AcWing 703 Sudoku Check

Title description:

Sudoku is a popular single player game.

The goal is to fill the 9x9 matrix with numbers so that each column, each row and all 9 non-overlapping 3x3 sub-matrices contain all numbers from 1 to 9.

Each 9x9 matrix will have some numbers already given at the beginning of the game, and there is usually a unique solution.

Given the completed N^2∗N^2 Sudoku matrix, your task is to determine whether it is a valid solution.

An effective solution must meet the following conditions:

Each line contains each number from 1 to N^2, once for each number.
Each column contains each number from 1 to N^2, once for each number.
Divide the N^2∗N^2 matrix into N^2 non-overlapping N∗N sub-matrices. Each sub-matrix contains every number from 1 to N^2, once for each number.

You don't need to worry about the uniqueness of the problem, just check whether the given matrix is an effective solution.

Input format

The first line contains an integer T, which means there are T groups of test data.

The first row of each group of data contains the integer N.

The next N^2 lines, each line contains N^2 numbers (none of which exceeds 1000), which are used to describe the complete Sudoku matrix.

Output format

Each group of data outputs a result, and each result occupies one line.

The result is expressed as "Case #x: y", where x is the group number (starting from 1), if the given matrix is a valid solution, then y is Yes, otherwise y is No.

data range

1≤T≤100,
3≤N≤6

Input sample:

3
3
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 5 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
3
5 3 4 6 7 8 9 1 2
6 7 2 1 9 5 3 4 8
1 9 8 3 4 2 5 6 7
8 5 9 7 6 1 4 2 3
4 2 6 8 999 3 7 9 1
7 1 3 9 2 4 8 5 6
9 6 1 5 3 7 2 8 4
2 8 7 4 1 9 6 3 5
3 4 5 2 8 6 1 7 9

Sample output:

Case #1: Yes
Case #2: No
Case #3: No

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>

using namespace std;
const int MAX = 50;

int a[MAX][MAX];
int n, T, N;
bool row[MAX][MAX], col[MAX][MAX], tip[MAX][MAX][MAX];

bool judge()
{
    for(int i = 0; i < N; i++)
    {
        for(int j = 0; j < N; j++)
        {
            int x = a[i][j];
            if(x >= 1 && x <= N && !row[i][x] && !col[j][x] && !tip[i / n][j / n][x])
            {
                row[i][x] = col[j][x] = tip[i / n][j / n][x] = true;
            }
            else
                return false;

        }
    }
    return true;
}

int main()
{
    scanf("%d", &T);

    int k = 1;

    while(T--)
    {
        memset(row, false, sizeof(row));
        memset(col, false, sizeof(col));
        memset(tip, false, sizeof(tip));

        scanf("%d", &n);
        N = n * n;

        for(int i = 0; i < N; i++)
        {
            for(int j = 0; j < N; j++)
                scanf("%d", &a[i][j]);
        }

        if(judge())
            printf("Case #%d: Yes\n", k++);
        else
            printf("Case #%d: No\n", k++);
    }
    return 0;
}

AcWing 703 Sudoku Check

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