Start of n-queens implementation

Author: calebmadrigal

nqueens.py

@@ -0,0 +1,94 @@
+""" N-Queens solutions. """
+
+__author__ = "Caleb Madrigal"
+__date__ = "2015-02-19"
+
+import numpy as np
+
+
+def right_to_left_diagonals_valid(board):
+    """ Returns True if there is no more than 1 queen in each diagonal, False otherwise.
+
+    [[  0.   1.   2.   3.   4.   5.   6.   7.]
+     [  8.   9.  10.  11.  12.  13.  14.  15.]
+     [ 16.  17.  18.  19.  20.  21.  22.  23.]
+     [ 24.  25.  26.  27.  28.  29.  30.  31.]
+     [ 32.  33.  34.  35.  36.  37.  38.  39.]
+     [ 40.  41.  42.  43.  44.  45.  46.  47.]
+     [ 48.  49.  50.  51.  52.  53.  54.  55.]
+     [ 56.  57.  58.  59.  60.  61.  62.  63.]]
+
+    The algorithm works like this:
+
+    TBD
+
+    """
+
+    flat = board.reshape((1, size*size))[0]
+    # Check right-to-left diagonals
+    for row_index in range(1, size):
+        #print("row_index:", row_index)
+        index = row_index
+        diag_sum = 0
+        for diag_index in range(row_index+1):
+            #print("\tdiag_index: {0}, value: {1}".format(index, flat[index]))
+            diag_sum += flat[index]
+            index += (size - 1)
+        if diag_sum > 1:
+            return False
+
+    col_diag_index = 0
+    diag_lengths = list(range(size-1, 0, -1))
+    for last_col_index in range(2*size-1, size*size-1, size):
+        #print("col_index:", last_col_index)
+        index = last_col_index
+        diag_sum = 0
+        diag_len = diag_lengths[col_diag_index]
+        col_diag_index += 1
+        for diag_index in range(diag_len):
+            #print("\tdiag_index: {0}, value: {1}".format(index, flat[index]))
+            diag_sum += flat[index]
+            index += (size - 1)
+        if diag_sum > 1:
+            return False
+
+    return True
+
+def diags_valid(board):
+    if not right_to_left_diagonals_valid(board):
+        return False
+    rotated_board = np.rot90(board)
+    return right_to_left_diagonals_valid(rotated_board)
+
+
+def rows_valid(board):
+    for row in board:
+        if np.sum(row) > 1:
+            return False
+    return True
+
+
+def cols_valid(board):
+    for col_index in len(board):
+        if np.sum(board[:,col_index]) > 1:
+            return False
+    return True
+
+
+def is_valid(board):
+    return rows_valid(board) and cols_valid(board) and diags_valid(board)
+
+
+def n_queens(size):
+    board = np.zeros((size, size))
+    for row in range(size):
+        for col in range(size):
+            board[row][col] = size * row + col
+    return board
+
+if __name__ == '__main__':
+    size = 8
+    solution = n_queens(size)
+    print(solution)
+    print(diags_valid(solution))
+