Sudoku solver

The solver is a backtracking search that always fills the most constrained cell first — the empty cell with the fewest legal digits. That single heuristic is the difference between instant and unusable: going left to right instead can take seconds on a hard grid, while choosing the tightest cell first solves a minimal 17-clue puzzle in well under a millisecond, because each choice eliminates most of the remaining tree.

The uniqueness check is the more useful output. A sudoku is defined as having exactly one solution, and it is a property of the puzzle rather than of the solver. If two solutions exist, the grid as typed is not a valid sudoku — in practice that almost always means a digit was misread from the newspaper. The search stops after finding a second solution, which is enough to answer the question without enumerating what can be millions of solutions for a nearly-empty grid.

Seventeen is the proven minimum number of clues for a unique solution. That was an open question for decades and was settled in 2012 by exhaustive computer search — there is no 16-clue sudoku with a single solution, and there never will be.

The grid is made of real input fields rather than drawn on a canvas, so it works with a keyboard and with a screen reader. A canvas grid looks tidier and is unusable for both.