48ms straitforward python DFS solution with explanations

  • 13

    It's similar to how human solve Sudoku.

    1. create a hash table (dictionary) val to store possible values in every location.
    2. Each time, start from the location with fewest possible values, choose one value from it and then update the board and possible values at other locations. If this update is valid, keep solving (DFS). If this update is invalid (leaving zero possible values at some locations) or this value doesn't lead to the solution, undo the updates and then choose the next value.

    Since we calculated val at the beginning and start filling the board from the location with fewest possible values, the amount of calculation and thus the runtime can be significantly reduced:

    The run time is 48-68 ms on LeetCode OJ, which seems to be among the fastest python solutions here.

    The PossibleVals function may be further simplified/optimized, but it works just fine for now. (it would look less lengthy if we are allowed to use numpy array for the board lol).

    def solveSudoku(self, board):
        self.board = board
        self.val = self.PossibleVals()
    def PossibleVals(self):
        a = "123456789"
        d, val = {}, {}
        for i in xrange(9):
            for j in xrange(9):
                ele = self.board[i][j]
                if ele != ".":
                    d[("r", i)] = d.get(("r", i), []) + [ele]
                    d[("c", j)] = d.get(("c", j), []) + [ele]
                    d[(i//3, j//3)] = d.get((i//3, j//3), []) + [ele]
                    val[(i,j)] = []
        for (i,j) in val.keys():
            inval = d.get(("r",i),[])+d.get(("c",j),[])+d.get((i/3,j/3),[])
            val[(i,j)] = [n for n in a if n not in inval ]
        return val
    def Solver(self):
        if len(self.val)==0:
            return True
        kee = min(self.val.keys(), key=lambda x: len(self.val[x]))
        nums = self.val[kee]
        for n in nums:
            update = {kee:self.val[kee]}
            if self.ValidOne(n, kee, update): # valid choice
                if self.Solver(): # keep solving
                    return True
            self.undo(kee, update) # invalid choice or didn't solve it => undo
        return False
    def ValidOne(self, n, kee, update):
        self.board[kee[0]][kee[1]] = n
        del self.val[kee]
        i, j = kee
        for ind in self.val.keys():
            if n in self.val[ind]:
                if ind[0]==i or ind[1]==j or (ind[0]/3,ind[1]/3)==(i/3,j/3):
                    update[ind] = n
                    if len(self.val[ind])==0:
                        return False
        return True
    def undo(self, kee, update):
        for k in update:            
            if k not in self.val:
                self.val[k]= update[k]
        return None

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