37. Sudoku Solver

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:

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.

 

Solutions

Solution: Backtracking

• Time complexity: O(NP-Complete)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {character[][]} board
 * @return {void} Do not return anything, modify board in-place instead.
 */
const solveSudoku = function (board) {
  const m = board.length;
  const n = board[0].length;
  const isValid = (current, num) => {
    for (let row = 0; row < m; row++) {
      if (board[row][current.col] === `${num}`) return false;
    }
    for (let col = 0; col < n; col++) {
      if (board[current.row][col] === `${num}`) return false;
    }
    const startRow = current.row - (current.row % 3);
    const startCol = current.col - (current.col % 3);

    for (let row = startRow; row < startRow + 3; row++) {
      for (let col = startCol; col < startCol + 3; col++) {
        if (board[row][col] === `${num}`) return false;
      }
    }
    return true;
  };
  const solveSudokuCell = (row, col) => {
    if (row === 9) return true;
    if (col === 9) return solveSudokuCell(row + 1, 0);
    if (board[row][col] !== '.') return solveSudokuCell(row, col + 1);

    for (let num = 1; num <= 9; num++) {
      if (!isValid({ row, col }, num)) continue;
      board[row][col] = `${num}`;
      if (solveSudokuCell(row, col + 1)) return true;
      board[row][col] = '.';
    }
    return false;
  };

  solveSudokuCell(0, 0);
  return board;
};