Sudoku Solver
Sudoku Solver uses backtracking to fill a 9×9 grid with digits 1-9, ensuring each row, column, and 3×3 box contains all digits exactly once. This classic constraint satisfaction problem demonstrates systematic exploration with constraint checking. The algorithm fills empty cells one by one, backtracking when constraints are violated, making it a perfect example of pruning in search algorithms.
Visualization
Interactive visualization for Sudoku Solver
Sudoku Solver (Backtracking)
• Backtracking with constraint propagation
• Tries values 1-9, backtracks on conflicts
• Classic constraint satisfaction problem
Interactive visualization with step-by-step execution
Implementation
1function solveSudoku(board: string[][]): boolean {
2 const isValid = (row: number, col: number, num: string): boolean => {
3 // Check row
4 for (let j = 0; j < 9; j++) {
5 if (board[row][j] === num) return false;
6 }
7
8 // Check column
9 for (let i = 0; i < 9; i++) {
10 if (board[i][col] === num) return false;
11 }
12
13 // Check 3x3 box
14 const boxRow = Math.floor(row / 3) * 3;
15 const boxCol = Math.floor(col / 3) * 3;
16 for (let i = 0; i < 3; i++) {
17 for (let j = 0; j < 3; j++) {
18 if (board[boxRow + i][boxCol + j] === num) return false;
19 }
20 }
21
22 return true;
23 };
24
25 const solve = (): boolean => {
26 for (let i = 0; i < 9; i++) {
27 for (let j = 0; j < 9; j++) {
28 if (board[i][j] === '.') {
29 for (let num = 1; num <= 9; num++) {
30 const numStr = num.toString();
31 if (isValid(i, j, numStr)) {
32 board[i][j] = numStr;
33 if (solve()) return true;
34 board[i][j] = '.';
35 }
36 }
37 return false;
38 }
39 }
40 }
41 return true;
42 };
43
44 return solve();
45}Deep Dive
Theoretical Foundation
Sudoku Solver uses backtracking with constraint checking. For each empty cell, it tries digits 1-9, checking three constraints: (1) digit not in same row, (2) not in same column, (3) not in same 3×3 box. If valid, it places the digit and recursively solves remaining cells. If recursion fails (no valid digit found), it backtracks by removing the digit and trying the next one. The algorithm finds the first empty cell, tries all possible digits, and recursively proceeds. Time complexity is O(9^m) where m is the number of empty cells, but constraint propagation reduces this dramatically in practice. The worst case is an empty board requiring 9^81 attempts, but typical puzzles with 40-50 given cells solve quickly.
Complexity
Time
O(1)
O(9^m)
O(9^m)
Space
O(1)
Applications
Industry Use
Sudoku mobile apps and websites
Puzzle validation and generation
Constraint satisfaction problem teaching
Logic game solvers
Automated puzzle difficulty rating
AI for puzzle-solving competitions
Educational tools for learning backtracking
Use Cases
Related Algorithms
N-Queens Problem
The N-Queens Problem asks: place N chess queens on an N×N chessboard so that no two queens threaten each other. This means no two queens can be on the same row, column, or diagonal. It's a classic constraint satisfaction problem that demonstrates backtracking, pruning, and systematic exploration of solution spaces. The problem has applications in parallel processing, resource allocation, and algorithm design education.
Combination Sum
Find all unique combinations in array where chosen numbers sum to target. Numbers can be reused. Classic backtracking problem with pruning optimization.
Generate Valid Parentheses
Generate all combinations of n pairs of well-formed parentheses. Uses backtracking with constraint that closing parentheses never exceed opening ones.
Word Search in Grid
Given 2D board and word, find if word exists in grid. Word must be constructed from letters of sequentially adjacent cells (horizontally or vertically). Uses backtracking with visited tracking.