蓝桥杯模拟一 数独

蒜头君今天突然开始还念童年了，想回忆回忆童年。他记得自己小时候，有一个很火的游戏叫做数独。便开始来了一局紧张而又刺激的高阶数独。蒜头君做完发现没有正解，不知道对不对？ 不知道聪明的你能否给出一个标准答案？

标准数独是由一个给与了提示数字的 9 imes 99×9 网格组成，我们只需将其空格填上数字，使得每一行，每一列以及每一个 3 imes 33×3 宫都没有重复的数字出现。

输出这个数独得正解，输出格式如下：

 

1 * 2 6 * * * * * *

2 * * * 5 * 2 * * 4

3 * * * 1 * * * * 7

4 * 3 * * 2 * 1 8 *

5 * * * 3 * 9 * * *

6 * 5 4 * 1 * * 7 *

7 5 * * * * 1 * * *

8 6 * * 9 * 7 * * *

9 * * * * * * 7 5 *

 

 

把上面的 * 替换成 1 - 91−9 就可以了

提醒：两个数字之间要有一个空格，其他地方不要输出多余的符号。

本题答案不唯一，符合要求的答案均正确

 

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <map>
#include <set>
#define maxn 10010
#define debug(a) cout << #a << " " << a << endl
using namespace std;
typedef long long ll;
int vis1[10][10] = {0}, vis2[10][10] = {0}, vis3[10][10] = {0};
int mapn[10][10] = {0}, num = 0;
int f( int x, int y ) {
    if( x >= 1 && x <= 3 ) {
        if( y >= 1 && y <= 3 ) {
            return 1;
        } else if( y >= 4 && y <= 6 ) {
            return 2;
        } else if( y >= 7 && y <= 9 ) {
            return 3;
        }
    } else if( x >= 4 && x <= 6 ) {
        if( y >= 1 && y <= 3 ) {
            return 4;
        } else if( y >= 4 && y <= 6 ) {
            return 5;
        } else if( y >= 7 && y <= 9 ) {
            return 6;
        }
    } else if( x >= 7 && x <= 9 ) {
        if( y >= 1 && y <= 3 ) {
            return 7;
        } else if( y >= 4 && y <= 6 ) {
            return 8;
        } else if( y >= 7 && y <= 9 ) {
            return 9;
        }
    }
}
void dfs( int x, int y ) {
    //cout << ++num << endl;
    if( x == 10 && y == 1 ) {
        ++num;
        for( int i = 1; i <= 9; i ++ ) {
            for( int j = 1; j <= 9; j ++ ) {
                cout << mapn[i][j] << " ";
            }
            cout << endl;
        }
        cout << "-----------" << endl;
        return ;
    }
    if( mapn[x][y] ) {
        if( y + 1 > 9 ) {
            dfs( x + 1, 1 );
        } else {
            dfs( x, y + 1 );
        }
    } else {
        for( int i = 1; i <= 9; i ++ ) {
            if( !vis1[x][i] && !vis2[y][i] &&
               !vis3[f(x,y)][i] ) {
                    if( y + 1 > 9 ) {
                        vis1[x][i] = 1,vis2[y][i] = 1,vis3[f(x,y)][i] = 1;
                        //debug(i);
                        mapn[x][y] = i;
                        dfs( x + 1, 1 );
                        mapn[x][y] = 0;
                        vis1[x][i] = 0,vis2[y][i] = 0,vis3[f(x,y)][i] = 0;
                    } else {
                        vis1[x][i] = 1,vis2[y][i] = 1,vis3[f(x,y)][i] = 1;
                        mapn[x][y] = i;
                        dfs( x, y + 1 );
                        mapn[x][y] = 0;
                        vis1[x][i] = 0,vis2[y][i] = 0,vis3[f(x,y)][i] = 0;
                    }
               }
        }
    }
}
int main() {

    vis1[1][2] = 1,vis1[1][6] = 1,vis1[2][5] = 1,
    vis1[2][2] = 1,vis1[2][4] = 1,vis1[3][1] = 1,
    vis1[3][7] = 1,vis1[4][3] = 1,vis1[4][2] = 1,
    vis1[4][1] = 1,vis1[4][8] = 1,vis1[5][3] = 1,
    vis1[5][9] = 1,vis1[6][5] = 1,vis1[6][4] = 1,
    vis1[6][1] = 1,vis1[6][7] = 1,vis1[7][5] = 1,
    vis1[7][1] = 1,vis1[8][6] = 1,vis1[8][9] = 1,
    vis1[8][7] = 1,vis1[9][7] = 1,vis1[9][5] = 1;

    vis2[1][5] = 1,vis2[1][6] = 1,vis2[2][2] = 1,
    vis2[2][3] = 1,vis2[2][5] = 1,vis2[3][6] = 1,
    vis2[3][4] = 1,vis2[4][5] = 1,vis2[4][1] = 1,
    vis2[4][3] = 1,vis2[4][9] = 1,vis2[5][2] = 1,
    vis2[5][1] = 1,vis2[6][2] = 1,vis2[6][9] = 1,
    vis2[6][1] = 1,vis2[6][7] = 1,vis2[7][1] = 1,
    vis2[7][7] = 1,vis2[8][8] = 1,vis2[8][7] = 1,
    vis2[8][5] = 1,vis2[9][4] = 1,vis2[9][7] = 1;

    vis3[1][2] = 1,vis3[1][6] = 1,vis3[2][5] = 1,
    vis3[2][2] = 1,vis3[2][1] = 1,vis3[3][4] = 1,
    vis3[3][7] = 1,vis3[4][3] = 1,vis3[4][4] = 1,
    vis3[4][5] = 1,vis3[5][1] = 1,vis3[5][2] = 1,
    vis3[5][3] = 1,vis3[5][9] = 1,vis3[6][1] = 1,
    vis3[6][7] = 1,vis3[6][8] = 1,vis3[7][5] = 1,
    vis3[7][6] = 1,vis3[8][1] = 1,vis3[8][7] = 1,
    vis3[8][9] = 1,vis3[9][5] = 1,vis3[9][7] = 1;

    mapn[1][2] = 2,mapn[1][3] = 6,mapn[2][4] = 5,
    mapn[2][6] = 2,mapn[2][9] = 4,mapn[3][4] = 1,
    mapn[3][9] = 7,mapn[4][2] = 3,mapn[4][5] = 2,
    mapn[4][7] = 1,mapn[4][8] = 8,mapn[5][4] = 3,
    mapn[5][6] = 9,mapn[6][2] = 5,mapn[6][3] = 4,
    mapn[6][5] = 1,mapn[6][8] = 7,mapn[7][1] = 5,
    mapn[7][6] = 1,mapn[8][1] = 6,mapn[8][4] = 9,
    mapn[8][6] = 7,mapn[9][7] = 7,mapn[9][8] = 5;

    dfs( 1, 1 );

    cout << num << endl;
    return 0;
}

/*
搜出来的第一种答案
1 2 6 7 3 4 5 9 8
3 7 8 5 9 2 6 1 4
4 9 5 1 6 8 2 3 7
7 3 9 4 2 5 1 8 6
8 6 1 3 7 9 4 2 5
2 5 4 8 1 6 3 7 9
5 4 7 2 8 1 9 6 3
6 1 3 9 5 7 8 4 2
9 8 2 6 4 3 7 5 1  */