Sudoku Solver

Problem

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.

Solution

class Solution {
    int rows = 9;
    int cols = 9;

    public void solveSudoku(char[][] board) {
        solve(board, 0, 0);
    }

    // increments row/col as appropriate and calls solve
    public boolean solveNext(char[][] board, int row, int col) {
        if (row == rows - 1 && col == cols - 1) {
            return true;
        }
        if (col >= cols - 1) {
            row += 1;
            col = 0;
        } else {
            col += 1;
        }
        return solve(board, row, col);
    }

    public boolean isValid(char[][] board, int row, int col) {
        // check that the row is valid
        var s = new HashSet<Character>();
        for (int i = 0; i < cols; i++) {
            var c = board[row][i];
            if (c != '.' && s.contains(c)) {
                return false;
            }
            s.add(c);
        }
        s.clear();

        // check that the col is valid
        for (int i = 0; i < rows; i++) {
            var c = board[i][col];
            if (c != '.' && s.contains(c)) {
                return false;
            }
            s.add(c);
        }
        s.clear();

        // check that the square is valid
        var gRow = (int) Math.floor(row / 3);
        var gCol = (int) Math.floor(col / 3);

        for (var r = gRow * 3; r < (gRow * 3) + 3; r++) {
            for (var c = gCol * 3; c < (gCol * 3) + 3; c++) {
                var ch = board[r][c];
                if (ch != '.' && s.contains(ch)) {
                    return false;
                }
                s.add(ch);
            }
        }

        return true;
    }

    public boolean solve(char[][] board, int row, int col) {
        if (board[row][col] == '.') {
            for (var i = 1; i <= 9; i++) {
                board[row][col] = Character.forDigit(i, 10);
                // check if this board state is valid
                // if it is valid, recurse
                if (isValid(board, row, col)) {
                    var result = solveNext(board, row, col);
                    if (result) {
                        return true;
                    }
                }
                // undo
                board[row][col] =  '.';
            }
        } else {
            return solveNext(board, row, col);
        }
        return false;
    }
}

Recent posts from blogs that I like

Paintings of the Franco-Prussian War: 2 The Siege of Paris

As winter grew colder, Parisians started to starve. A city known for its food and restaurants had to scavenge meals based on horse, dog, cat and even rat.

via The Eclectic Light Company

Impromptu disaster recovery

via fasterthanlime

Notes on implementing Attention

Some notes on implementing attention blocks in pure Python + Numpy. The focus here is on the exact implementation in code, explaining all the shapes throughout the process. The motivation for why attention works is not covered here - there are plenty of excellent online resources explaining it. Seve...

via Eli Bendersky