5

  38. ".*..."

    {"*.*...." }

    Returns: 1

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