Generation

Planning   

Solving according to strategies is pretty straightforward. Generating puzzles is more complex and exercises your comfort with recursion. In general terms generating a puzzle follows these steps
  • Create an empty grid
  • Use brute force to solve
  • Remove random 'sures' to reach a target number of givens, ensuring that the result is solvable using the level of difficulty strategies you are aiming for.

We are going to deal with the brute force solving part here. The general flow is
    while grid Solvable and not Solved
        for each random cell not Solved
            make a random possibility into a sure
                recurs

.. and here is the code

This is interesting in that it is not only recursive in of itself, but it also calls .Solve which resurses through with .Solveiterate.
Brute is implemented as method of the cPuzzle class. It will create a cloned instance of cSudGrid for each recursion, and destroy it if that path is not successful.

It also chooses which cells and which possibilities to try next, randomly, except that for efficiency reasons, the cells are kept sorted into least possibilities first order.

This will keep going,  trying alternate paths and backtracking until it finds a solution to what starts as a blank Sudoku. Since there should always be a solution, it will only reach wrapup if something has gone wrong. 


Private Sub Brute()
    Dim ic As Long, indexOfCell As Long, ip As Long, iCollectionIndex As Long, iz As Long, indexInList As Long, idx As Long
    Dim sc As cSudCell
    'this one solves by brute force, and would be used for generating

    ' first find the next unsure cell
    Set sc = pGrid.nextrandomUnSure
    Debug.Assert Not sc Is Nothing
    indexOfCell = sc.Index

    
    ' this instance of brute will deal solely with this cell, and recurse for the next one
    ' try every possibilty in a random order for this cell till one sticks
    ip = pGrid.Item(indexOfCell).nextRandomPossibility
    While ip <> 0
    '   clone a new grid for this particular route
        iCollectionIndex = pGrid.CollectionIndex
        newGrid pGrid
        With pGrid
            .Item(indexOfCell).makeSure ip
            .solve

            If .isSolved Then GoTo wrapup
            
            ' if still solvable then guess for the next cell along
            If Not .isScrewedUp Then Brute
            
            ' the puzzle is solved...?
            If isSolved Then GoTo wrapup

            ' if we get here then we have used a non viable guess, so backtrack by scrapping the current grid
            pCollection.Remove (.CollectionIndex)
        
        End With
        ' go back to the grid before we tried that abortive possibility and try another
        Set pGrid = pCollection(iCollectionIndex)
        ip = pGrid.Item(indexOfCell).nextRandomPossibility
                    
    Wend

wrapup:
    ' should only get here if all is solved
    Debug.Assert isSolved
    
    
End Sub

Next steps

As before the entire code will be is downloadable here. Now we have created a completed grid, the next step will be to remove items to the required level of difficulty, and we will have completed the generation of a puzzle.

You want to learn Google Apps Script?

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