Solve a 9x9 Sudoku puzzle

You are given a partially completed nine-by-nine Sudoku grid. Empty cells are represented by '.'. Fill every empty cell with a digit from '1' to '9' so that the completed board satisfies all Sudoku rules. A completed board is valid when: every row contains each digit from '1' to '9' exactly once; every column contains each digit from '1' to '9' exactly once; every one of the nine three-by-three boxes contains each digit from '1' to '9' exactly once. board is stored as nine…