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

bool isValid(int grid[9][9], int r, int c, int num);

void generateIncompleteGrid(int grid[9][9]) {
    srand(time(NULL));
    int i, j, block; 
    for (i = 0; i < 9; i++) {
        for (j = 0; j < 9; j++) {
            grid[i][j] = 0;
        }
    }
    for (block = 0; block < 3; block++) {
        int used[10] = {0}; 
        for (i = 0; i < 3; i++) {
            int r = block * 3 + i;
            int placedNum = 0;
            while (placedNum < 3) {
                int num = (rand() % 9) + 1; 
                int c = rand() % 9;
                if (grid[r][c] == 0 && isValid(grid, r, c, num) && used[num] == 0) {
                    grid[r][c] = num;
                    used[num] = 1; 
                    placedNum++;
                }
            }
        }
    }
}

void print(int grid[9][9]) {
    int i, j;
    for (i = 0; i < 9; i++) {
        for (j = 0; j < 9; j++) {
            printf("%2d ", grid[i][j]);
            if ((j + 1) % 3 == 0 && j < 8) {
                printf("| ");
            }
        }
        printf("\n");
        if ((i + 1) % 3 == 0 && i < 8) {
            printf("-----------------------\n");
        }
    }
}

bool isValid(int grid[9][9], int r, int c, int num) {
    int x, i, j;
    for (x = 0; x < 9; x++) {
        if (grid[r][x] == num || grid[x][c] == num) {
            return false;
        }
    }

    int startR = r - r % 3, startC = c - c % 3;
    for (i = 0; i < 3; i++) {
        for (j = 0; j < 3; j++) {
            if (grid[i + startR][j + startC] == num) {
                return false;
            }
        }
    }
    return true;
}

bool solve(int grid[9][9]) {
    int r, c;
    bool empty = false;
    
    for (r = 0; r < 9; r++) {
        for (c = 0; c < 9; c++) {
            if (grid[r][c] == 0) {
                empty = true;
                break;
            }
        }
        if (empty) break;
    }

    if (!empty) return true;

    int num;
    for (num = 1; num <= 9; num++) {
        if (isValid(grid, r, c, num)) {
            grid[r][c] = num;

            if (solve(grid)) {
                return true;
            }
            
            grid[r][c] = 0;
        }
    }
    return false;
}

bool validate(int grid[9][9]) {
    int r, c;
    for (r = 0; r < 9; r++) {
        for (c = 0; c < 9; c++) {
            if (grid[r][c] != 0) {
                int num = grid[r][c];
                grid[r][c] = 0; 
                if (!isValid(grid, r, c, num)) {
                    return false;
                }
                grid[r][c] = num; 
            }
        }
    }
    return true;
}

int main() {
    int grid[9][9];
    int board0[9][9] = {{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}};
    
    generateIncompleteGrid(grid);
    printf("The original Sudoku matrix:\n");
    print(board0);
    
    if (validate(board0)) {
        printf("True:Valid initial Sudoku matrix!\n");
        if (solve(board0)) {
            printf("Completed Sudoku Grid:\n");
            print(board0);
        } else {
            printf("No solution exists for this Sudoku.\n");
        }
    } else {
        printf("False:Invalid initial Sudoku matrix!\n");
    }
    return 0;
}