Add NQueens backtracking search implementation (#504)

Author: DaveAxiom

other/nqueens.py

@@ -0,0 +1,77 @@
+#! /usr/bin/python3
+import sys
+
+def nqueens(board_width):
+	board = [0]
+	current_row = 0
+	while True:
+		conflict = False
+		
+		for review_index in range(0, current_row):
+			left = board[review_index] - (current_row - review_index)
+			right = board[review_index] + (current_row - review_index);
+			if (board[current_row] == board[review_index] or (left >= 0 and left == board[current_row]) or (right < board_width and right == board[current_row])):
+				conflict = True;
+				break
+	
+		if (current_row == 0 and conflict == False):
+			board.append(0)
+			current_row = 1
+			continue
+
+		if (conflict == True):
+			board[current_row] += 1
+			
+			if (current_row == 0 and board[current_row] == board_width):
+				print("No solution exists for specificed board size.")
+				return None
+			
+			while True:
+				if (board[current_row] == board_width):
+					board[current_row] = 0
+					if (current_row == 0):
+						print("No solution exists for specificed board size.")
+						return None
+					
+					board.pop()
+					current_row -= 1
+					board[current_row] += 1
+					
+				if board[current_row] != board_width:
+					break
+		else:
+			current_row += 1
+			if (current_row == board_width):
+				break
+
+			board.append(0)
+	return board
+
+def print_board(board):
+	if (board == None):
+		return
+
+	board_width = len(board)
+	for row in range(board_width):
+		line_print = []
+		for column in range(board_width):
+			if column == board[row]:
+				line_print.append("Q")
+			else:
+				line_print.append(".")
+		print(line_print)
+
+
+if __name__ == '__main__':
+	default_width = 8
+	for arg in sys.argv:
+		if (arg.isdecimal() and int(arg) > 3):
+			default_width = int(arg)
+			break
+		
+	if (default_width == 8):
+		print("Running algorithm with board size of 8. Specify an alternative Chess board size for N-Queens as a command line argument.")
+	
+	board = nqueens(default_width)
+	print(board)
+	print_board(board)