Build an Efficient Sudoku Solver in C++ | Smart Algorithm Explained (2025)

Sudoku Solver in C++ is a popular puzzle that requires filling a 9×9 grid so that each row, column, and 3×3 subgrid contains all digits from 1 to 9 without repetition. This blog will walk through an efficient backtracking approach to sudoku solver algorithm.

What’s Sudoku Solver in C++ algorithm?

The Sudoku Solver algorithm uses backtracking, which systematically explores all possible placements for a number in the grid. If a valid placement is found, the algorithm moves forward; otherwise, it backtracks to try another possibility.

The steps for Solving Sudoku Using C++:

1. Find an Empty Cell: Search for a cell containing 0.
2. Check for Validity: Try numbers 1-9 and check if placing a number is valid according to Sudoku rules.
3. Recursive Backtracking: If a valid number is found, place it and recursively solve the rest of the board.
4. Undo and Try Another Number: If no solution exists for the current number, reset the cell and try another number.
5. Print the Solution: If the entire board is filled correctly, print the solution.

Sudoku Solver in C++ Source Code Implementation

#include <iostream>

bool isValid(int board[9][9], int row, int col, int num)
{
    for (int i = 0; i < 9; i++)
    {
        if (board[row][i] == num || board[i][col] == num ||
            board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == num)
            return false;
    }
    return true;
}

void printBoard(int board[9][9])
{
    for (int row = 0; row < 9; row++)
    {
        for (int col = 0; col < 9; col++)
        {
            std::cout << board[row][col] << " ";
        }
        std::cout << std::endl;
    }
}

void sudokuSolver(int board[9][9])
{
    int row, col;
    for (row = 0; row < 9; row++)
    {
        for (col = 0; col < 9; col++)
        {
            if (board[row][col] == 0)
            {
                for (int num = 1; num <= 9; num++)
                {
                    if (isValid(board, row, col, num))
                    {
                        board[row][col] = num;
                        sudokuSolver(board);
                        board[row][col] = 0; // Backtrack
                    }
                }
                return;
            }
        }
    }
    printBoard(board);
}

int main()
{
    int board[9][9] = {
        {0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 5, 0, 0, 0, 0, 8, 0, 1},
        {0, 0, 0, 3, 2, 4, 9, 0, 0},
        {0, 7, 0, 9, 0, 0, 4, 3, 0},
        {2, 0, 0, 4, 0, 6, 0, 0, 7},
        {0, 8, 4, 0, 0, 2, 0, 9, 0},
        {0, 0, 6, 8, 5, 3, 0, 0, 0},
        {9, 0, 8, 0, 0, 0, 0, 5, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0}
    };
    
    sudokuSolver(board);
    return 0;
}

Output

The program prints a valid solved Sudoku board when executed.

Complexity Analysis

• Time Complexity: The worst-case complexity is O(9^(N*N)), where N = 9. However, optimizations like constraint propagation can improve performance.
• Space Complexity: O(1) since we use the board itself without extra memory.

Conclusion

This C++ program successfully solves Solving Sudoku using C++ using a backtracking approach. Though efficient for small grids, more advanced techniques like constraint programming and heuristic search can further enhance performance for larger puzzles.

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