Problem E: Su-Su-Sudoku/center>

题目连接：

http://codeforces.com/gym/100646/attachments

Description

By now, everyone has played Sudoku: you’re given a 9-by-9 grid of boxes which you are to fill in with
the digits 1 through 9 so that 1) every row has all nine digits, 2) every column has all nine digits, and
3) all nine 3-by-3 subgrids have all nine digits. To start the game you are given a partially completed
grid and are asked to fill in the remainder of the boxes. One such puzzle is shown below.
4 8 1 2 5 3 6 9 7
2 6 7 9 4 8 1 5
5 3 9 6 7 1 2 4
6 5 4 3 8 9 7 1 2
9 8 7 4 5 6 3
1 7 3 5 6 2 8 4 9
7 2 1 3 6 9 5 8
3 1 5 8 9 7 4 2 6
8 9 6 4 2 5 3 7 1
In this problem, you will be given Sudoku grids which you have nearly completed; indeed you’ve filled
in every box except five. You are asked to complete the grid, or determine that it’s impossible. (You
might have already made an error!)

Input

The first line of input will contain a positive integer indicating the number of test cases to follow. Each
test case will be a nearly completed Sudoku grid consisting of 9 lines, each containing 9 characters from
the set of digits 0 through 9. There will be exactly five 0’s in each test case, indicating the five unfilled
boxes.

Output

Output for each test case should be either
Could not complete this grid.
if it is impossible to complete the grid according to the rules of the game, or the completed grid, in the
form given below. (There are no blank spaces in the output.) If there is a way to complete the grid, it
will be unique. Separate test cases with a blank line.

Sample Input

2
481253697
267948105
539671204
654389712
908704563
173562849
702136958
315897426
896425371
481253697
267948105
539671284
654289710
908704562
173562849
702136958
315897426
896425371

Sample Output

481253697
267948135
539671284
654389712
928714563
173562849
742136958
315897426
896425371
Could not complete this grid.

Hint

题意

给你个数独，问你有没有解。

但是这个数独最多只有5个空位。

题解：

智障题，只有五个空，那就XJBdfs就好了

代码

#include<bits/stdc++.h>
using namespace std;

string s[9];
struct node{
    int x,y;
    node(int X,int Y):x(X),y(Y){};
};
vector<node> V;
int flag = 0;
int vis[10];
bool check(){
    for(int i=0;i<9;i++){
        for(int j=0;j<10;j++)vis[j]=0;
        for(int j=0;j<9;j++){
            vis[s[i][j]-'0']=1;
        }
        for(int j=1;j<=9;j++)if(!vis[j])return false;
    }
    for(int i=0;i<9;i++){
        for(int j=0;j<10;j++)vis[j]=0;
        for(int j=0;j<9;j++){
            vis[s[j][i]-'0']=1;
        }
        for(int j=1;j<=9;j++)if(!vis[j])return false;
    }
    for(int i=0;i<10;i++)vis[i]=0;
    vis[s[0][0]-'0']=1;
    vis[s[0][1]-'0']=1;
    vis[s[0][2]-'0']=1;
    vis[s[1][0]-'0']=1;
    vis[s[1][1]-'0']=1;
    vis[s[1][2]-'0']=1;
    vis[s[2][0]-'0']=1;
    vis[s[2][1]-'0']=1;
    vis[s[2][2]-'0']=1;
    for(int j=1;j<=9;j++)if(!vis[j])return false;
    for(int i=0;i<10;i++)vis[i]=0;
    vis[s[0][3]-'0']=1;
    vis[s[0][4]-'0']=1;
    vis[s[0][5]-'0']=1;
    vis[s[1][3]-'0']=1;
    vis[s[1][4]-'0']=1;
    vis[s[1][5]-'0']=1;
    vis[s[2][3]-'0']=1;
    vis[s[2][4]-'0']=1;
    vis[s[2][5]-'0']=1;
    for(int j=1;j<=9;j++)if(!vis[j])return false;
    for(int i=0;i<10;i++)vis[i]=0;
    vis[s[0][6]-'0']=1;
    vis[s[0][7]-'0']=1;
    vis[s[0][8]-'0']=1;
    vis[s[1][6]-'0']=1;
    vis[s[1][7]-'0']=1;
    vis[s[1][8]-'0']=1;
    vis[s[2][6]-'0']=1;
    vis[s[2][7]-'0']=1;
    vis[s[2][8]-'0']=1;
    for(int j=1;j<=9;j++)if(!vis[j])return false;

    for(int i=0;i<10;i++)vis[i]=0;
    vis[s[3][0]-'0']=1;
    vis[s[3][1]-'0']=1;
    vis[s[3][2]-'0']=1;
    vis[s[4][0]-'0']=1;
    vis[s[4][1]-'0']=1;
    vis[s[4][2]-'0']=1;
    vis[s[5][0]-'0']=1;
    vis[s[5][1]-'0']=1;
    vis[s[5][2]-'0']=1;
    for(int j=1;j<=9;j++)if(!vis[j])return false;
    for(int i=0;i<10;i++)vis[i]=0;
    vis[s[3][3]-'0']=1;
    vis[s[3][4]-'0']=1;
    vis[s[3][5]-'0']=1;
    vis[s[4][3]-'0']=1;
    vis[s[4][4]-'0']=1;
    vis[s[4][5]-'0']=1;
    vis[s[5][3]-'0']=1;
    vis[s[5][4]-'0']=1;
    vis[s[5][5]-'0']=1;
    for(int j=1;j<=9;j++)if(!vis[j])return false;
    for(int i=0;i<10;i++)vis[i]=0;
    vis[s[3][6]-'0']=1;
    vis[s[3][7]-'0']=1;
    vis[s[3][8]-'0']=1;
    vis[s[4][6]-'0']=1;
    vis[s[4][7]-'0']=1;
    vis[s[4][8]-'0']=1;
    vis[s[5][6]-'0']=1;
    vis[s[5][7]-'0']=1;
    vis[s[5][8]-'0']=1;
    for(int j=1;j<=9;j++)if(!vis[j])return false;

    for(int i=0;i<10;i++)vis[i]=0;
    vis[s[6][0]-'0']=1;
    vis[s[6][1]-'0']=1;
    vis[s[6][2]-'0']=1;
    vis[s[7][0]-'0']=1;
    vis[s[7][1]-'0']=1;
    vis[s[7][2]-'0']=1;
    vis[s[8][0]-'0']=1;
    vis[s[8][1]-'0']=1;
    vis[s[8][2]-'0']=1;
    for(int j=1;j<=9;j++)if(!vis[j])return false;
    for(int i=0;i<10;i++)vis[i]=0;
    vis[s[6][3]-'0']=1;
    vis[s[6][4]-'0']=1;
    vis[s[6][5]-'0']=1;
    vis[s[7][3]-'0']=1;
    vis[s[7][4]-'0']=1;
    vis[s[7][5]-'0']=1;
    vis[s[8][3]-'0']=1;
    vis[s[8][4]-'0']=1;
    vis[s[8][5]-'0']=1;
    for(int j=1;j<=9;j++)if(!vis[j])return false;
    for(int i=0;i<10;i++)vis[i]=0;
    vis[s[6][6]-'0']=1;
    vis[s[6][7]-'0']=1;
    vis[s[6][8]-'0']=1;
    vis[s[7][6]-'0']=1;
    vis[s[7][7]-'0']=1;
    vis[s[7][8]-'0']=1;
    vis[s[8][6]-'0']=1;
    vis[s[8][7]-'0']=1;
    vis[s[8][8]-'0']=1;
    for(int j=1;j<=9;j++)if(!vis[j])return false;

    return true;
}
void dfs(int x){
    if(flag)return;
    if(x==V.size()){
        if(check()){
            for(int i=0;i<9;i++)
                cout<<s[i]<<endl;
            flag = 1;
            return;
        }
        return;
    }
    for(int i=1;i<=9;i++){
        s[V[x].x][V[x].y]=i+'0';
        dfs(x+1);
        if(flag)return;
        s[V[x].x][V[x].y]='0';
    }
}
void solve(){
    flag = 0;
    V.clear();
    for(int i=0;i<9;i++)
        cin>>s[i];
    for(int i=0;i<9;i++){
        for(int j=0;j<9;j++){
            if(s[i][j]=='0'){
                V.push_back(node(i,j));
            }
        }
    }
    dfs(0);
    if(flag==0){
        printf("Could not complete this grid.\n");
    }
    printf("\n");
}
int main(){
    //freopen("1.in","r",stdin);
    int t;
    scanf("%d",&t);
    while(t--)solve();
    return 0;
}