sudoku.py

import random
from collections import deque, namedtuple
from copy import deepcopy
import tkinter as tk
from tkinter import messagebox, simpledialog
from textwrap import wrap
from enum import Enum


MARGIN =  20 # Pixels around the board
SIDE = 50 # Height of each board cell
WIDTH = HEIGHT = MARGIN * 2 + SIDE * 9 # Width and height of the whole board
# Highlight colours
HLANSWER = "light goldenrod"
HLCAND = "light blue"
COLOURS = [None, "pale green", "sienna1", "khaki1", "cornflower blue", "mediumpurple1", "peachpuff2", "tomato", "sandy brown", "hot pink"]

class Mode(Enum):
    solution = 1
    candidate = 2
    colour = 3
    colour_candidate = 4

class SudokuBoard(object):
    """
    Sudoku Board Representation
    """
    def __init__(self, puzzle_string):
        self.__create_board(puzzle_string)
    
    def update(self, puzzle_string):
        self.__create_board(puzzle_string)
    
    def get(self):
        return self.board[:]

    def set_board(self, board):
        self.board = board
    
    def __create_board(self, puzzle_string):
        rows = wrap(puzzle_string, 9)
        rows = [row.replace('.', '0') for row in rows]
        self.board = [ [int(ch) for ch in row] for row in rows ]

    def generate(self, difficulty):
        file_name = difficulty + ".seed"
        with open(file_name) as file:
            puzzles = [line.strip() for line in file]
            self.__create_board(random.choice(puzzles)) 
        
        # Rotate puzzle between 0 to 3 times
        for i in range(random.randint(0,3)):
            self.rotate90()
        
        # Either don't flip or do flips
        i = random.randint(0,3)

        if i == 0:
            self.flip_hor()
        elif i == 1:
            self.flip_vert()
        elif i == 2:
            self.flip_hor()
            self.flip_vert()
        
        self.translate()
    
    def rotate90(self):
        new_board = [[0 for y in range(9)] for x in range(9)]
        for i in range(9):
            for j in range(9):
                new_board[j][8-i] = self.board[i][j]
        self.board = new_board

    def flip_hor(self):
        new_board = [[0 for y in range(9)] for x in range(9)]
        for i in range(9):
            for j in range(9):
                new_board[8-i][j] = self.board[i][j]
        self.board = new_board

    def flip_vert(self):
        new_board = [[0 for y in range(9)] for x in range(9)]
        for i in range(9):
            for j in range(9):
                new_board[i][8-j] = self.board[i][j]
        self.board = new_board
        
    def translate(self):
        numbers = [1,2,3,4,5,6,7,8,9]
        random.shuffle(numbers)
        new_board = [[0 for y in range(9)] for x in range(9)]
        for i in range(9):
            for j in range(9):
                if self.board[i][j] != 0:
                    new_board[i][j] = numbers[self.board[i][j] - 1]
                else:
                    new_board[i][j] = 0
        self.board = new_board

Hint = namedtuple('Hint', "technique cells1 cells2 good_cands bad_cands text")

class HintEngine(object):
    """
    Here will be methods that searches hints for solving a sudoku

    Most functions will return Hints
    """
    def __init__(self, game):
        self.hint = None
        self.game = game
        self.techs = [self.__naked_single]
    
    def get_hint(self):
        for tech in self.techs:
            tech()
            if not self.hint is None:
                break
        
        return self.hint

    def __naked_single(self):
        good_cells = []
        good_cands = []
        for row in range(9):
            for col in range(9):
                cands = self.game.get_candidates(row, col)
                if len(cands) == 1 and self.game.get_cell(row, col) == 0:
                    good_cells.append((row,col))
                    good_cands.append((row,col,cands[0]))
        
        if len(good_cells) > 0:
            self.hint = Hint("Naked single", good_cells, None, good_cands, None, "The only number that can go in this cell is")

    def get_naked(self):
        self.__naked_single()
        return self.hint

class SudokuGame(object):
    """
    A Sudoku game, in charge of storing the state of the board and checking
    whether the puzzle is completed.
    """

    def __init__(self):
        self.board = SudokuBoard("0" * 81)
        self.puzzle = self.board.get()
        self.start_puzzle = self.board.get()
        self.candidates = [[set() for x in range(9)] for y in range(9)]
        self.undostack = deque()
        self.null_board()
        self.current_to_origin()
        self.colours = [[0 for i in range(9)] for j in range(9)]
        self.candidate_colours = [[[0 for x in range(10)] for y in range(9)] for z in range(9)]

    def start(self):
        self.game_over = False
        self.candidates = [[set() for x in range(9)] for y in range(9)]
        self.puzzle = []
        self.colours = [[0 for i in range(9)] for j in range(9)]
        self.candidate_colours = [[[0 for x in range(10)] for y in range(9)] for z in range(9)]

        for i in range(9):
            self.puzzle.append([])
            for j in range(9):
                self.puzzle[i].append(self.start_puzzle[i][j])
        self.board.set_board(self.puzzle)
        self.save_undo_state()
    
    def save_undo_state(self):
        self.undostack.append((deepcopy(self.puzzle), deepcopy(self.start_puzzle), deepcopy(self.candidates),deepcopy(self.colours), deepcopy(self.candidate_colours)))

    def hint(self):
        self.reset_colours()
        hint = HintEngine(self).get_hint()

        if hint is None:
            return

        if not hint.cells1 is None:
            for cell in hint.cells1:
                row, col = cell
                self.colours[row][col] = 3

        if not hint.cells2 is None:
            for cell in hint.cells2:
                row, col = cell
                self.colours[row][col] = 4

        if not hint.good_cands is None:
            for cand in hint.good_cands:
                row, col, cand = cand
                self.candidate_colours[row][col][cand] = 1

        if not hint.bad_cands is None:
            for cand in hint.bad_cands:
                row, col, cand = cand
                self.candidate_colours[row][col][cand] = 2
        
        return hint.technique

    def undo(self):
        self.puzzle, self.start_puzzle, self.candidates, self.colours, self.candidate_colours = self.undostack.pop()

    def get_cell(self, row, col):
        return self.puzzle[row][col]
    
    def set_cell(self, row, col, val, undo=True):
        self.puzzle[row][col] = val
        self.update_candidates(row, col, undo=False)
        if undo:
            self.save_undo_state()
    
    def calculate_all_candidates(self):
        for row in range(9):
            for col in range(9):
                self.calculate_candidates(row, col, undo=False)
        self.save_undo_state()

    def calculate_candidates(self, row, col, undo=True):
        if self.puzzle[row][col] == 0:
            candidates = list(set(range(10)).difference(self.__set_buddies(row, col)))
            for candidate in candidates:
                self.add_candidate(row, col, candidate, undo=False)
        
        if undo:
            self.save_undo_state()


    def get_candidates(self, row, col):
        return list(self.candidates[row][col])
    
    def get_candidate_set(self,row, col):
        return self.candidates
    
    def get_cell_colour(self, row, col):
        return COLOURS[self.colours[row][col]]
    
    def get_candidate_colour(self, row, col, candidate):
        return COLOURS[self.candidate_colours[row][col][candidate]]
    
    def set_candidate_colour(self, row, col, candidate, colour_number, undo=True):
        self.candidate_colours[row][col][candidate] = colour_number
        if undo:
            self.save_undo_state()
    
    def set_cell_colour(self, row, col, colour_number, undo=True):
        self.colours[row][col] = colour_number
        if undo:
            self.save_undo_state()


    def toggle_candidate(self, row, col, val, undo=True):
        if val not in self.candidates[row][col]:
            self.candidates[row][col].add(val)
        else:
            self.candidates[row][col].remove(val)
        if undo:
            self.save_undo_state()

    def reset_colours(self):
        self.colours = [[0 for i in range(9)] for j in range(9)]
        self.candidate_colours = [[[0 for x in range(10)] for y in range(9)] for z in range(9)]
    
    def remove_candidate(self, row, col, val, undo=True):
        self.candidates[row][col].discard(val)
        if undo:
            self.save_undo_state()
    
    def add_candidate(self, row, col, val, undo=True):
        self.candidates[row][col].add(val)
        if undo:    
            self.save_undo_state()

    def get_origin(self, row, col):
        return self.start_puzzle[row][col]
    
    def update_candidates(self, row, col, undo=True):
        answer = self.puzzle[row][col]
        buddies = self.__find_buddies(row, col)
        for r, c in buddies:
            self.remove_candidate(r, c, answer, undo=False)
        if undo:
            self.save_undo_state()

    def __find_buddies(self, row, col):
        buddies = [] 
        # Row buddies
        buddies.extend([(row, c) for c in range(9)])
        # Column buddies
        buddies.extend([(r, col) for r in range(9)])
        # Box buddies
        box_row = row // 3
        box_col = col // 3
        buddies.extend([
                (r, c)
                for r in range(box_row * 3, (box_row + 1) * 3)
                for c in range(box_col * 3, (box_col + 1) * 3)
        ])
        return buddies

    def current_to_origin(self):
        self.game_over = False
        self.start_puzzle = []
        for i in range(9):
            self.start_puzzle.append([])
            for j in range(9):
                self.start_puzzle[i].append(self.puzzle[i][j])
        self.save_undo_state()
    
    def null_board(self):
        for i in range(9):
            for j in range(9):
                self.start_puzzle[i][j] = 0
        self.start()
                
    def load_puzzle(self, file_name, line_number):
        with open(file_name) as file:
            puzzles = [line.strip() for line in file]
            self.from_string(puzzles[line_number])
        self.save_undo_state()

    def generate(self, difficulty):
        self.board.generate(difficulty)
        self.start_puzzle = self.board.get()
        self.start()
    
    def rotate90(self):
        self.board.rotate90()
        self.start_puzzle = self.board.get()
        self.start()

    def flip_hor(self):
        self.board.flip_hor()
        self.start_puzzle = self.board.get()
        self.start()

    def flip_vert(self):
        self.board.flip_vert()
        self.start_puzzle = self.board.get()
        self.start()

    def translate(self):
        self.board.translate()
        self.start_puzzle = self.board.get()
        self.start()

    def load_random_puzzle(self, file_name):
        with open(file_name) as file:
            puzzles = [line.strip() for line in file]
            self.from_string(random.choice(puzzles))
        self.save_undo_state()

    def from_string(self, puzzle_string):
        self.board.update(puzzle_string)
        self.start_puzzle = self.board.get()
        self.start()
        self.save_undo_state()
    
    def check_win(self):
        for row in range(9):
            if not self.__check_row(row):
                return False
        for column in range(9):
            if not self.__check_column(column):
                return False
        for row in range(3):
            for column in range(3):
                if not self.__check_square(row, column):
                    return False
        self.game_over = True
        return True

    def __check_group(self, block):
        return set(block) == set(range(1,10))

    def __check_row(self, row):
        return self.__check_group(self.puzzle[row])

    def __set_row(self, row):
        return set(self.puzzle[row])

    def __check_column(self, col):
        return self.__check_group(
            [self.puzzle[row][col] for row in range(9)]
        )
    
    def __set_column(self, col):
        return set([self.puzzle[row][col] for row in range(9)])

    def __check_square(self, row, col):
        return self.__check_group(
            [
                self.puzzle[r][c]
                for r in range(row * 3, (row + 1) * 3)
                for c in range(col * 3, (col + 1) * 3)
            ]
        )
    
    def __set_square(self, box_row, box_col):
        return set(
            [
                self.puzzle[r][c]
                for r in range(box_row * 3, (box_row + 1) * 3)
                for c in range(box_col * 3, (box_col + 1) * 3)
            ]
        )
    
    def __set_buddies(self, row, col):
        return self.__set_row(row).union(self.__set_column(col), self.__set_square(row // 3, col // 3))

    
class SudokuUI(tk.Frame):
    """
    The Tkinter UI, responsible for drawing the board and accepting user input.
    """
    def __init__(self, parent, game):
        self.game = game
        self.parent = parent
        tk.Frame.__init__(self, parent)

        self.margin =  20 # Pixels around the board
        self.side = 50 # Height of each board cell
        self.width = self.height = self.margin * 2 + self.side * 9 # Width and height of the whole board
        self.cluesize = self.side // 2
        self.candidatesize = self.side // 4
        self.candidatediff = self.side // 3

        self.row, self.col = 0, 0
        self.mode = Mode.solution
        self.highlight = 0
        self.puzzle_num = 0
        self.file_name = ""
        self.technique = ""
        self.autosolve_naked_singles = tk.BooleanVar(value=False)

        self.__initUI()

    def __initUI(self):
        self.parent.title("Simple Sudoku")
        self.pack(fill=tk.BOTH, expand=1)

        # Menubar
        menubar = tk.Menu(self.parent)
        filemenu = tk.Menu(menubar, tearoff=0)
        filemenu.add_command(label="Open", command=self.__from_file)
        filemenu.add_command(label="Import from clipboard", command=self.__from_clip)
        menubar.add_cascade(label="File", menu=filemenu)
        puzzlemenu = tk.Menu(menubar, tearoff=0)
        puzzlemenu.add_command(label="Calculate candidates", command=self.__calculate_candidates)
        puzzlemenu.add_command(label="Get hint", command=self.__hint)
        puzzlemenu.add_checkbutton(label="Autosolve naked singles", onvalue=True, offvalue=0, variable=self.autosolve_naked_singles)
        puzzlemenu.add_command(label="Reset", command=self.__clear_answers)
        puzzlemenu.add_command(label="Clear", command=self.__null_board)
        puzzlemenu.add_command(label="Set Origin", command=self.__to_origin)
        generatemenu = tk.Menu(puzzlemenu, tearoff=0)
        generatemenu.add_command(label="Easy", command=self.__generate_easy)
        generatemenu.add_command(label="Medium", command=self.__generate_medium)
        generatemenu.add_command(label="Hard", command=self.__generate_hard)
        generatemenu.add_command(label="Unfair", command=self.__generate_unfair)
        generatemenu.add_command(label="Extreme", command=self.__generate_extreme)
        puzzlemenu.add_cascade(label="Generate", menu=generatemenu)
        menubar.add_cascade(label="Puzzle", menu=puzzlemenu)
        collectionmenu = tk.Menu(menubar, tearoff=0)
        collectionmenu.add_command(label="Next Puzzle", command=self.__next_puzzle)
        collectionmenu.add_command(label="Previous Puzzle", command=self.__previous_puzzle)
        collectionmenu.add_command(label="Go to specific Puzzle...", command=self.__goto_puzzle)
        collectionmenu.add_command(label="Random Puzzle", command=self.__random_from_file)
        menubar.add_cascade(label="Collection", menu=collectionmenu)
        debugmenu = tk.Menu(menubar, tearoff=0)
        debugmenu.add_command(label="rotate90", command=self.__rotate90)
        debugmenu.add_command(label="flip horizontal", command=self.__flip_hor)
        debugmenu.add_command(label="flip vertical", command=self.__flip_vert)
        debugmenu.add_command(label="translate", command=self.__translate)
        menubar.add_cascade(label="Debug", menu=debugmenu)
        self.parent.config(menu=menubar)

        self.canvas = tk.Canvas(self, width=WIDTH, height=HEIGHT)
        self.canvas.pack(fill=tk.BOTH, expand=True)

        self.__draw_grid()
        self.__draw_puzzle()
        self.__draw_cursor()
        self.canvas.focus_set()
        
        self.canvas.bind("<Left>", self.__cursor_left)
        self.canvas.bind("<Right>", self.__cursor_right)
        self.canvas.bind("<Up>", self.__cursor_up)
        self.canvas.bind("<Down>", self.__cursor_down)
        
        self.canvas.bind("<a>", self.__cursor_left)
        self.canvas.bind("<d>", self.__cursor_right)
        self.canvas.bind("<w>", self.__cursor_up)
        self.canvas.bind("<s>", self.__cursor_down)
        
        self.canvas.bind("<u>", self.__undo)
        self.canvas.bind("<q>", self.__toggle_mode_colouring)
        self.canvas.bind("<e>", self.__erase_colouring)
        self.canvas.bind("<f>", self.__toggle_mode_colour_candidate)
        self.canvas.bind("<c>", self.__calculate_candidates)
        self.canvas.bind("<h>", self.__hint)

        self.canvas.bind("<F1>", self.__toggle_highlight)
        self.canvas.bind("<F2>", self.__toggle_highlight)
        self.canvas.bind("<F3>", self.__toggle_highlight)
        self.canvas.bind("<F4>", self.__toggle_highlight)
        self.canvas.bind("<F5>", self.__toggle_highlight)
        self.canvas.bind("<F6>", self.__toggle_highlight)
        self.canvas.bind("<F7>", self.__toggle_highlight)
        self.canvas.bind("<F8>", self.__toggle_highlight)
        self.canvas.bind("<F9>", self.__toggle_highlight)

        self.canvas.bind("<Button-1>", self.__cell_clicked)
        self.canvas.bind("<Key>", self.__key_pressed)
        self.canvas.bind("<Configure>", self.__canvas_resize)
    
    def __erase_colouring(self, event):
        self.game.reset_colours()
        self.technique = ""
        self.__draw_puzzle()

    def __hint(self, event=None):
        self.technique = self.game.hint()
        self.highlight = 0
        self.__draw_puzzle()
    
    def __autofill_naked_singles(self):
        hint = HintEngine(self.game).get_naked()
        if hint is None:
            return
        else:
            for row, col, val in hint.good_cands:
                self.game.set_cell(row, col, val, undo=False)

        self.__draw_puzzle()
    
    def __undo(self, event):
        self.game.undo()
        self.__draw_puzzle()

    def __generate_easy(self):
        self.game.generate("Easy")
        self.file_name = "Easy.seed"
        self.puzzle_num = 0
        self.__draw_puzzle()

    def __generate_medium(self):
        self.game.generate("Medium")
        self.file_name = "Medium.seed"
        self.puzzle_num = 0
        self.__draw_puzzle()

    def __generate_hard(self):
        self.game.generate("Hard")
        self.file_name = "Hard.seed"
        self.puzzle_num = 0
        self.__draw_puzzle()

    def __generate_unfair(self):
        self.game.generate("Unfair")
        self.file_name = "Unfair.seed"
        self.puzzle_num = 0
        self.__draw_puzzle()

    def __generate_extreme(self):
        self.game.generate("Extreme")
        self.file_name = "Extreme.seed"
        self.puzzle_num = 0
        self.__draw_puzzle()

    def __rotate90(self):
        self.game.rotate90()
        self.__draw_puzzle()

    def __flip_hor(self):
        self.game.flip_hor()
        self.__draw_puzzle()

    def __flip_vert(self):
        self.game.flip_vert()
        self.__draw_puzzle()

    def __translate(self):
        self.game.translate()
        self.__draw_puzzle()

    def __from_file(self):
        self.file_name = tk.filedialog.askopenfilename(title="Open puzzle file")
        self.puzzle_num = 0
        self.game.load_puzzle(self.file_name, self.puzzle_num)
        self.__draw_puzzle()

    def __goto_puzzle(self):
        in_num = simpledialog.askinteger("Go to puzzle", "Go to which puzzle number")
        if in_num is not None:
            self.puzzle_num = in_num - 1
            self.game.load_puzzle(self.file_name, self.puzzle_num)
            self.__draw_puzzle()
        
    def __previous_puzzle(self):
        if self.puzzle_num != 0:
            self.puzzle_num -= 1
        self.game.load_puzzle(self.file_name, self.puzzle_num)
        self.__draw_puzzle()

    def __next_puzzle(self):
        self.puzzle_num += 1
        self.game.load_puzzle(self.file_name, self.puzzle_num)
        self.__draw_puzzle()

    def __random_from_file(self):
        self.game.load_random_puzzle(self.file_name)
        self.__draw_puzzle()
    
    def __calculate_candidates(self, event=None):
        self.game.calculate_all_candidates()
        self.__draw_puzzle()

    def __toggle_highlight(self, event):
        number = int(event.keysym[1])
        if self.highlight == number:
            self.highlight = 0
        else:
            self.highlight = number
        
        self.__draw_puzzle()

    def __null_board(self):
        self.game.null_board()
        self.__draw_puzzle()

    def __to_origin(self):
        self.game.current_to_origin()
        self.__draw_puzzle()

    def __from_clip(self):
        puzzle_string = self.clipboard_get()
        self.game.from_string(puzzle_string)
        self.__draw_puzzle()

    def __canvas_resize(self, event):
        base = min(event.width, event.height)

        self.side = (base - 2 * self.margin) // 9 
        self.width = self.height = self.margin * 2 + self.side * 9 # Width and height of the whole board
        self.cluesize = self.side // 2
        self.candidatesize = self.side // 4
        self.candidatediff = self.side // 3

        self.__draw_grid()
        self.__draw_puzzle()
        self.__draw_cursor()

    def __draw_grid(self):
        """
        Draws grid divided with blue lines into 3x3 squares
        """
        self.canvas.delete("grid")
        for i in range(10):
            color = "gray22" if i % 3 == 0 else "gray70"

            x0 = self.margin + i * self.side
            y0 = self.margin
            x1 = self.margin + i * self.side
            y1 = self.height - self.margin
            self.canvas.create_line(x0, y0, x1, y1, fill=color, width=1, tags="grid")

            x0 = self.margin
            y0 = self.margin + i * self.side
            x1 = self.width - self.margin
            y1 = self.margin + i * self.side
            self.canvas.create_line(x0, y0, x1, y1, fill=color, width=1, tags="grid")
    
    def __draw_puzzle(self):
        self.canvas.delete("numbers")
        self.canvas.delete("candidates")
        self.canvas.delete("highlights")
        self.canvas.delete("puzzleinfo")
        self.canvas.delete("cellcolouring")
        self.canvas.delete("candidatecolour")
        self.canvas.delete("hint")
        for i in range(9):
            for j in range(9):
                x0 = self.margin + j * self.side + 1
                y0 = self.margin + i * self.side + 1
                x1 = self.margin + (j + 1) * self.side - 1
                y1 = self.margin + (i + 1) * self.side - 1
                answer = self.game.get_cell(i,j)
                candidates = self.game.get_candidates(i,j)

                # First draw the highlight or else the candidates won't be visible
                do_highlight = True
                if self.highlight == 0 or self.mode is Mode.colour_candidate:
                    do_highlight = False

                if do_highlight and answer == self.highlight: 
                    self.canvas.create_rectangle(x0, y0, x1, y1, tags="highlights", fill=HLANSWER, outline=HLANSWER)
                elif do_highlight and self.highlight in candidates and answer == 0:
                    self.canvas.create_rectangle(x0, y0, x1, y1, tags="highlights", fill=HLCAND, outline=HLCAND)

                # Then draw cell colouring
                colour = self.game.get_cell_colour(i,j)
                if not colour is None and answer == 0:
                    self.canvas.create_rectangle(x0, y0, x1, y1, tags="cellcolouring", fill=colour , outline=colour)
                
                if answer != 0:
                    # Draw big character
                    x = self.margin + j * self.side + self.side / 2
                    y = self.margin + i * self.side + self.side / 2
                    original = self.game.get_origin(i, j)
                    color = "black" if answer == original else "olive drab"
                    self.canvas.create_text(x,y, text=answer, tags="numbers", fill=color, font=("Arial",self.cluesize))
                else:
                    # Draw candidate colouring
                    for candidate in candidates:
                        self.__draw_candidate_colour(i, j, candidate)
                    # Draw candidates
                    for candidate in candidates:
                        self.__draw_candidate(i, j, candidate)
        
        # Write puzzle info in the middle bottom of the puzzle
        pix = self.width / 2
        piy = self.height - self.margin / 2
        puzzle_info = ""
        if self.file_name != "":
            collection_name = self.file_name.split("/")[-1].split(".")[-2]
            if self.puzzle_num == 0:
                puzzle_info = collection_name
            else:
                puzzle_info = "{}: {}".format(collection_name, self.puzzle_num + 1)
        self.canvas.create_text(pix, piy, text=puzzle_info, tags="puzzleinfo", fill="gray", font=("Arial", 12))

        # Write the name of the Technique that was hinted in the top middle
        piy = self.margin / 2
        puzzle_info = "Hint: {}".format(self.technique)
        if self.technique != "":
            self.canvas.create_text(pix, piy, text=puzzle_info, tags="hint", fill="gray", font=("Arial", 12))
        
        # If we're autosolving singles, check once more
        if self.autosolve_naked_singles.get():
            self.__autofill_naked_singles()

    def __get_candidate_pos(self, row, col, candidate):
        diff = self.candidatediff
        cx = self.margin + col * self.side + self.side / 2
        cy = self.margin + row * self.side + self.side / 2
        if candidate == 1:
            x = cx - diff
            y = cy - diff
        elif candidate == 2:
            x = cx 
            y = cy - diff
        elif candidate == 3:
            x = cx + diff
            y = cy - diff
        elif candidate == 4:
            x = cx - diff
            y = cy
        elif candidate == 5:
            x = cx
            y = cy
        elif candidate == 6:
            x = cx + diff
            y = cy
        elif candidate == 7:
            x = cx - diff
            y = cy + diff
        elif candidate == 8:
            x = cx
            y = cy + diff
        elif candidate == 9:
            x = cx + diff
            y = cy + diff

        return x, y


    def __draw_candidate(self, row, col, candidate):
        x,y = self.__get_candidate_pos(row, col, candidate)
        self.canvas.create_text(x,y, text=candidate, tags="candidates", fill="gray", font=("Arial", self.candidatesize))

    def __draw_candidate_colour(self, row, col, candidate):
        diff = self.candidatediff / 2 - 1
        colour = self.game.get_candidate_colour(row, col, candidate)
        if colour is None:
            return
        x,y = self.__get_candidate_pos(row, col, candidate)
        x0 = x - diff
        x1 = x + diff
        y0 = y - diff
        y1 = y + diff
        self.canvas.create_oval(x0, y0, x1, y1, tags="candidatecolour", fill=colour, outline=colour)
    
    def __clear_answers(self):
        self.game.start()
        self.canvas.delete("victory")
        self.__draw_puzzle()

    def __cell_clicked(self, event):
        if self.game.game_over:
            return

        x, y = event.x, event.y
        if(self.margin < x < self.width - self.margin and self.margin < y < self.height - self.margin):
            self.canvas.focus_set()

            # get row and col numbers from x,y coordinates
            row, col = (y - self.margin) // self.side, (x - self.margin) // self.side

            # if cell was selected already - deselect it
            if (row, col) == (self.row, self.col):
                self.row, self.col = -1, -1
            elif self.game.get_origin(row,col) == 0:
                self.row, self.col = row, col
        else:
            self.row, self.col = -1, -1

        self.__draw_cursor()

    def __cursor_left(self, event):
        self.canvas.delete("cursor")
        if self.__deselected():
            self.row = 0
            self.col = 8
        else:
            if self.col == 0:
                self.col = 8
            else:
                self.col -= 1
        self.__draw_cursor()
    
    def __cursor_right(self, event):
        self.canvas.delete("cursor")
        if self.__deselected():
            self.row = 0
            self.col = 0
        else:
            if self.col == 8:
                self.col = 0
            else:
                self.col += 1
        self.__draw_cursor()

    def __cursor_up(self, event):
        self.canvas.delete("cursor")
        if self.__deselected():
            self.row = 8
            self.col = 0
        else:
            if self.row == 0:
                self.row = 8
            else:
                self.row -= 1
        self.__draw_cursor()

    def __cursor_down(self, event):
        self.canvas.delete("cursor")
        if self.__deselected():
            self.row = 0
            self.col = 0
        else:
            if self.row == 8:
                self.row = 0
            else:
                self.row += 1
        self.__draw_cursor()

    def __deselected(self):
        if self.row == -1 and self.col == -1:
            return True
        else:
            return False

    def __draw_cursor(self):
        self.canvas.delete("cursor")
        if self.row >= 0 and self.col >= 0:
            x0 = self.margin + self.col * self.side + 1
            y0 = self.margin + self.row * self.side + 1
            x1 = self.margin + (self.col + 1) * self.side - 1
            y1 = self.margin + (self.row + 1) * self.side - 1
            color = ""
            if self.mode is Mode.candidate:
                color = "blue"
            elif self.mode is Mode.solution:
                color = "red"
            elif self.mode is Mode.colour:
                color = "green"
            elif self.mode is Mode.colour_candidate:
                color = "yellow3"
            else:
                color = "pink"
            self.canvas.create_rectangle(x0, y0, x1, y1, outline=color, tags="cursor", width=3)

    def __key_pressed(self, event):
        if self.game.game_over:
            return

        if self.row >= 0 and self.col >= 0 and event.char in "1234567890":
            if self.mode is Mode.solution and self.game.get_origin(self.row,self.col) == 0:
                self.game.set_cell(self.row, self.col, int(event.char))
            elif self.game.get_origin(self.row,self.col) != 0:
                self.highlight = int(event.char)
            elif self.mode is Mode.candidate:
                self.game.toggle_candidate(self.row, self.col, int(event.char))
            elif self.mode is Mode.colour:
                self.game.set_cell_colour(self.row, self.col,int(event.char))
            elif self.mode is Mode.colour_candidate and self.game.get_origin(self.row,self.col) != 0:
                self.highlight = int(event.char)
            elif self.mode is Mode.colour_candidate:
                self.game.set_candidate_colour(self.row, self.col, int(event.char), self.highlight)
            self.__draw_puzzle()
            self.__draw_cursor()
            if self.game.check_win():
                messagebox.showinfo("Completed", "Congratulations, you solved the puzzle!")

        elif event.char == " ":
            self.__toggle_mode_candidate()
            self.__draw_cursor()
        else:
            self.__draw_puzzle()
            self.__draw_cursor()
            return
    
    def __toggle_mode_candidate(self):
        if self.mode is Mode.candidate:
            self.mode = Mode.solution
        else:
            self.mode = Mode.candidate
        self.__draw_cursor()
        self.__draw_puzzle()

    def __toggle_mode_colouring(self, event):
        if self.mode is Mode.colour:
            self.mode = Mode.solution
        else:
            self.mode = Mode.colour
        self.__draw_cursor()
        self.__draw_puzzle()
    
    def __toggle_mode_colour_candidate(self, event):
        if self.mode is Mode.colour_candidate:
            self.mode = Mode.solution
        else:
            self.mode = Mode.colour_candidate
        self.__draw_cursor()
        self.__draw_puzzle()


if __name__ == '__main__':
    game = SudokuGame()
    game.start()

    root = tk.Tk()
    SudokuUI(root,game)
    root.geometry("{}x{}".format(WIDTH, HEIGHT))
    root.mainloop()