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Back in the day when the famous sixteen-bit three-letter operating system most often used on an 25x80 terminal dominated the PC market, "Nibbles" was everyone's favorite computer game. This problem, however, is not related to Nibbles – it is related to a game called "Connect" which is almost, but not quite, entirely unlike Nibbles.
Connect is played on a board composed of squares organized into R rows and C columns, where both R and C are odd numbers. Rows and columns are numbered 1 to R and 1 to C, respectively. Each position on the board is either free or blocked by a wall. Additionally, each board satisfies the following constraints:
Barriers are represented by the '+' (plus) character, blocked horizontal corridors by the '|' (pipe) character, while blocked vertical corridors are represented by the '–' (minus) character. Rooms and free corridors are represented by the blank character.
At the beginning of the game an even number of figures (represented by the uppercase letter 'X') are placed on the board – each in a separate room. A path between figures A and B is a sequence of free squares starting from A, ending with B and moving in one of the four possible directions in each step (the path includes both endpoint squares, A and B). The length of the path is the total number of steps needed to get from A to B (which is equal to the number of squares contained in the path minus one).
The goal of the player is to first divide all the figures into pairs, and then, for each pair, connect the two figures with a path. The pairs should be connected in such a way that no two paths share a common square. For a completed game, the score is defined as the sum of the lengths of all paths.
+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+ | | | ....... | + + + + + + + + + +.+ + +.+ + + |X | | | |X..| |. | + + + + + + + + + + + + +.+ + + | | | X | | | |..X | +-+ + + + + + + +-+ + + + + + + | | | | | | + + + +-+-+-+-+ + + + +-+-+-+-+ | X| | X| + + +-+-+-+-+ + + + +-+-+-+-+.+ | | | ...........| + + + + + + + + + +.+ + + + + + | X| | | X| | + + + + + + + + + + + + + + + + | | | | | | +-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+
Write a program that, given the starting position of the Connect game, plays the game in such a way that the minimum possible score is achieved.
The test data will guarantee that a solution, although not necessarily unique, will always exist.
The first line of input contains two odd integers R and C, (5 ≤ R ≤ 25, 5 ≤ C < 80) – the numbers of rows and columns.
Each of the following R lines of input contains C characters representing one row of the board. Every character will either be one of the three characters '+', '|' and '–', representing a barrier or a blocked corridor, the blank character representing a free corridor or room, or the 'X' character representing a figure in a room.
There will be at least two figures on the board.
The first line of output should contain a single integer, the minimum possible score.
The following R lines of output should contain the description of the board after the game has been played. The board should be formatted exactly the same way as in the input, except that each unoccupied square contained in some path should be represented by the '.' (dot) character.
Note: If there are multiple solutions, you should output any one of them.
17 15 +-+-+-+-+-+-+-+ | | + + + + + + + + |X | | | + + + + + + + + | | | X | +-+ + + + + + + | | | + + + +-+-+-+-+ | X| + + +-+-+-+-+ + | | + + + + + + + + | X| | + + + + + + + + | | | +-+-+-+-+-+-+-+
30 +-+-+-+-+-+-+-+ | ......... | + +.+ + + +.+ + |X..| | . | + + + + + +.+ + | | | X | +-+ + + + + + + | | | + + + +-+-+-+-+ | X| + + +-+-+-+-+.+ | ...........| + +.+ + + + + + | X| | + + + + + + + + | | | +-+-+-+-+-+-+-
15 15 +-+-+-+-+-+-+-+ |X| | + + + +-+ + + + | | |X| X | + + + + + + +-+ | | | |X| + +-+-+ + + + + | | | | +-+-+ + + +-+ + | | | | + + + +-+-+ + + | |X | | | + +-+-+ + + + + | X| | +-+-+-+-+-+-+-+
56 +-+-+-+-+-+-+-+ |X| | +.+ + +-+ + + + |.| |X| X | +.+ + +.+ +.+-+ |. |.| .|X| +.+-+-+.+ +.+.+ |..... .|...|.| +-+-+.+.+.+-+.+ | .|... |.| + + +.+-+-+ +.+ |.....|X..| |.| +.+-+-+ +.+ +.+ |....X| .....| +-+-+-+-+-+-+-+