# Sudoku Solver (Backtracking)

This utility solves a 9x9 Sudoku puzzle using the **Backtracking** algorithm. It demonstrates recursion and constraint satisfaction.

**Modules Used:**
*   Standard Library only.

## The Algorithm

1.  **Find an empty cell**: Look for a cell containing `0`.
2.  **Try numbers 1-9**: Attempt to place a number in the empty cell.
3.  **Check validity**: Ensure the number doesn't exist in the current row, column, or 3x3 subgrid.
4.  **Recurse**: If valid, move to the next empty cell.
5.  **Backtrack**: If the recursion fails (leads to an unsolvable state), reset the cell to `0` and try the next number.

## The Code

Save this as `sudoku.py`.

```python
def print_board(board):
    for i in range(len(board)):
        if i % 3 == 0 and i != 0:
            print("- - - - - - - - - - - -")

        for j in range(len(board[0])):
            if j % 3 == 0 and j != 0:
                print(" | ", end="")

            if j == 8:
                print(board[i][j])
            else:
                print(str(board[i][j]) + " ", end="")

def find_empty(board):
    for i in range(len(board)):
        for j in range(len(board[0])):
            if board[i][j] == 0:
                return (i, j)  # row, col
    return None

def valid(board, num, pos):
    # Check row
    for i in range(len(board[0])):
        if board[pos[0]][i] == num and pos[1] != i:
            return False

    # Check column
    for i in range(len(board)):
        if board[i][pos[1]] == num and pos[0] != i:
            return False

    # Check box
    box_x = pos[1] // 3
    box_y = pos[0] // 3

    for i in range(box_y*3, box_y*3 + 3):
        for j in range(box_x*3, box_x*3 + 3):
            if board[i][j] == num and (i,j) != pos:
                return False

    return True

def solve(board):
    find = find_empty(board)
    if not find:
        return True
    else:
        row, col = find

    for i in range(1, 10):
        if valid(board, i, (row, col)):
            board[row][col] = i

            if solve(board):
                return True

            board[row][col] = 0

    return False

if __name__ == "__main__":
    # Example Board (0 represents empty cells)
    board = [
        [7, 8, 0, 4, 0, 0, 1, 2, 0],
        [6, 0, 0, 0, 7, 5, 0, 0, 9],
        [0, 0, 0, 6, 0, 1, 0, 7, 8],
        [0, 0, 7, 0, 4, 0, 2, 6, 0],
        [0, 0, 1, 0, 5, 0, 9, 3, 0],
        [9, 0, 4, 0, 6, 0, 0, 0, 5],
        [0, 7, 0, 3, 0, 0, 0, 1, 2],
        [1, 2, 0, 0, 0, 7, 4, 0, 0],
        [0, 4, 9, 2, 0, 6, 0, 0, 7]
    ]

    print("Original Board:")
    print_board(board)
    
    print("\nSolving...\n")
    
    solve(board)
    
    print("Solved Board:")
    print_board(board)
```

## Usage

```bash
python sudoku.py
```

[[programming/python/python]]