Optimize sudoku.isSolved

[metal-pony]

Currently, isSolved calls isFull, then isValid for each row, column, and region.

• [ ] Merge these two checks into a single function call that checks the entire board and fails fast if either invalid or partially full.
• [ ] Additionally, track validity and fullness as numbers are added or removed to the sudoku. This could add a little bit of extra work to the set/removeDigit functions, but get isSolved and other checks in constant time.

Further ideas to think about:

• Should set/removeDigit reject if the result of the operation caused the sudoku to be invalid?

[metal-pony]

This will encompass several optimizations via caching certain data points used throughout the code. Each time a cell is updated, we will:

• keep track of fullness and validity of all rows, columns, and regions, as well as flags for the whole board.
• keep track of all empty cells

Currently, the solver (searchForSolutions3) is creating many extra Sudoku instances to populate node.nexts. Change node data to track (1) the index of the cell being tried and (2) the remaining candidates (as an encoded 9-bit int, same as board values in state). That should eliminate some garbage and should be faster - benchmark it to see. Then, each time the search backtracks, if remaining candidates > 0, replace the cell digit with a new candidate, remove the candidate from node.nexts, and continue the search. While remaining candidates is 0, just keep backtracking. Also note that because reduce() is called between guesses and fills in empty spaces, we'll need a way to remove the reduced cells when backtracking. Maybe a 3rd node data point board mask could be tracked before guessing, and each backtrack resets cells to empty via the mask.