I am trying to solve a basic puzzle by using Google OR-Tools, this is my first try with OR-Tools and I am trying to learn. I completed almost everything and was ready to conclude the program until I came across this problem.

For information my game_board is a dictionary including entire board, with already given values and not given values that are set to IntVar.

I have several values in each cell as following:

  • Variable, cell is set as IntVar which were initially 0 in board, so it will be determined to be filled or not, values are 0 for empty, 1 for filled)
  • 8, the cell is free connection, indicating this is just a virtual cell added to represent the game in a matrix so cell above this, is connected to cell below it directly
  • 9, the cell is a solid block, so it separates its above and below cells.

What I do is, I iterate over the board and I am try to fill water according to gravity (and some other rules), so I assigned A cell should be equal to the cell below it if there is no block between them. However I forgot that, cell below can be full and the cell above can be empty, however with the constraint set above they can only be equal.

I used the part below the set the constraint mentioned above and I have 2 problems at this point.

if (row+1 <= max(row_variable_indices)) and (game_board[(row+1,column)] == 8):
  if (game_board[(row+1,column)] == -1):
    model.Add(game_board[(row,column)] == game_board[(row+1,column)])
    model.Add(game_board[(row,column)] == game_board[(row+2,column)])
  1. I overcame this by other methods, but still wanted to ask how can I differentiate IntVar from something else. I can not differentiate IntVar as checking IntVar == Int or IntVar != Int since thety both return True for any given Int. So I checked if cell is equal to 8 first, if cell is 8 then cell is either a free connection or a variable, and then I checked if cell is -1 as -1 is not used in the board anywhere, it would only choose the variables.

  2. My main problem is I need to change this constraint to A cell should be equal to the cell below it if there is no block between them and the cell below is assigned to 0. I tried doing it .OnlyEnforceIf() by something like following, but it didn't work and gave following error. How can I solve this. I understand I need to use BoolVar however I am not sure how to set a BoolVar for this condition (and for every other cell I have) because if I can not say if a variable A is set to value x, I can not set the bool based on if A is set to x either

model.Add(game_board[(row,column)] == game_board[(row+1,column)]).OnlyEnforceIf(game_board[(row+1,column)] == 1)

Note I actually tried it on some dummy matrix as following:


/usr/local/lib/python3.6/dist-packages/ortools/sat/python/cp_model.py in OnlyEnforceIf(self, boolvar)
    607                     self.__constraint.enforcement_literal.append(b.Index())
    608         else:
--> 609             self.__constraint.enforcement_literal.append(boolvar.Index())
    610         return self

AttributeError: 'BoundedLinearExpression' object has no attribute 'Index'

Edited to add that, I can not change (or I don't know if I can) my IntVar variables to BoolVar variables and check this filling problem, because I also use sum() somewhere else counting the filled cells of that row/column by adding up the all IntVar variables of that row/column. I don't think it works in BoolVar as they don't have a value to be summed up unlike integer value of IntVar which is summable.


1 Answer 1


Okay I solved the main problem (2) after researching and playing around a bit with BoolVar. So unlike I thought, I don't have to assign BoolVar myself based on other things. Instead I could use its two cases True and False to check and bind the two cases I have. I made the modification below:

if (row+1 <= max(row_variable_indices)) and (game_board[(row+1,column)] == 8):
  a = model.NewBoolVar('a')
  if (game_board[(row+1,column)] == -1):
    model.Add(game_board[(row+1,column)] == 0).OnlyEnforceIf(a)
    model.Add(game_board[(row,column)] == game_board[(row+1,column)]).OnlyEnforceIf(a)

    model.Add(game_board[(row+1,column)] == 1).OnlyEnforceIf(a.Not())

    model.Add(game_board[(row+2,column)] == 0).OnlyEnforceIf(a)
    model.Add(game_board[(row,column)] == game_board[(row+2,column)]).OnlyEnforceIf(a)

    model.Add(game_board[(row+2,column)] == 1).OnlyEnforceIf(a.Not())

It assigns the cell below as 1 if and only if BoolVar == False. Assigns the cell below 0 if and only if BoolVar == True, and in this case assigns the top to bottom.

Don't forget to add BoolVar == False case, even if this case doesn't specify any relation between the top and bottom; If this is not set the bottom can be 0 with BoolVar == False and in this case top wouldn't be assigned to bottom and the violation of the required constraint (the top is equal to bottom if bottom is 0) may occur.


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