add knight's tour

knights-tour.py

@@ -0,0 +1,95 @@
+#!/usr/bin/python
+# vim:set fileencoding=utf-8:
+
+"""
+A backtracking Knight's Tour solver.
+"""
+
+from __future__ import division, print_function
+import numpy as np
+import random
+import sys
+
+
+visual = True
+
+
+def clear_board(n):
+    ANSI_CPL = "\033[%dF"  # CPL = Cursor Previous Line
+    ANSI_EL = "\033[2K"  # EL = Erase Line
+    print(n*(ANSI_CPL % 1 + ANSI_EL), end='')
+
+
+def print_board(board, clear=False):
+    if clear:
+        n = board.shape[0]
+        clear_board(n)
+
+    print(board)
+
+
+def next_moves(position, n):
+    offsets = [(r, c) for r in range(-2, 2+1) for c in range(-2, 2+1)
+               if abs(r*c) == 2]
+
+    moves = [tuple(np.add(position, offset)) for offset in offsets]
+    moves = [move for move in moves
+             if all(coord in range(0, n) for coord in move)]
+
+    return moves
+
+
+def possible_next_moves(position, n, board):
+    return [move for move in next_moves(position, n) if board[move] == 0]
+
+
+def ordered_possible_next_moves(position, n, board):
+    # Warnsdorf's Rule
+    moves = sorted([(len(possible_next_moves(move, n, board)), move)
+                    for move in possible_next_moves(position, n, board)])
+    return [move[1] for move in moves]
+
+
+def set_next_knight(board, position, k):
+    n = board.shape[0]
+
+    assert board[position] == 0
+    board[position] = k
+
+    if visual and random.random() < 0.001:
+        print_board(board, clear=True)
+
+    if 0 not in board:
+        # Solved
+        return board
+
+    for move in ordered_possible_next_moves(position, n, board):
+
+        ret = set_next_knight(board, move, k+1)
+        if ret is not None:
+            board = ret
+            return board
+
+    # dead end ⇒ backtrack
+    board[position] = 0
+    return None
+
+
+def main():
+    np.set_printoptions(linewidth=999)  # if n>19 or so
+
+    print(__doc__)
+
+    for n in range(1, 31+1):
+        print('\nn = {}\n'.format(n))
+        board = np.zeros((n, n), dtype=np.int)
+        print_board(board)
+        board = set_next_knight(board, (0, 0), 1)
+        if board is not None:
+            print_board(board, clear=True)
+        else:
+            clear_board(n)
+            print('No solution')
+
+
+main()