Question

My sudoku solver does exactly what it’s supposed to do – except returning the correct thing. It prints what it should right before the return (a correctly solved grid), but then it seems to keep running for a bit and returns None. I can’t figure out what’s going on.

Grid is a list of lists. Assume that check_sudoku returns True if the grid is valid (solved or not), and False otherwise.

def solve_sudoku(grid, row=0, col=0):
    "Searches for valid numbers to put in blank cells until puzzle is solved."
    # Sanity check
    if not check_sudoku(grid): 
        return None
    # Sudoku is solved
    if row > 8: 
        return grid
    # not a blank, try next cell
    elif grid[row][col] != 0:
        next_cell(grid, row, col)
    else:
        # try every number from 1-9 for current cell until one is valid
        for n in range(1, 10):
            grid[row][col] = n
            if check_sudoku(grid):
                next_cell(grid, row, col)
        else:
            # Sudoku is unsolvable at this point, clear cell and backtrack
            grid[row][col] = 0
            return

def next_cell(grid, row, col):
    "Increments column if column is < 8 otherwise increments row"
    return solve_sudoku(grid, row, col+1) if col < 8 else solve_sudoku(grid, row+1, 0)

Answer 1

It seems to me like this will never actually return something useful. The first time we enter your solve_sudoku, you check to see if the grid is solved, and if so you return it. After that, you begin a bunch of recursion which ultimately will end up coming back out towards the end of the function and returning None. No matter what, you are returning None all the time. The only thing that you end up with is a modified grid argument that you passed in to start.

def solve_sudoku(grid, row=0, col=0):
    # possible return at the first entry point
    if not check_sudoku(grid): 
        return None

    # only time you would ever NOT get None
    if row > 8: 
        return grid

    ...recurse...

    # come back out when the stack unwinds,
    # and there is no return value other than None

What I speculate is happening, is that you are printing the values along the way, and you do properly see a solved grid at the moment it happens, but your function isn’t set up to properly completely break out when that is done. It continues to loop around until it exhausts some range and you see a bunch of extra work.

The important thing to do is to check the return value of the recursive call. You would either return None if its not solved, or grid if it is. As it stands, you never care about the result of your recursions in the calling scope.

Because I don’t have all the details about your specific code, here is a simple equivalent:

def solver(aList):
    if aList[0] == 10:
        print "SOLVED!"
        return None

    print "NOT SOLVED..."
    return next(aList)

def next(aList):
    # do some stuff
    # check some stuff
    aList[0] += 1
    return solver(aList)


if __name__ == "__main__":
    data = [0]
    solver(data)
    print data

Notice that the indirectly recursive call to checker() -> solver() has its value returned all the way up the chain. In this case we are saying None means solved, and otherwise it should keep recursing. You know that at some point deep in your recursion stack, the solution will be solved. You will need to communicate that back up to the top right away.

The communication looks like this:

aList == [0]
solver(aList)
  next(...)
    next(...)
      next(...)
        next(...) 
          #SOLVED
        <- next(...)
      <- next(...)
    <- next(...)
  <- next(...)
<-solver(aList)
aList == [10]

And here is what your version might look like if applied to my simple example:

aList == [0]
solver(aList)
  next(...)
    next(...)
      # SOLVED
      next(...)
        next(...) 
          ...
        <- next(...)
      <- next(...)
    <- next(...)
  <- next(...)
<-solver(aList)
aList == [10]