Write a program to solve a Sudoku puzzle by filling the empty cells.
Empty cells are indicated by the character '.'.
You may assume that there will be only one unique solution.
A sudoku puzzle...
...and its solution numbers marked in red.
1 class Solution(object): 2 def validset(self ): 3 s='123456789' 4 return set(s) 5 6 def initTbl(self, tbl, board): 7 for i in range(9): 8 for j in range(9): 9 if board[i][j] == '.': 10 tbl[(i,j)]=[] 11 12 13 def solveSudoku(self, board): 14 """ 15 :type board: List[List[str]] 16 :rtype: bool 17 """ 18 resultTbl={} 19 visited=[] 20 self.initTbl(resultTbl, board) 21 reuse=False 22 unvisited = resultTbl.keys() 23 unvisited.sort() 24 unvisited.reverse() 25 26 while unvisited != []: 27 (x, y) = unvisited.pop() 28 if reuse==False: 29 resultTbl[(x,y)] = self.possibleValues((x,y), board) 30 if resultTbl[(x,y)] == None: # invalid sudoku 31 print False 32 break 33 34 if len( resultTbl[(x,y)] ) == 0: # DEAD END, BACKTRACK 35 unvisited.append((x, y)) 36 if visited != []: 37 reuse=True 38 prev=visited.pop() 39 unvisited.append(prev) 40 x=prev[0] 41 y=prev[1] 42 board[x][y]='.' 43 else: 44 break 45 continue 46 board[x][y]=resultTbl[(x,y)].pop() 47 visited.append((x,y)) 48 reuse=False 49 for line in board: 50 if '.' in line: 51 print False 52 53 54 def possibleValues(self, coord, board): 55 vals = {'.':0} 56 for i in range(1,10): #init 57 vals[str(i)]=0 58 59 for y in range(0,9): 60 node=board[coord[0]][y] 61 vals[node]+=1 62 if vals[node]>1 and node!='.': return None 63 for x in range(0,9): 64 node=board[x][coord[1]] 65 vals[node]+=1 66 if vals[node] > 2 and node!='.': return None 67 x = coord[0]/3*3 68 y = coord[1]/3*3 69 for i in range(x, x+3): 70 for j in range(y, y+3): 71 node=board[i][j] 72 vals[node]+=1 73 if vals[node]>3 and node!='.': return None 74 s = set() 75 for k in vals.keys(): 76 if vals[k]>=1: s.add(k) 77 return self.validset() - s