1128. N Queens Puzzle (20)

水深无声 2022-05-28 11:50 155阅读 0赞

The "eight queens puzzle" is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other. Thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general N queens problem of placing N non-attacking queens on an N×N chessboard. (From Wikipedia - "Eight queens puzzle".)

Here you are NOT asked to solve the puzzles. Instead, you are supposed to judge whether or not a given configuration of the chessboard is a solution. To simplify the representation of a chessboard, let us assume that no two queens will be placed in the same column. Then a configuration can be represented by a simple integer sequence (Q1, Q2, ..., QN), where Qi is the row number of the queen in the i-th column. For example, Figure 1 can be represented by (4, 6, 8, 2, 7, 1, 3, 5) and it is indeed a solution to the 8 queens puzzle; while Figure 2 can be represented by (4, 6, 7, 2, 8, 1, 9, 5, 3) and is NOT a 9 queens' solution.

<table> 
 <tbody> 
  <tr> 
   <td>  <img src="http://nos.patest.cn/nf_ol5ygnynwww.jpg" alt=""> </td> 
   <td>&nbsp;</td> 
   <td>  <img src="http://nos.patest.cn/nf_ol5yhbyve1t.jpg" alt=""> </td> 
  </tr> 
  <tr> 
   <td>  Figure 1 </td> 
   <td>&nbsp;</td> 
   <td>  Figure 2 </td> 
  </tr> 
 </tbody> 
</table>

**Input Specification:**

Each input file contains several test cases. The first line gives an integer K (1 < K <= 200). Then K lines follow, each gives a configuration in the format "N Q1 Q2 ... QN", where 4 <= N <= 1000 and it is guaranteed that 1 <= Qi <= N for all i=1, ..., N. The numbers are separated by spaces.

**Output Specification:**

For each configuration, if it is a solution to the N queens problem, print "YES" in a line; or "NO" if not.

**Sample Input:**

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

**Sample Output:**

YES
    NO
    NO
    YES

--------------------

题目大意：

代码：

#include<stdio.h>
    #include<string.h>
    int a[1010][1010];
    int main()
    {
        int i,j,n,m,k,t,l1,l2;
        scanf("%d",&n);
        for(i=0;i<n;i++)
        {
            scanf("%d",&m);
            memset(a,0,sizeof(a));
            int flag=0;
            for(j=1;j<=m;j++)
            {
    
                scanf("%d",&k);
                if(flag==0)
                {
                    for(l1=k,l2=j;l1>=1&&l2<=m;l1--,l2++)
                    if(a[l1][l2]==1)
                {
                    flag=1;
                    break;
                }
                for(l1=k,l2=j;l1<=m&&l2>=1;l1++,l2--)
                    if(a[l1][l2]==1)
                {
                    flag=1;
                    break;
                }
                for(l1=k,l2=j;l1>=1&&l2>=1;l1--,l2--)
                    if(a[l1][l2]==1)
                {
                    flag=1;
                    break;
                }
                for(l1=k,l2=j;l1<=m&&l2<=m;l1++,l2++)
                    if(a[l1][l2]==1)
                {
                    flag=1;
                    break;
                }
                for(l1=1;l1<=m;l1++)
                {
                    if(a[k][l1])
                    {
                       flag=1;
                       break;
                    }
                }
                }
                if(flag==0)
                {
                    a[k][j]=1;
                }
            }
            if(flag==0)
            {
                printf("YES\n");
            }
            else
            {
                printf("NO\n");
            }
        }
        return 0;
    }