1. Find empty cell
Skip filled cells; only an empty '.' needs a digit.
if (board[r][c] !== ".") continueTyporithm · hard
Sudoku Solver
▷ Interactive algorithm labsudoku-solverbacktrackingconstraintsgrid-fillchoose-explore-undo
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Full lesson · 8 learning steps Open any exercise for focused practice
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Step 1 of 8 · intro card
Learn Sudoku Solver
Backtracking
Fill each empty cell by trying digits 1..9, keeping only ones valid in their row, column, and 3x3 box.
Scan for the first empty '.' cell, then try each digit from 1 to 9 in turn.
A digit is valid only if it does not already appear in the same row, column, or 3x3 box.
Place a valid digit and recurse; if the recursion fails, reset the cell and try the next digit.
Preparing algorithm lab…
01
Find an empty cell, try 1..9.
02
Validate row, column, and box.
03
Place, recurse, reset on failure.
function solveSudoku(board) {
function isValid(board, r, c, ch) {
for (let i = 0; i < 9; i += 1) {
if (board[r][i] === ch) return false;
if (board[i][c] === ch) return false;
const boxR = 3 * Math.floor(r / 3) + Math.floor(i / 3);
const boxC = 3 * Math.floor(c / 3) + (i % 3);
if (board[boxR][boxC] === ch) return false;
}
return true;
}
function solve() {
for (let r = 0; r < 9; r += 1) {
for (let c = 0; c < 9; c += 1) {
if (board[r][c] !== ".") continue;
for (let d = 1; d <= 9; d += 1) {
const ch = String(d);
if (!isValid(board, r, c, ch)) continue;
board[r][c] = ch;
if (solve()) return true;
board[r][c] = ".";
}
return false;
}
}
return true;
}
solve();
return board;
}Read the implementation
Connect each part of the code to the concept before you type.
2. Reject conflict
Skip a digit that clashes in its row, column, or 3x3 box.
if (!isValid(board, r, c, ch)) continue3. Place digit
Write the candidate digit into the empty cell.
board[r][c] = ch4. Explore
Recurse; a true result means the rest of the board was solved.
if (solve()) return true5. Reset (undo)
Reset the cell so a different digit can be tried.
board[r][c] = "."A complete learning loop
01
Understand
Read the concept map and follow the code breakdown.
02
Reconstruct
Type the implementation, repair mistakes and work through every recall exercise.
03
Verify
Use the final check without hints; revisit weak concepts in short practice sessions.