Sudoku

#include <cstdio>
#include <iostream>
#include <cstring>
using namespace std;

const int maxn = 12;
int T;
char s[maxn][maxn];
int a[maxn][maxn];
int r[maxn][maxn], c[maxn][maxn], g[maxn][maxn];

int G[maxn][maxn];

int ans;

void init() {
    ans = 0;
    memset(r, 0, sizeof r);
    memset(c, 0, sizeof c);
    memset(g, 0, sizeof g);
}

// 求第几宫
int u(int x, int y) {
    x = x / 3;
    y = y / 3;
    return 3 * x + y;
}

void dfs(int num) {
    if(num == 81) {
        ans = 1;
        return;
    }

    int x = num / 9, y = num % 9;
    if(a[x][y] != 0) {
        dfs(num + 1);
        if(ans == 1) return;
    } else {
        for(int i = 1; i <= 9; i ++) {
            if(r[x][i] || c[y][i] || g[G[x][y]][i]) continue;
            a[x][y] = i;
            r[x][i] = 1;
            c[y][i] = 1;
            g[G[x][y]][i] = 1;

            dfs(num + 1);
            if(ans == 1) return;

            a[x][y] = 0;
            r[x][i] = 0;
            c[y][i] = 0;
            g[G[x][y]][i] = 0;
        }
    }
}

int main() {
    scanf("%d", &T);
    for(int cas = 1; cas <= T; cas ++) {
        init();
        
        for(int i = 0; i < 9; i ++) {
            scanf("%s", s[i]);
            for(int j = 0; s[i][j]; j ++) {
                G[i][j] = u(i, j);
                if(s[i][j] == ‘*‘) s[i][j] = ‘0‘;
                a[i][j] = s[i][j] - ‘0‘;
                if(a[i][j] != 0) {
                    r[i][a[i][j]] = 1; // 第 i 行已经出现了 a[i][j]
                    c[j][a[i][j]] = 1; // 第 j 列已经出现了 a[i][j]
                    g[G[i][j]][a[i][j]] = 1; // 第 G(i, j) 宫已经出现了 a[i][j]
                }
            }
        }

        dfs(0);

        if(ans == 1) {
            for(int i = 0; i < 9; i ++) {
                for(int j = 0; j < 9; j ++) {
                    printf("%d", a[i][j]);
                }
                printf("\n");
            }
            printf("\n");
        } else {
            printf("No solution\n");
        }

    }
    return 0;
}