Problem B: Go
Go is played on a square board with an odd number of
vertical and horizontal lines. The usual board sizes are 9x9, 13x13 and 19x19.
But we'll assume the size in nxn for 3 ≤ n ≤ 19.
Black and White alternately play stones on the intersection between two
lines. Black starts. At any time one player may pass - not play a stone - but if
both players pass the game ends. We'll denote playing a stone by P(x,y) where P
is either B (for Black) or W (for White) and (1-n)/2 ≤ x,y &le (n-1)/2 gives
the grid position of the stone to be played. The centre intersection of the
board has coordinates (0,0).
The rules of Go are reasonably straightforward, but the nuances of strategy
make it an extremely challenging game. You are to use the following rules.
- Black plays first.
- Black and White alternate; at each turn a player may place a stone or may
pass. The game ends when Black and White pass consecutively.
- A stone may be played only on an unoccupied intersection.
- If one player P places a stone so that his or her stones (along with the
edge of the board) completely surround a connected area occupied by stones
belonging to the other player, Q, Q's stones are said to be captured and
removed from the board. More precisely, two intersections are connected if
they are horizontally or vertically (but not diagonally) adjacent. Stones in
an area are completely surrounded if no stone is connected with a vacant
intersection.
- If P places a stone that causes Q's stones to be captured, P's stone is
not captured.
- A connected area surrounded by P's stones which contains none of Q's
stones is said to be owned by P.
- The score for player P is the number of vacant intersections owned by P in
the final board configuration plus the number of Q's stones captured by P at
any time during the game.
The input consists of several test cases.
Each test case begins with a line containing n - the size of the board -
and m - the number of stones placed in the game. m lines follow,
each giving a placement in the format above. Note that m counts only
stone placements - passes may result in two consecutive placements by the same
player. You may assume that each move is legal. A line containing 0 0 follows
the last test case.
For each test case, output a line with two numbers: Black's score followed by
White's score.
Sample Input
7 6
B(-2,-2)
W(2,2)
B(-2,-3)
W(2,3)
B(-3,-2)
W(3,2)
7 6
B(-2,-3)
W(-3,-3)
B(-2,-2)
W(3,2)
B(-3,-2)
W(2,3)
0 0
Output for Sample Input
1 1
2 1
Gordon V. Cormack