Sudoku Solver

Sudoku is a number-placement puzzle: fill a 9×9 grid so that every row, every column, and each of the nine 3×3 boxes contains the digits 1 through 9 exactly once. You are handed a partially filled board — a 0 marks an empty cell, and the digits 1–9 are fixed clues — and must complete it. This is LeetCode 37; every puzzle you receive is guaranteed to have exactly one solution. See Sudoku for the rules and history.

Signature

sudokuSolver(board)  // board: number[][], a 9x9 grid; 0 = empty, 1..9 = clues
                     // fills the board IN PLACE and returns the same board

You mutate the grid you are given and return that same reference — not a fresh copy.

Examples

// The board is a 9x9 array of numbers. A 0 is an empty cell to fill.
const board = [
  [5, 3, 0,  0, 7, 0,  0, 0, 0],
  [6, 0, 0,  1, 9, 5,  0, 0, 0],
  [0, 9, 8,  0, 0, 0,  0, 6, 0],
  [8, 0, 0,  0, 6, 0,  0, 0, 3],
  [4, 0, 0,  8, 0, 3,  0, 0, 1],
  [7, 0, 0,  0, 2, 0,  0, 0, 6],
  [0, 6, 0,  0, 0, 0,  2, 8, 0],
  [0, 0, 0,  4, 1, 9,  0, 0, 5],
  [0, 0, 0,  0, 8, 0,  0, 7, 9],
];

const solved = sudokuSolver(board);
solved === board; // true — the same array, now filled in

// solved is:
// [
//   [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],
// ]

Notes

• One solution guaranteed — each puzzle has exactly one valid completion, so you never choose between competing answers, and you will never be handed an unsolvable grid.
• Solve in place — write into the board you were given and return that same reference. Do not build and return a new grid.
• The three constraints — a digit may go in a cell only if it does not already appear in that cell's row, its column, or its 3×3 box. All three must hold at once.
• The 3×3 box — the box that contains cell (r, c) has its top-left corner at row 3 * Math.floor(r / 3) and column 3 * Math.floor(c / 3); its nine cells span that corner plus the next two rows and columns.
• Digits, not strings — cells hold the numbers 1–9, with 0 for empty. You do not need to validate the input or handle any grid shape other than 9×9.