37 - Sudoku Solver.

Hard

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

• Each of the digits 1-9 must occur exactly once in each row.

• Each of the digits 1-9 must occur exactly once in each column.

• Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

Example 1:

Input: board = ["5","3",".",".","7",".",".",".",".",

"6",".",".","1","9","5",".",".",".",

".","9","8",".",".",".",".","6",".",

"8",".",".",".","6",".",".",".","3",

"4",".",".","8",".","3",".",".","1",

"7",".",".",".","2",".",".",".","6",

".","6",".",".",".",".","2","8",".",

".",".",".","4","1","9",".",".","5",

".",".",".",".","8",".",".","7","9"]

Output: ["5","3","4","6","7","8","9","1","2",

"6","7","2","1","9","5","3","4","8",

"1","9","8","3","4","2","5","6","7",

"8","5","9","7","6","1","4","2","3",

"4","2","6","8","5","3","7","9","1",

"7","1","3","9","2","4","8","5","6",

"9","6","1","5","3","7","2","8","4",

"2","8","7","4","1","9","6","3","5",

"3","4","5","2","8","6","1","7","9"]

Explanation: The input board is shown above and the only valid solution is shown below:

Constraints:

• board.length == 9

• board[i].length == 9

• board[i][j] is a digit or '.'.

• It is guaranteed that the input board has only one solution.