Gym 100646 Problem E: Su-Su-Sudoku 水题

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;
}