Sudoku Checker
Problem Description
Sudoku is a popular single player game. The objective is to fill a 9x9 matrix with digits so that each column, each row, and all 9 non-overlapping 3x3 sub-matrices contain all of the digits from 1 through 9. Each 9x9 matrix is partially completed at the start of game play and typically has a unique solution.
Given a completed N2×N2 Sudoku matrix, your task is to determine whether it is a valid solution.
A valid solution must satisfy the following criteria:
- Each row contains each number from 1 to N2, once each.
- Each column contains each number from 1 to N2, once each.
- Divide the N2×N2 matrix into N2 non-overlappingN×N sub-matrices. Each sub-matrix contains each number from 1 to N2, once each.
You don't need to worry about the uniqueness of the problem. Just check if the given matrix is a valid solution.
Input
The first line of the input gives the number of test cases, T(1 ≤ T ≤ 100).
T test cases follow. Each test case starts with an integer N(3 ≤ N ≤ 6).
The next N2 lines describe a completed Sudoku solution, with each line contains exactlyN2 integers.
All input integers are positive and less than 1000.
Output
For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) andy is "Yes" (quotes for clarity only) if it is a valid solution, or "No" (quotes for clarity only) if it is invalid.
Sample Input
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
大致题意：给一个数独。看看符不符合要求。
PS：做个题还长姿势了。曾经仅仅听过数独，可是没玩过，这次A道题，搞懂了其本规则，哈哈。收获不小。
好了。那就介绍一下规则吧，现给出n^2*n^2的数独，推断是否满足：
1.每行要用1～n^2的数填满,而且每一个数仅仅出现一次。就是把1～n^2排列到每一行。
2.行的要求跟列一样；
3.还要满足均分成的n^2个n*n的矩形的元素也要满足1～n^2个数的排列。
AC代码：
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
int a[40][40], b[40][1000], c[40][1000], d[1000];
int T,t,n;
int main(){
#ifndef ONLINE_JUDGE
freopen("in.txt","r",stdin);
#endif
scanf("%d", &T);
for(int t=1; t<=T; t++){
memset(b,0,sizeof(b));
memset(c,0,sizeof(c));
scanf("%d", &n);
for(int i=1; i<=n*n; i++){ //处理行列
for(int j=1; j<=n*n; j++){
scanf("%d", &a[i][j]);
b[i][a[i][j]]++;
c[j][a[i][j]]++;
}
}
int flag = 1;
for(int i=1; i<=n*n; i++){ //推断行列
for(int j=1; j<=n*n; j++){
if(b[i][j]!=1 || c[i][j]!=1){
flag = 0;
break;
}
}
}
if(flag){
for(int i=1; i<=n; i++){ //推断每一个n*n矩阵
for(int j=1; j<=n; j++){
memset(d,0,sizeof(d));
for(int k=1; k<=n; k++){
for(int s=1; s<=n; s++){
d[a[(i-1)*n+k][(j-1)*n+s]]++;
}
}
for(int k=1; k<=n*n; k++){
if(d[k]!=1){
flag = 0;
break;
}
}
if(!flag) break;
}
if(!flag) break;
}
}
if(flag) printf("Case #%d: Yes
", t);
else printf("Case #%d: No
", t);
}
return 0;
}