用C语言实现递归和回溯求解数独字段

#include <stdio.h>
#include <stdbool.h>

#define N 9

bool isValid(int board[N][N], int row, int col, int num) {
    for (int x = 0; x < N; x++) {
        if (board[row][x] == num || board[x][col] == num) {
            return false;
        }
    }

    int startRow = row - row % 3, startCol = col - col % 3;
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            if (board[i + startRow][j + startCol] == num) {
                return false;
            }
        }
    }

    return true;
}

bool solveSudoku(int board[N][N], int row, int col) {
    if (row == N - 1 && col == N) {
        return true;
    }

    if (col == N) {
        row++;
        col = 0;
    }

    if (board[row][col] > 0) {
        return solveSudoku(board, row, col + 1);
    }

    for (int num = 1; num <= N; num++) {
        if (isValid(board, row, col, num)) {
            board[row][col] = num;
            if (solveSudoku(board, row, col + 1)) {
                return true;
            }
            board[row][col] = 0;
        }
    }

    return false;
}

void printBoard(int board[N][N]) {
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            printf("%d ", board[i][j]);
        }
        printf("\n");
    }
}

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

    if (solveSudoku(board, 0, 0)) {
        printBoard(board);
    } else {
        printf("No solution exists\n");
    }

    return 0;
}