<html><head><title>Recursion: N Queens Lab</title>
<link href="mailto:abrady@kzoo.edu">
<link rel="STYLESHEET" type="text/css" href="labs.css"></head>
<body>
<DIV ID=siteTitle>
<H1> Recursion Lab: N Queens Problem</H1>
</DIV>
<DIV ID=author>
<a href="http://max.cs.kzoo.edu/~abrady/">Alyce Brady</a><br>
<a href="http://www.kzoo.edu/">Kalamazoo College</a>
</DIV>
<hr WIDTH="100%">
<p> In this lab you will implement the N Queens Problem, using the <code>BoundedGrid</code>
class.<sup>‡</sup>
In this lab you will implement an algorithm that places N queens on an N x N
board (like a chess board) in such a way that no queen can attack another queen.</p>
<table width="90%" border="1" align="center">
<tbody><tr><td>
<h4>Exercise Set</h4>
<ol>
<li>Download the zip file that contains the starting code files for
the N Queens Lab (<code><a href="NQueens.zip">NQueens.zip</a></code>)
and unzip it. When you unzip the file you will see the
following files and folders.
<ul>
<li>The file <code><a
href="NQueensLab.shtml">NQueensLab.shtml</a></code> contains this
write-up.
<li>Two image files, <code>GoldCrown.gif</code> and
<code>SilverCrown.gif</code> (images of crowns).
<li>The <code>grid.jar</code> Java archive
(<code>jar</code>) file
contains a library of classes that can be used to
model a two-dimensional grid as described above.
<ul>
<li><code>BoundedGrid</code> (class that represents
the two-dimensional grid)<sup>‡</sup></li>
<li><code>Location</code> (class that represents the
row and column positions of a location in the
grid)<sup>‡</sup></li>
<li><code>ColorBlock</code> (class whose objects
represent blocks of color put in a grid)</li>
</ul>
The documentation for these files can be found by
downloading the
<a href="http://www.cs.kzoo.edu/GridPkg/GridPkgClassDocs.zip">GridPkgClassDocs.zip</a> file.
</li>
<p></p>
<li>The <code>JavaSourceFiles</code> folder contains the
source files for the NQueens Lab.
<ul>
<li><code>NQueensLab</code> (contains the <code>main</code> method)</li>
<li><code>NQueens</code> (the class that implements the solution
to the N Queens Problem) </li>
<li><code>Queen</code> (represents a queen on the board)</li>
</ul>
</ul>
<br>
Note: All of the
classes in the <code>JavaSourceFiles</code> folder and the
<code>grid.jar</code> Java archive file are covered by the <a
href="/License.txt">GNU General Public License.</a>
</ul>
<p> </p>
<li>Compile and run the program. You should see an 8 x 8 "chess
board" with no queens.
<p> </p>
</li>
<li>Complete the <code>numQueens</code> and <code>removeQueen</code>
methods, without adding any additional instance variables. To
test the <code>removeQueen</code> method, modify the <code>placeQueen</code>
method to add a queen to any arbitrary column (your choice) of the
correct row for that queen, display the environment, and then remove
the queen and redisplay the environment. Modify the <code>solve</code>
method to place one queen. Run the program. You should
see one queen (or color block) appear and then disappear from the
environment.
<p> </p>
</li>
<li>Modify the <code>placeQueen</code> method to recursively place all
the queens in arbitrary columns (or the same arbitrary column).
Think about where you should place the recursive call if you want
to see the queens appear in each row, one-by-one, and then disappear
in reverse order. Make sure you remember to include a base case.
Do you need to modify the <code>solve</code> method to place all the
queens? If so, do it.
<p> </p>
</li>
<li>Fully implement the <code>placeQueen</code> method so that it checks
column by column to find an OK location to place this queen, until
the queen has been successfully placed in a column and all the queens
after her have been successfully placed also. Since the <code>locationIsOK</code>
method always returns <code>true</code>, the queens should fill in
the first column.
<p> </p>
</li>
<li>Modify the <code>locationIsOK</code> method to return <code>false</code>
if any queens have already be placed in the same column as the location
parameter. When you have this working you should see the queens
fill in the diagonal from location (0, 0) to location (n-1, n-1).
<p> </p>
</li>
<li>Modify the <code>locationIsOK</code> method again to also return
<code>false</code> if any queens have already been placed on the board
in locations that are on the diagonal from the location parameter.
</li>
</ol>
</td></tr>
</tbody></table>
<hr>
<hr>
<div id=footer>
<sup>‡</sup>The <code>Location</code> class comes directly
from the AP<sup>®</sup> Marine Biology Simulation case study;
<code>BoundedGrid</code> was inspired by the MBS <code>BoundedEnv</code>
class. AP is a registered trademark
of the College Entrance Examination Board. The Marine Biology Simulation case
study was copyrighted in 2002 by the College Entrance Examination Board.
It is available on the web from the College Board web site (<a href="http://www.collegeboard.com/ap/students/compsci/download.html">www.collegeboard.com</a>
and <a href="http://apcentral.collegeboard.com">apcentral.collegeboard.com</a>).<br>
<br>
Copyright Alyce Brady, 2002. </div>
</body></html>