mirror of
https://github.com/xlucn/PAT.git
synced 2026-10-30 00:37:37 +08:00
43 lines
2.2 KiB
HTML
43 lines
2.2 KiB
HTML
<!DOCTYPE html>
|
||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
|
||
<h1>1128. N Queens Puzzle (20)</h1>
|
||
<div id="problemContent">
|
||
<p>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".)</p>
|
||
<p>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 (Q<sub>1</sub>, Q<sub>2</sub>, ..., Q<sub>N</sub>), where Q<sub>i</sub> 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.</p>
|
||
<center>
|
||
<table>
|
||
<tr>
|
||
<td><center><img src="http://nos.patest.cn/nf_ol5ygnynwww.jpg"/></center></td>
|
||
<td> </td>
|
||
<td><center><img src="http://nos.patest.cn/nf_ol5yhbyve1t.jpg"/></center></td>
|
||
</tr>
|
||
<tr>
|
||
<td><center>Figure 1</center></td>
|
||
<td> </td>
|
||
<td><center>Figure 2</center></td>
|
||
</tr>
|
||
</table>
|
||
</center>
|
||
<p><b>
|
||
Input Specification:
|
||
</b></p>
|
||
<p>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 Q<sub>1</sub> Q<sub>2</sub> ... Q<sub>N</sub>", where 4 <= N <= 1000 and it is guaranteed that 1 <= Q<sub>i</sub> <= N for all i=1, ..., N. The numbers are separated by spaces.</p>
|
||
<p><b>
|
||
Output Specification:
|
||
</b></p>
|
||
<p>For each configuration, if it is a solution to the N queens problem, print "YES" in a line; or "NO" if not.
|
||
</p>
|
||
<b>Sample Input:</b><pre>
|
||
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
|
||
</pre>
|
||
<b>Sample Output:</b><pre>
|
||
YES
|
||
NO
|
||
NO
|
||
YES
|
||
</pre>
|
||
</div> |