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Sudoku Solver⚓︎

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Description⚓︎

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

A sudoku solution must satisfy all of the following rules:

  1. Each of the digits 1-9 must occur exactly once in each row.
  2. Each of the digits 1-9 must occur exactly once in each column.
  3. 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:

question

  • Input:
1
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:
1
[["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:

solution

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⚓︎

Way 1⚓︎

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class Solution {
private:
    bool backtracking(vector<vector<char>>& board) {
        for (int i = 0; i < board.size(); i++) {
            for (int j = 0; j < board[0].size(); j++) {
                if (board[i][j] == '.') {
                    for (char k = '1'; k <= '9'; k++) {
                        if (isValid(i, j, k, board)) {
                            board[i][j] = k;
                            if (backtracking(board)) return true;
                            board[i][j] = '.';
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }

    bool isValid(int row, int col, char val, vector<vector<char>>& board) {
        for (int i = 0; i < 9; i++) {
            if (board[row][i] == val)
                return false;
        }
        for (int j = 0; j < 9; j++) {
            if (board[j][col] == val)
                return false;
        }
        int rowIndex = (row / 3) * 3;
        int colIndex = (col / 3) * 3;
        for (int i = rowIndex; i < rowIndex + 3; i++) {
            for (int j = colIndex; j < colIndex + 3; j++) {
                if (board[i][j] == val)
                    return false;
            }
        }
        return true;
    }

public:
    void solveSudoku(vector<vector<char>>& board) {
        backtracking(board);
    }
};

Way 2⚓︎

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class Solution {
private:
    bool line[9][9], column[9][9], cell[3][3][9];

    bool backtracking(vector<vector<char>>& board, int row, int col) {
        if (col == 9) row++, col = 0;
        if (row == 9) return true;

        if (board[row][col] != '.') return backtracking(board, row, col + 1);

        for (int i = 0; i < 9; i++) {
            if (!line[row][i] && !column[col][i] && !cell[row / 3][col / 3][i]) {
                board[row][col] = '1' + i;
                line[row][i] = column[col][i] = cell[row / 3][col / 3][i] = true;
                if (backtracking(board, row, col + 1)) return true;
                board[row][col] = '.';
                line[row][i] = column[col][i] = cell[row / 3][col / 3][i] = false;
            }
        }
        return false;
    }
public:
    void solveSudoku(vector<vector<char>>& board) {
        memset(line, 0, sizeof(line));
        memset(column, 0, sizeof(column));
        memset(cell, 0, sizeof(cell));

        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] != '.') {
                    int t = board[i][j] - '1';
                    line[i][t] = column[j][t] = cell[i / 3][j / 3][t] = true;
                }
            }
        }

        backtracking(board, 0, 0);
    }
};