Sudoku Solver | Problems

Complete a partially filled 9x9 Sudoku grid so that every row, every column, and each of the nine 3x3 boxes contains the digits 1 through 9 with no repeats. Fill in the empty cells directly to produce a valid, fully solved board.

Input Format

Implement solveSudoku(board). Inputs below show JavaScript function arguments; there is no stdin parsing.

Output Format

Modify argument 1 in place. The editor compares its final value; the function return value is ignored.

Sample Input and Output

Example 1 · Run Sample

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"]]

Example 2

Input

board = [["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"]]

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"]]

Constraints

board is a 9 × 9 grid of characters 1 through 9 or dot.
The given clues are valid and the puzzle has exactly one solution.

Test Cases (2)

Case 1

Args: [[["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"]]] Expected: [["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"]]

Case 2

Args: [[["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"]]] Expected: [["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"]]

Topics

Backtracking Recursion

Use backtracking to fill empty cells one by one. For each cell, try digits 1–9 and validate against Sudoku row, column, and 3×3 box constraints. If no digit works, backtrack.

javascript

function solveSudoku(board) {
  function isValid(row, col, ch) {
    const boxRow = Math.floor(row / 3) * 3;
    const boxCol = Math.floor(col / 3) * 3;
    for (let i = 0; i < 9; i++) {
      if (board[row][i] === ch) return false;
      if (board[i][col] === ch) return false;
      if (board[boxRow + Math.floor(i / 3)][boxCol + (i % 3)] === ch) return false;
    }
    return true;
  }

  function solve() {
    for (let r = 0; r < 9; r++) {
      for (let c = 0; c < 9; c++) {
        if (board[r][c] !== '.') continue;
        for (let d = 1; d <= 9; d++) {
          const ch = String(d);
          if (isValid(r, c, ch)) {
            board[r][c] = ch;
            if (solve()) return true;
            board[r][c] = '.';
          }
        }
        return false;
      }
    }
    return true;
  }

  solve();
}

Time: O(9^(empty cells)) — bounded by the fixed board size Space: O(81) recursion depth

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