Question

Does anyone know a simple algorithm to check if a Sudoku-Configuration is valid? The simplest algorithm I came up with is (for a board of size n) in Pseudocode

for each row   for each number k in 1..n     if k is not in the row (using another for-loop)       return not-a-solution  ..do the same for each column 

But I’m quite sure there must be a better (in the sense of more elegant) solution. Efficiency is quite unimportant.

Answer 1

You need to check for all the constraints of Sudoku :

• check the sum on each row
• check the sum on each column
• check for sum on each box
• check for duplicate numbers on each row
• check for duplicate numbers on each column
• check for duplicate numbers on each box

that’s 6 checks altogether.. using a brute force approach.

Some sort of mathematical optimization can be used if you know the size of the board (ie 3×3 or 9×9)

Edit: explanation for the sum constraint: Checking for the sum first (and stoping if the sum is not 45) is much faster (and simpler) than checking for duplicates. It provides an easy way of discarding a wrong solution.