A Sudoku of rank n is an n² n² square grid, subdivided into n² blocks, each of these blocks has the size of (n n). The problem is that given distinct integer numbers 1, 2, 3, ..., n² , fill the grid in with these numbers such that every integer should appear only once in each raw, in each column, and in each block. The Sudoku problem is known to be an NP-complete.

a) Suppose that you are given an instance (n²n² ) grid filled in with distinct integer numbers 1, 2, 3, ..., n² . What is the formula that can be applied to check if the desired conditions are met by the given instance?

b) Design an algorithm to check if the given grid is a solution for the Sudoku problem.

c) Analyze your algorithm in (b).