TopCoder Statistics - Problem Statement

Problem Statement

You are placed in a maze represented by a rectangular board. Each cell of the board can be one of the following:

empty: is always passable (represented by a '.')
a wall: is never passable (a '#')
a key: is always passable; when you enter it for the first time, you pick up the key (a lowercase letter 'a'-'f')
a door: is passable only if you have a corresponding key (an uppercase letter 'A'-'F')
your starting position: an empty cell where you are placed at the beginning (a '0' digit)
exit point: an empty cell you must enter to get out of the maze (a '1' digit).

You must get out of the maze using a minimal number of moves. In one move you can get to a cell which is adjacent to your current position vertically or horizontally.
You will be given a String[] maze. Each character in maze will represent a single cell of the maze. A key denoted with a certain lowercase letter opens the door denoted with the corresponding uppercase letter only. Return the minimal number of moves that will bring you to an exit point. There can be several exit points, in which case you can get to any of them. If you can't get to any exit point, return -1.

Definition

Class:: LockedDoors
Method:: pathOutside
Parameters:: String[]
Returns:: int
Method signature:: int pathOutside(String[] maze)
(be sure your method is public)

Notes

It is possible to have several keys or several doors of the same type on the map.
It is possible to have a door without the corresponding key, and vice versa.
Once you have picked up a key, you can use it multiple times.

Constraints

maze will contain between 1 and 50 elements, inclusive.
Each element of maze will contain between 1 and 50 characters, inclusive.
All elements of maze will contain the same number of characters.
Each character in maze will be '.', '#', '0' (digit), '1' (digit), 'A'-'F' or 'a'-'f'.
There will be exactly one '0' character and at least one '1' character in maze.

Examples

{"1..0", "###.", "1..."}

Returns: 3

There are no keys or doors in the maze.
{"..0..", ".###.", "..1.A"}

Returns: 6

We can get to the exit without opening the door.
{"f0.F..1"}

Returns: 7
{"0....", ".#B#A", ".#.#.", "b#a#1"}

Returns: 19

You have to get the 'b' key first, open the 'B' door, get the 'a' key and open the 'A' door to get to the exit.
{"c.0.C.C.C.1"}

Returns: 12

The 'c' key opens all 'C' doors.
{"###...", "#0A.1a", "###..."}

Returns: -1
{"a#c#eF.1", ".#.#.#..", ".#B#D###", "0....F.1", "C#E#A###", ".#.#.#..", "d#f#bF.1"}

Returns: 55

You have to get all 6 keys in the correct order to open the 'F' door.
{"0abcdef.FEDCBA1"}

Returns: 14

You can carry several types of keys at once.
{"d.0.d.D.1"}

Returns: 6
{"01"}

Returns: 1
{"a...#.", "0...#1", "..abAB"}

Returns: 7
{ "...#.#.#e.....##..#...#D...#...", ".#E............#.#a.#C.........", ".....#.#.####...#....###..C....", "..#.b##..#F#...##...##..#e..#..", "...e.#..###..##..##.....#..#.#.", ".#.df#.#..#..#...#f.#.#.....#D#", ".0E.#...#.#..#.....F#...d......", "..##...#.#Be##.#..#....#.a..#..", "A#.F#.......#.....##..#....d..#", "##..D.......#.#.#..#..A.#.f#c..", "##..##c..C#.#b.##.#..#.D###.e#b", "....##.....e..#..#.#.d.#.#.....", "..#.CE.##.#..#..D..C...#.##.e.#", "#..#.#c.###....#C#.##E.....#..#", ".f#..###.##.C#.....##..#......1", "d#F#.....f......#.#.BE#.a...#..", "dBc##..E###..#.#.##.e##...b..##", "#....#......##....#.F.#.e..F.##", ".###.....F..#A...D...Aa#dF.....", "1..B.###.....#.#..##E##.#......", ".##...##.a#c.e#B..d#....#.Fa...", "#C.#...FB...#c....F.e.......f.#", "#.##...##..#.#..#.#.#.#.#..#.Ea", "...##...F..##....##d##.......#.", "##..#..#..FB#E.....##.#C.#..e..", "..#..##...##.#......F.#.##...##", ".###.#.A...#..#.....F..#.....d#", "..#....#.#F..##...#E.....#...B.", ".f##.###.....#....#...#.....#..", "...d.#...#..#...1.B.a.....F.###", "##.###.##E.#..#..A##..##F##.b.#", ".#.##f#...#F.......#..#d##....#", ".#.f#...#.#....##..#####..###ee", "..#c#Def.....#....##Da.a.##...#", ".c........FA##Ce.....##c#......", "#.#..#F..A#.....#...A.#.##..#.#", ".......#..d...#c#..#.#.#.E...E.", "a.#..#..##..####......#.#...###", ".E.###.#..#..#ba#.......#...#.#", "......#...##....##..##.e.......", "....#..####.a##..#.##....#b##.#", "f...#.......#.#.##.#........F..", ".D.e.........d#.###.....A#.a#.d", "...##..fe#.a.#..#.B#......#.#EE", "##.....#.#..#.E##..###..#..##.#", "#.#...#.##e.##.#..F..1B.....#..", ".d#.#........b#..#.#..B.#.F#.#." }

Returns: 44

rnd 1
{ "###", ".1#", "..1", "F##", "..0", "..#", "cf#" }

Returns: 10
{ ".1b.eF#.#F1e#..##.#EC#.##.###...#...#.#....#..", "...E#..####.D###E........#...##b...c..#.#..#..", "##a.D#D#.#.#..#..#..D....##......#.....#....#.", "#...#.#.##...F.##......#C...........##..#..#..", ".##.#...#..#.db...##.#...C.#..f.####.c..#.##.#", ".#...###..#.#.E...#.#.#.....#.#.##.#......#...", ".#.#a....Cf...#...#.#.##..#.#.0C..#.bF.####.#." }

Returns: 32
{ "#..###.#.D..#.#..", "####....#..b#....", "#...B.#.c.....#..", ".f.#.##....#..F#.", "##...#.A.#.#...D#", ".....c#c.##...e..", "......Fe..f#....#", "..###......#.#..#", "..#f..#.D#a.f....", ".#.a.....#.#..#D#", "##..##.#...#..###", "0....#.D..D#.f...", "####..#.....#.##.", "#f.#...##.....##.", "..#.#....C#.#f..#", "a.#...b....#ebC..", ".##.A.e..#ad###..", ".#.###.#..#####..", "..D.##..###.#1..." }

Returns: 28
{ ".#c.#", "#....", "F.f.d", "#..b.", "#.#.#", "#....", "E##..", "#..#.", "...##", "B.###", "#.aa.", ".#.#.", ".#E##", ".#...", "...##", "#...#", "..#c.", "...#A", "#.#.C", "#.#a.", "#D#D.", "..#..", ".#.#.", ".###.", ".###C", "..#c.", "..#..", "..e#f", "...#.", ".##.F", "d.#.#", "#0#1#" }

Returns: 52
{ "..F....e#.......#.###.#", "#.#..#.A.1..#.B#.B#..#.", ".d##.###.........d..#..", "....#...####...##.C..#.", ".##...FEcA...#db.##...#", "##.#..#.#.#..#.a..###..", ".1##..#..#.#....b.E...f", "#......Df.#.dc#.###....", ".#.#..e..#...#.........", "..####F.f#F#.B#.#.AB.#.", "..#..bE.#.A##.F.D..#...", "##.##.eA.#.d..dA.###.#1", "#..C..##.##...1...#..aC", "..#.E...#......##d#....", "#.......#.......#..a...", "......A#a.#a...#...#...", ".#.#.......a.##D....###", "###..#.1.#....b.D..#1#.", "0.##.......#.#D##.#..#.", "f.#.A...#..##.#E.##..#.", "#....##bc.#.#.##F#..b.#" }

Returns: -1
{ "b#.....#.F#.FD..#..b.#...#c......##.", "#.....F.E.##.#E##..E..#.#.#d.#...b.#", "a#..#..##...###.####f#.#....c#.##e.1", ".......#..#b....f#...C#....#.#...dd#", "..#B..D........##.....#....E...#..D.", "#.#eABd##e#..#.e##.#.#....#.##.#.#.#", "#b#.####..###e.....aF.E..###.A..#a..", "#.0#....#.C....Bd#b.#..##F#.#..c...#", ".##....d.##..#..#...c.##A###....#...", ".#....#..Bb##...#..#C..#..#f..a#....", "c#.#..ceCA..#..####..#.###.#F.##..A#", ".#CA.##..#...C..d...#..#...#.E#.....", ".#.#.C..#.#D#E#....#.....##B.#A..#..", "##..#.##..Bf.E..Ed...E#.#.#.....#.##", "#D.F.##.#.#..##.#...#..#.##.E.#..#..", "..#.....#.b..##..e.A##.B#.#...f#B.f.", "##c...#F.#..##.#....C..#...#..#c...#", ".F#.#..#.f.EA....#...#a##.......#..#", "f.#...b..#..#.##.#.CA#...FA#.A.##..f", ".#....#...##.###c..###.....#..##....", "#.....#.#..##.##d.b..#...D#..#..###.", "..d#f#e.#F#...##.......#.#.....##..#" }

Returns: 52
{ "....c.....#.#.#..#......#...f....#...#..", ".#....#.c...b#..........#B##...#.CE#.#.A", "....#..#.....d..1....###..D####..c..#...", "#...##F##D#.........#.E...f....#..#.C..B", ".###..#..####....#..#..###..#.#.b.......", "d###.E.ed..B#.#..##.#..d..#...##..##.d.#", "#...B....#....###.#..#C#.##.fE..#.####..", "A##..##....#....e.#........##...E..#f##.", "e...EE#A..##d###.E..#.E...#c..e...#...#.", "E....#......#b..#..#..c##.#.#.D#.....#..", "..#..#.#.e...a..#.#..c#....#D##.A#......", "#.#.#.#....#.#.b.........#e...##d.#..#..", "...##...#.#.cC.........#c....c#E.A##..e.", "...#B#A......#.C.#.E.#..##D..##..F.#.##.", "....#c..F#.#.........#.#...e##C#..##....", ".##..#.......#.##.....B...#..#......D...", "#...#...........b.#.#A.#.#..####........", "...F..##..C#.#..E.#.E....e.D...e.....E.b", "....#..#.....d...#....#.#.#..a....f..###", ".....#..#..##...#.#.A.#..#.d....##a..C#.", "..1..#b#..aC..#...#c..e.#..C.....##.#.#.", ".........#d...E..C.#.b#.#....#.#...a#..#", "........##....##......#.#.....F##......#", "#.B.##...##C##..#....#.##a.......a.##e##", "....#.b....#...#.A#.A.#.....b......###..", "...#..#.#...#.a#....##.##.##...e....#...", "AB.D.....#c#F#....###..#a.##...####.cf#.", ".....d.B...#.#.........#...###.#.....B.#", ".C#.#..##A.##...#..#.....##ad.C###...B..", "..#.#.#.##...#..#.#..##........e.#.b.##.", "e...#..##.D..#F#...#....c#..#..c#f..#.d.", "EF..#..d#.#.#..#B###fa.....#...#C.#.#.f.", "...........#c#...#......A#b.#.##...bEa#.", ".#..#...#.#..A.###.........###.#.######D", "..b...##.......d#.#b#.#..b..e###.##.....", "B....#.#...#...#.#.#..#..b.F...#..##.e..", "..##..#.##.##..B..a.cF..##.#.##..#.#..##", "#...##..#.a##..#.##.#....f##E.D...#B.##.", "b.###....####a.......#.##.#.C###.###..#d", "..#.##.e.#...f....b....#d.#.df....#..#.#", "#.A...a.#.#..##c#..#a##.#..D.#....#...#.", "...###...#....#....#.C.e#....a.##.##.#..", "##.Bf.B.....#...###....#...##..#..##.###", "..e......#..#..A...C.f#.......B0.##.E..1" }

Returns: 48
{ "..#...##...#", "##...f1#.#B.", ".###.##....#", "...#.##..#.f", "...b.E.d....", "##..####.f#.", "..###.#...##", ".#b#.Ea..#..", ".#...C..e...", "###Ca.....##", ".#F.##...##0", ".....C.f..#.", ".##..#......", "....#.#..a..", "....#...#.a.", "..##.##E.#..", ".##..b##.dC#", "...###.b##..", "..d##.#..#..", "..##....#..#", ".##.#....ec.", "....#F..###.", "..##...#.##.", "c#......#...", "...f#..##...", "....#..#.###", "..e#....c...", "f.D#.#..E.##", "...#.d.d...#", "D.##..#.#...", "F.b..d.##..#", "#.F1#f#d..#A" }

Returns: 22
{ "###.#...D...#.....f#.B#...#.##.", "..B.#..#.......#.....##.##.#..#", "B.#a#.f...####..##...#....#...#", "...##..##...##.A.......##....#.", ".#bA..#.#E.#...fA.#.#.###..b...", "####.##..#...#....d#...#.E.#..#", "E..#0#.#....#...#.............#", "F...##..#....D####....##.##...#", ".#..#.#...a#.#..B#..##.D.##.#..", "#...#..###.F##D##..###........a", "#D..D...aC..#..#.#####..E#..#.a", "#.#..##........#..#..##...##...", ".#.....d.##b....#E#B##...b....#", "#.#..f..##.#B.#.###F....#.#D...", "#...###....##...##e##...a.F...d", "#.##..##.#..#.#b...#.e.#...#...", ".##......###.#..C.B.#...##.#.#.", "#..#.B#....#f....F.....bA.#....", "d#...##.#.#.#.#e..#...eD...#...", "....#.f.B.B##...#e....#..#.#e.#", "#FE...F.#..#B..a####E#c..#A...#", "###......b....##.......E#.#.#.#", "..#...Fe....#..##D.#..#..#f.#D.", "#b.#.#..#.#..#.......#E#...f..#", ".1c.a#a....#..#...#.#....###..b", "#c...#.#....#.#B....#.#.....#..", ".#.#....d#....#.#d...#.....##.#", "C......#...#.Fc.#.....#...###.#", ".#f.d###....e...####..###a..c.F", ".be#....##....#..f##a.#.#B...#.", "#D...###.##...b..#...#.....#..b", ".#..#D.....f#..e.#.e.#d...#.#..", ".#........##..a.#....#..#...#..", ".#...##.#.C#....#..#b.B.B#..##.", ".....##..###.##A...#...E....##.", "#.#D.E.###...#.C.#..E#...d.#1..", "#f...C##....#..##d...#.##..##.#", "##..#1....f.#c###A.#C.A.#..#.#.", "#.##..#...#..#..##......#B..#.d", ".##.#.#....#.#...##.#...c..#..c", ".#e.#..#.#.#C..##..##.d#......." }

Returns: 43

rnd 10
{"0.................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", ".#...#...#...#...#...#...#...#...#...#...#...#...#", "...#...#...#...#...#...#...#...#...#...#...#...#.1"}

Returns: 1298

big, no keys
{"..#...#...#...#...#...#...#...#...#...#...#......0", "###.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#C#A#F", "....#...#...#...#...#...#...#...#...#...#...#d#b#1", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..................................................", "#################################################.", "..................................................", ".#################################################", "..#...#...#...#...#...#...#...#...#...#...#...#BcD", "#...#...#...#...#...#...#...#...#...#...#...#..a#f"}

Returns: 7720

big, with keys
{"..1..#....#.#.#.....b#...#####0###"}

Returns: -1
{"F.#.1#.##.#..#..#.##..#......C.#", "..###.#.#.##.A#.F##C........B...", "...#...ad#E#...B...#....###...#D", "f.#Ad###..#.B...##D..#.##B#D.d##", "..#..#.##.#.#..E##....#....#.a..", ".E..##..#..c.#..#...F.#.#.....##", "..#.#.A##.##a##e#.ADc#...A##....", "E#.#....#C#.#..##.c###.#..#.C..A", ".........#...#.c.#.#..a###.###..", "...#.#...#.##...c.##..#..#.####F", "f.#.##.B#.#....##....#....bC.C#.", "#a#.###.#.#..#..##.###.#..##..##", "#..#.#E.#.#..D....#..#.###.#...C", "##e##...#D.....#B##...e#........", "#B#..d#C.#..###.#.D.#A.#.c......", "A.....D.#..#...####...###...#...", ".#..#...#.a#...a...c##..........", "...c...##.#..#.A#####....##..##.", ".######...##.#.#.C....A.........", ".....#...D....d#...B.###.#..#.#.", "..#...#.#.#..##..#..#..#.#A.#C.B", ".D#b#B#..#.##..##..f.####.##....", "..#E#.f####..#.##..d#....#a.##.#", ".#.B#A#.#..#..E....#1...d...#.#.", ".##.#.#.....#.a..##.###.#..#.f..", "#.A#..#F..##....#......#..#.....", ".1.#.#...#...###Db....C...#b#.#.", "..#..D#.B.#.e.#..........##.#...", "##...#.AD.D.....##########.e#.#.", "...##...C....#.#..........d.#.F#", ".B...####.Ce..#.#..#.A..EA#B.##0", "##....#....###B...#.#.##.#..#.#.", "...#...#####..#..###..#.#...e...", "d.a........cD...###.##.#...#b..#"}

Returns: 254
{"F...#.###.#...d..#....##..#.#..B.A.####", "#........#...#A#.F....E#.....ae.C....c#", "##....#.d##F#.dd##......##D.....##Bf..e", "....#a......#....#..##.#............#..", "#...c#B..#.#aD#..#D..a.......#E#...#A..", "..f...D..###D.b.##..B.a##fEDb.....##.#.", "..#.##..B#.##..F#....##..#.#.#....eC##.", ".#.#..D..##..c.....##...#.#.#F.......#1", "b#1#ca#d...##..#.###...C....#F#...a.C.#", "#ae.#...#...##.AB......##.EA#.#C..#..#.", "#######....##..##..B#.......#.#....B..A", "0.aE....b#E.C.......#....b#..F..A.#.#d.", "#..#..#..#.B#...###..#C#.E#.##.B..F#B#C", "#....#.........E...##.#.#.#..Fc.###D1#c"}

Returns: 60
{".d..#FC.a.#.#.", "f#..#.#...F...", ".B..D#..F.C#..", "#c..Cb#.#..#..", "...##D...#.D.#", "....#e0.......", "..B..##D.#....", "#...#..###.##.", "###D.#.##A..#d", ".d#.#.C...#.F#", "#.#.B.##.b#c..", "..#.....Ca...f", "..#.B...#b..##", "D##......#...#", "##.c....#.f...", "F.bBe##a.##...", "..D#..b....#..", "a.B.##...###.#", ".#...C..##...#", "#...#.###..#.#", "DA...#....#a..", "....d#.....F..", ".##.C...#A.#..", ".b......#.....", "##.##..b#d#.BF", ".##.##E.b.#...", ".#.#....#.....", "##b#...##...#.", "..#....e..#..#", "...###c#..##..", "...A..#.......", "#f...f...##.f.", "...#..#.#.###.", ".E#.#..fF#....", "..#.....c..#.#", "...##.#..#c.#.", "...##..C####..", "..E..#.#......", ".##..###1#....", "#.#...D.#..E..", "..###.#...#..."}

Returns: 69
{".BD.#...f...#AEcb.#.#..d.#.#..e##", "A#.....D###.#.....##...#...##a.#0", ".#a#....e...F####....#.B....#....", "###....#D#.a...#ce#F##..#...##.#b", ".##.##d.##....d.##.#.##F#..#..bF#", ".##.....#Bd..#..##Dd.#....D...Fb.", "......b..e.....E#..#B#..#..#.#...", "..##..B....##.##.##.#......#.#...", "#...#...#cC##.e###.d.c#...##..#.#", "...#E.A#.##.f.##...#b##.......c##", "D...#.#.#....#..Eb..f..D.#.E#....", "c.##.#D...e.C..f.##.....##.b.c..#", "...#.Fd#.#E#.#...#####.A...#..D..", ".#...#.##B.#..c..CA#....f.##F..##", "##f#..b....#....#c.##.fbF..##....", "###F.D#..#.....#....#..c.#.b..A##", "#A....b...#..D.#..#......c..E....", ".B.......#fe##..#..#.##.B.#.#....", ".#BC.####...#....FB...E#....#....", "..#..#..#...f#.##dC....#.b#.#.###", ".#E.....C.#B......a.#b..###.##...", "...#...##.#A.bf#.....#.#.A##F..#.", ".B.....d.#....##.....#..D##.#.#d.", "#....e#.#.B##.D.#D#.B..#.........", "#.ed...#.A##b..###.f#...##..#b.#.", "#.#.#.e....E....#dc...##c.....#.D", "....#...#...#.#C...d#..##.####.##", ".##...##.#....#.#..#.#.##.#f##...", "#..A.###.##..#..........##.b.#...", "D...#E.#.##..####d.#...#..#.ae..#", "#....E.c##.######.Fb.#.#.e.C##..e", "#b...#.##1#.#.............c...#..", "..#.##.....#......#...B#e...c...."}

Returns: 67
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Returns: -1
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Returns: -1
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Returns: 9
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Returns: 16
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Returns: 9
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Returns: 4
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Returns: 2
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Returns: 19
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Returns: 5
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Returns: 3
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Returns: 19
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Returns: 2
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Returns: 17
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Returns: -1

Statistics

Problem Statement for "LockedDoors"

Problem Statement

Definition

Notes

Constraints

Examples