Python implementation of Sudoku Algorithm

Author: kyscg

BackTracking/SudokuAlgorithm/sudoku.py

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+# A Backtracking program in Python to solve Sudoku problem 
+
+
+# A Utility Function to print the Grid 
+def print_grid(arr): 
+	for i in range(9): 
+		for j in range(9): 
+			print arr[i][j], 
+		print ('n') 
+
+		
+# Function to Find the entry in the Grid that is still not used 
+# Searches the grid to find an entry that is still unassigned. If 
+# found, the reference parameters row, col will be set the location 
+# that is unassigned, and true is returned. If no unassigned entries 
+# remain, false is returned. 
+# 'l' is a list variable that has been passed from the solve_sudoku function 
+# to keep track of incrementation of Rows and Columns 
+def find_empty_location(arr,l): 
+	for row in range(9): 
+		for col in range(9): 
+			if(arr[row][col]==0): 
+				l[0]=row 
+				l[1]=col 
+				return True
+	return False
+
+# Returns a boolean which indicates whether any assigned entry 
+# in the specified row matches the given number. 
+def used_in_row(arr,row,num): 
+	for i in range(9): 
+		if(arr[row][i] == num): 
+			return True
+	return False
+
+# Returns a boolean which indicates whether any assigned entry 
+# in the specified column matches the given number. 
+def used_in_col(arr,col,num): 
+	for i in range(9): 
+		if(arr[i][col] == num): 
+			return True
+	return False
+
+# Returns a boolean which indicates whether any assigned entry 
+# within the specified 3x3 box matches the given number 
+def used_in_box(arr,row,col,num): 
+	for i in range(3): 
+		for j in range(3): 
+			if(arr[i+row][j+col] == num): 
+				return True
+	return False
+
+# Checks whether it will be legal to assign num to the given row,col 
+# Returns a boolean which indicates whether it will be legal to assign 
+# num to the given row,col location. 
+def check_location_is_safe(arr,row,col,num): 
+	
+	# Check if 'num' is not already placed in current row, 
+	# current column and current 3x3 box 
+	return not used_in_row(arr,row,num) and not used_in_col(arr,col,num) and not used_in_box(arr,row - row%3,col - col%3,num) 
+
+# Takes a partially filled-in grid and attempts to assign values to 
+# all unassigned locations in such a way to meet the requirements 
+# for Sudoku solution (non-duplication across rows, columns, and boxes) 
+def solve_sudoku(arr): 
+	
+	# 'l' is a list variable that keeps the record of row and col in find_empty_location Function	 
+	l=[0,0] 
+	
+	# If there is no unassigned location, we are done	 
+	if(not find_empty_location(arr,l)): 
+		return True
+	
+	# Assigning list values to row and col that we got from the above Function 
+	row=l[0] 
+	col=l[1] 
+	
+	# consider digits 1 to 9 
+	for num in range(1,10): 
+		
+		# if looks promising 
+		if(check_location_is_safe(arr,row,col,num)): 
+			
+			# make tentative assignment 
+			arr[row][col]=num 
+
+			# return, if sucess, ya! 
+			if(solve_sudoku(arr)): 
+				return True
+
+			# failure, unmake & try again 
+			arr[row][col] = 0
+			
+	# this triggers backtracking		 
+	return False
+
+# Driver main function to test above functions 
+if __name__=="__main__": 
+	
+	# creating a 2D array for the grid 
+	grid=[[0 for x in range(9)]for y in range(9)] 
+	
+	# assigning values to the grid 
+	grid=[[3,0,6,5,0,8,4,0,0], 
+		[5,2,0,0,0,0,0,0,0], 
+		[0,8,7,0,0,0,0,3,1], 
+		[0,0,3,0,1,0,0,8,0], 
+		[9,0,0,8,6,3,0,0,5], 
+		[0,5,0,0,9,0,6,0,0], 
+		[1,3,0,0,0,0,2,5,0], 
+		[0,0,0,0,0,0,0,7,4], 
+		[0,0,5,2,0,6,3,0,0]] 
+	
+	# if sucess print the grid 
+	if(solve_sudoku(grid)): 
+		print_grid(grid) 
+	else: 
+		print "No solution exists"