[USACO08DEC] Winning Checkers G

The cows have taken up the game of checkers with a vengeance. Unfortunately, despite their unlimited enjoyment of playing, they are terrible at the endgame and want your help. Given an NxN (4 <= N <= 500) checkboard, determine the optimal set of moves (i.e., smallest number of moves) to end the game on the next move. Checkers move only on the '+' squares and capture by jumping 'over' an opponent's piece in the traditional way. The piece is removed as soon as it is jumped. See the example below where N=8: ```cpp - + - + - + - + The K's mark Bessie's kings; the o's represent the + - + - + - + - opponent's checkers. Bessie always moves next. The - + - K - + - + Kings jump opponent's checkers successively in any + - + - + - + - diagonal direction (and removes pieces when jumped). - o - o - + - + + - K - + - + - For this board, the best solution requires the lower - o - + - + - + left King to jump successively across all three of the + - K - + - K - opponents' checkers, thus ending the game (moving K marked as >K<): Original After move 1 After move 2 After move 3 - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - - + - K - + - + - + - K - + - + - + - K - + - + - + - K - + - + + - + - + - + - + - + - + - + - + ->K<- + - + - + - + - + - + - - o - o - + - + - o - o - + - + - + - o - + - + - + - + - + - + + - K - + - + - >K<- K - + - + - + - K - + - + - + - K ->K<- + - - o - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + + ->K<- + - K - + - + - + - K - + - K - + - K - + - K - + - K - The moves traversed these squares: 1 2 3 4 5 6 7 8 R C 1 - + - + - + - + start: 8 3 2 + - + - + - + - move: 6 1 3 - + - K - + - + move: 4 3 4 + - * - + - + - move: 6 5 5 - o - o - + - + 6 * - K - * - + - 7 - o - + - + - + 8 + - K - + - K - ``` Write a program to determine the game-ending sequence for an NxN input board if it exists. There is at least a king and at least one opponent piece on the board. The king can jump a piece on every move of the optimal solution. POINTS: 330

\* Line 1: A single integer: N \* Lines 2..N+1: Line i+1 contains N characters (each one of: '-', '+', 'K', or 'o') that represent row i of a proper checkboard. Line 2 always begins with '-'.

\* Lines 1..?: If there is no winning sequence of jump, output 'impossible' on a line by itself. If such a sequence exists, each line contains two space-separated integers that represent successive locations of a king whose moves will win the game. Any such sequence is acceptable.

8 
-+-+-+-+ 
+-+-+-+- 
-+-K-+-+ 
+-+-+-+- 
-o-o-+-+ 
+-K-+-+- 
-o-+-+-+ 
+-K-+-K- 

8 3 
6 1 
4 3 
6 5