Any column contains the same number more than once.Any row contains the same number more than once.Thus, we can also conclude that a Sudoku is considered wrongly filled if it satisfies any of these criteria: You can see that every row, column, and sub-matrix (3x3) contains each digit from 1 to 9. For example, a Sudoku problem is given below. We are provided with a partially filled 9x9 matrix and have to fill every remaining cell in it. Sudoku is a 9x9 matrix filled with numbers 1 to 9 in such a way that every row, column and sub-matrix (3x3) has each of the digits from 1 to 9. If you don't know about backtracking, then just brush through the previous post.
With that modified recursion, Sudoko problems should be quickly solved even with slow languages on slow computers.In this post, I will introduce a Sudoku-solving algorithm using backtracking. This could even be a field with 0 alternatives. The function find_most_constrained_square() counts for each empty field, how many different numbers can still be put there, and returns the index to that field, that had the lowest number of possibilities. Next_square = game->find_most_constrained_square()įoreach value = next_square->possible_values Backtrack, if any contradictions arise, and then try the next value for a field, that had several alternatives.
If no more empty fields exist, for which only one value is legal, look for fields, that allow at most two (or generally, the minimum number of possible) values, and try one of those values, and continue with the recursion. Therefore, my recommendation is to solve Sudoku like a human does: Find a field, for which the already filled in numbers allow only one specific value, and fill in that field. Therefore, any "dumb" backtracking algorithm starting from the top left field and processing towards bottom right is likely to get stuck in an seemingly "endless" loop. The point about Sudoku is, that you have a massive number of states: 9^81 is a number of 78 digits. variables in the system are inferred from the number ofĪrities(arityBegin, arityEnd), done(false)įill_n (back_inserter(values), arities.size(), 0) the usual conventions for C++ iterators. as integers stored in positions arityBegin. a different number of possible values. Create a backtracking state in which each variable may have can be reached by subsequent ++ or prune operaations.īackTrack::BackTrack (Iterator arityBegin, Indicates whether additional candidate solutions exist that Returns the number of potential values that can be assigned Unsigned BackTrack::arity (unsigned variableNumber) const Returns the number of variables in the backtracking system. Unsigned BackTrack::numberOfVariables() const Returns the current value associated with the indicated Unsigned BackTrack::operator (unsigned variableNumber) const While(!not solved & not the end of the vector) puzzle = the initial state 9x9 grid from left to right of integers Included is the backtracking algorithm and its definition.Įdit: "Again, took out the class definition, left the declaration and put up the pseudo code"īacktrack game (81,9) // represents all possible combinations of input and values for game //All info is loading into a vector of size 81 with the initial state The backtracking algorithm I'm trying to use seems standard but I can't follow the logic and know whats happening underneath. I've been still unable to wrap the general algorithm around in my head given the problem domain I'm working in. I'm trying to solve a sudoku puzzle using recursive backtracking. Answer: My pseudo is fuzzy in the recursive aspect but this video is helpful along with the resources belowĬan't grasp the implementation of this backtrack recursive algorithm in respect to a sudoku puzzle.
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