SlideGame

PROBLEM STATEMENT

The game 'Stones' is played on a String of '.'s and 'X's, such as:

"..X......X..X"

Squares with a stone are represented by 'X', and empty squares are represented
by '.'.
There will be between 0 and 10 stones, inclusive.

Here are the rules to the game:

1.  Play alternates between player 1 and player 2.
2.  A player must move one stone on their turn.
3.  If a player can't move, he/she loses.
4.  A valid move consists of moving one stone 'X' one or two squares to the
left. 
5.  A player can't move a stone off the edge of the board.
6.  A player can't move a stone past another stone.
7.  A player can't move a stone on top of another stone.

It is player 1's turn. Given the current state of the board as a String, return
how many different winning moves player 1 has on that turn.

A winning move for player 1 is a move such that no matter how player 2 plays,
player 1 can insure (by playing perfectly) that player 2 will run out of moves
before player 1 will. (i.e. player 1 can insure that the last possible move of
the game will be on player 1's turn, winning by rule 3)

Example:

board = ".X.X"

player 1 has two possible (not necessarily winning) moves:
(a) to "X..X"  (moving the left X one to the left)
(b) to ".XX."  (moving the right X one to the left)
player 1 can't move either X two squares without violating rule 5 or 7. 

if player 1 moves to (a),  player 2 has two moves:
(a1) to "XX.." (moving the right X two to the left)
(a2) to "X.X." (moving the right X one to the left)

if player 2 plays to (a1), player 1 has no move and so loses.  Because player 2
has a winning move, (a) isn't a winning move for player 1.

if player 1 moves to (b) instead, player 2 has only one move:
(b1) to "X.X." (moving the left X one to the left)

This leaves player 1 with only one move, to "XX.."
after the move to "XX..", player 2 has no move and loses, so (b) is a winning
move for player 1.

(a) is not a winning move, and (b) is a winning move, so player 1 has only one
winning move, and the method would return 1.

DEFINITION

Class: SlideGame
Method: waysToWin
Parameters: String
Returns: int
Method signature (be sure your method is public):  int waysToWin(String board);

TopCoder will ensure the validity of the inputs.  Inputs are valid if all of
the following criteria are met:

- board will be between 1 and 50 characters, inclusive.
- board will consist only of the characters 'X' and '.'.
- board will contain between 0 and 10 'X's, inclusive.

EXAMPLES

(1) 
board: "...X.."
waysToWin would return: 0

(2)
board: "...X..X..X"
waysToWin would return: 3

(3)
board: "...X.X..X"
waysToWin would return: 3

(4)
board: ".X.X..X.X..XX.....X"
waysToWin would return: 3

(5)
board: "..X..X..X..X..X..X..X..X..X..X."
waysToWin would return: 10

(6)
board: "......"
waysToWin would return: 0

(7)
board: "X"
waysToWin would return: 0