Box Canonicalization of a Floor

A band of 3 rows from a Sudoku solution grid can be modified to its minimum lexicographic equivalent.

For a Sudoku grid with only givens a different algorithm is used, to account for missing digits.

Steps to find all 36 starting permutations

• Permute the 3 rows. (6 permutations)
• Permute the 3 boxes. (6 permutations)

Steps to normalize a starting permutation

• Relabel the numbers so that box 1 reads:

123
456
789

• Sort box 2 and 3 so that box 2 contains 4 in the top row.
• Sort the columns in box 2 so that r1c4=4, r1c5 < r1c6
• Sort the columns in box 3 so that r1c7 < r1c8 < r1c9.