【PAT】【Advanced Level】1128. N Queens Puzzle (20)

最新推荐文章于 2020-03-28 21:46:18 发布

最新推荐文章于 2020-03-28 21:46:18 发布 · 386 阅读

PAT 专栏收录该内容

132 篇文章

订阅专栏

该博客讨论了如何判断一个给定的配置是否为N皇后问题的解决方案。它解释了简化后的棋盘表示方法，其中每个配置由整数序列表示，表示每一列中皇后所在的行。博客提供了输入和输出规格，并提及了解决此问题的思路，涉及使用map来跟踪列和两条斜对角线上的皇后位置。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

1128. N Queens Puzzle (20)

时间限制

300 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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, ..., Q_N), where Q_i 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.


Figure 1		Figure 2

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 ... Q_N", where 4 <= N <= 1000 and it is guaranteed that 1 <= Q_i <= 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

原题链接：

https://www.patest.cn/contests/pat-a-practise/1128

思路：

map映射列，两条斜对角线（i+j,i-j）

CODE：

#include<iostream>
#include<map>
using namespace std;
int main()
{
	int n;
	cin>>n;
	for (int i=0;i<n;i++)
	{
		int m;
		cin>>m;
		map<int,int> row;
		map<int,int> d1;
		map<int,int> d2;
		int flag=0;
		for (int j=1;j<=m;j++)
		{
			int t;
			cin>>t;
			if (row[t]==1)
			{
				flag=1;
			}
			if (d1[j+t]==1)
			{
				flag=1;
			}
			if (d2[t-j]==1)
			{
				flag=1;
			}
			row[t]=1;
			d1[j+t]=1;
			d2[t-j]=1;
		}
		if (flag==0)
		{
			cout<<"YES"<<endl;
		}
		else
		{
			cout<<"NO"<<endl;
		}
	}
	return 0;
}