37. Sudoku Solver.cpp

[shafaq16]

Approach: Backtracking

I use a backtracking algorithm to fill the empty cells ('.') one by one with digits '1' to '9'.
For each empty cell, try all possible digits.
Before placing, check if it's valid (row, column, and 3×3 subgrid rules).
If valid → place it, then recursively try to solve the rest.
If no digit works → backtrack (undo placement and try another option).
If all cells are filled correctly → solution is found.
This ensures we systematically explore possibilities until we reach the correct valid Sudoku configuration.

Intuition

Think of Sudoku solving as filling a puzzle step by step with trial and error:
Whenever you see an empty cell, you test numbers just like a human would.
If the number violates Sudoku rules, skip it.
If a number works, assume it’s correct and move forward.
If later you hit a dead-end, backtrack to the previous step and try another option.

This mimics how humans solve Sudoku, but the computer does it exhaustively and efficiently.

Solution in Code (C++)

class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        backtrack(board);
    }

private:
    bool backtrack(vector<vector<char>>& board) {
        for (int r = 0; r < 9; r++) {
            for (int c = 0; c < 9; c++) {
                if (board[r][c] == '.') {
                    for (char ch = '1'; ch <= '9'; ch++) {
                        if (isValid(board, r, c, ch)) {
                            board[r][c] = ch;
                            if (backtrack(board)) return true; // continue with this placement
                            board[r][c] = '.'; // undo if failed
                        }
                    }
                    return false; // no valid digit, backtrack
                }
            }
        }
        return true; // all cells filled
    }

    bool isValid(vector<vector<char>>& board, int r, int c, char ch) {
        // Row & Column check
        for (int i = 0; i < 9; i++) {
            if (board[r][i] == ch) return false;
            if (board[i][c] == ch) return false;
        }
        // 3x3 sub-box check
        int startRow = (r / 3) * 3;
        int startCol = (c / 3) * 3;
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                if (board[startRow + i][startCol + j] == ch) return false;
            }
        }
        return true;
    }
};

[github-actions]

Thanks for raising the PR, the owner will be review it soon' keep patience, keep contributing>>>!!! make sure you have star ⭐ the repo

[SjxSubham]

Well @shafaq16

Star the repo ⭐...

Happy HAcktober... keep contributing

[SjxSubham]

@shafaq16 can you solve #51 problem ...this one already solved by soemone

[shafaq16]

hey @SjxSubham pls assign this to me as you told me before to solve this one

[shafaq16]

Hey @SjxSubham kindly check my pr #63 under #51 problem