Sudoku solver in C++

The program solves a Sudoku in two distinct sequential phases: (1) deduction and (2) recursion.

During the deduction phase, The board is modelled as a 3D array of booleans representing row, column and possible digits (in that order). The function calculate_valid_digits(..) assigns a value of true to digits that can be validly placed in each square, with invalid digits marked false. For each row, column, box and square in turn, the board is updated to reflect digits which can only validly be placed in one square. This process is repeated until no more deductions are possible, at which point the board is passed into the recursive function fill_next_square(..) to test if it is complete or requires guessing.

During the recursive phase, the program attempts to fill all remaining empty squares with a valid digit. The function get_next_square(..) is used to find the next empty square, which is then assigned the value of the lowest digit that can be validly placed in it. The function fill_next_square(..) is then called again. This is repeated until either (i) the board is complete (function returns true) or (ii) there are no digits which can be validly placed in a particular square, indicating a mistake in an earlier digit assignemnt. In the case of the latter, the program moves back to the most recently assigned square and attempts to places the next highest valid digit in that square (if there is one). If there is no valid solution, the function returns false (when there are no more valid digits that can be place in square [0][0]).