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	<title>Daniel Hepper &#187; Python</title>
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		<title>Using Python Packages &#8211; An Overview</title>
		<link>http://daniel.hepper.net/blog/2011/01/using-python-packages-an-overview/</link>
		<comments>http://daniel.hepper.net/blog/2011/01/using-python-packages-an-overview/#comments</comments>
		<pubDate>Thu, 13 Jan 2011 21:47:14 +0000</pubDate>
		<dc:creator>Daniel Hepper</dc:creator>
				<category><![CDATA[Python]]></category>
		<category><![CDATA[packaging]]></category>
		<category><![CDATA[pycologne]]></category>
		<category><![CDATA[talk]]></category>

		<guid isPermaLink="false">http://daniel.hepper.net/blog/?p=210</guid>
		<description><![CDATA[Yesterday I gave a presentation at PyCologne about Python packages. It was meant as a kind of sequel to the &#8220;Cooking Eggs&#8221; talk given by Christopher Arndt (in German) in September. While he presented ways to create Python packages, I &#8230; <a href="http://daniel.hepper.net/blog/2011/01/using-python-packages-an-overview/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>Yesterday I gave a presentation at <a href="http://pycologne.de">PyCologne</a> about Python packages. It was meant as a kind of sequel to the <a href="http://chrisarndt.de/talks/cooking-eggs/cooking-eggs-vortrag.html">&#8220;Cooking Eggs&#8221; talk given by Christopher Arndt (in German)</a> in September. While he presented ways to create Python packages, I focused on how to use Python packages.</p>
<p>Python comes with batteries included, but sometimes, battery power is not enough. Thankfully, there are countless packages available for use. Given that there &#8220;<a href="http://www.python.org/dev/peps/pep-0020/">should be one&#8211; and preferably only one &#8211;obvious way to do it</a>,&#8221; using Python packages can be quite intimidating. The documentation of your package might say to download, unzip und run <code>python setup.py install</code>. Meet distutils. Or just do <code>easy_install MyPackage</code>, which is uses <a href="http://pypi.python.org/pypi/setuptools">setuptools</a>. But then you <a href="http://guide.python-distribute.org/introduction.html#current-state-of-packaging">hear</a> that setuptools is superseeded by <a href="http://packages.python.org/distribute/">distribute</a> and instead of <code>easy_install</code>, you should use <code><a href="http://pip.openplans.org/">pip</a></code>. And then there is <code><a href="http://virtualenv.openplans.org/">virtualenv</a></code>, which is awesome, but can be even more awesome with <code><a href="http://www.doughellmann.com/projects/virtualenvwrapper/">virtualenvwrapper</a></code>. What a mess! </p>
<p>My conclusion: use <code><a href="http://packages.python.org/distribute/">distribute</a></code>, <code><a href="http://pip.openplans.org/">pip</a></code>, <code><a href="http://virtualenv.openplans.org/">virtualenv</a></code> and <code><a href="http://www.doughellmann.com/projects/virtualenvwrapper/">virtualenvwrapper</a></code>.</p>
<p>You can <a href='http://daniel.hepper.net/blog/wp-content/python_packages_pycologne.pdf'>download the slides</a> or view them with Slideshare:</p>
<div style="width:425px" id="__ss_6553097"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/danielhepper/using-python-packages-an-overview" title="Using Python Packages - An Overview">Using Python Packages &#8211; An Overview</a></strong><object id="__sse6553097" width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=pythonpackagespycologne-110113151547-phpapp01&#038;rel=0&#038;stripped_title=using-python-packages-an-overview&#038;userName=danielhepper" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed name="__sse6553097" src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=pythonpackagespycologne-110113151547-phpapp01&#038;rel=0&#038;stripped_title=using-python-packages-an-overview&#038;userName=danielhepper" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object>
<div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/danielhepper">danielhepper</a>.</div>
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		<title>How to solve the 36 Cube puzzle &#8211; hints &amp; solution</title>
		<link>http://daniel.hepper.net/blog/2010/01/how-to-solve-the-36-cube-puzzle/</link>
		<comments>http://daniel.hepper.net/blog/2010/01/how-to-solve-the-36-cube-puzzle/#comments</comments>
		<pubDate>Sun, 10 Jan 2010 19:00:51 +0000</pubDate>
		<dc:creator>Daniel Hepper</dc:creator>
				<category><![CDATA[Howto]]></category>
		<category><![CDATA[Python]]></category>

		<guid isPermaLink="false">http://daniel.hepper.net/blog/?p=128</guid>
		<description><![CDATA[For Christmas, I got the ThinkFun 36 Cube. It is consists of 36 towers in 6 colors and 6 different sizes and a base plate with 6 by 6 slots to plug in the towers. These slots are of different &#8230; <a href="http://daniel.hepper.net/blog/2010/01/how-to-solve-the-36-cube-puzzle/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>For Christmas, I got the <a href="http://www.amazon.com/gp/product/B001F7VI30/ref=as_li_ss_tl?ie=UTF8&#038;tag=danihepp-20&#038;linkCode=as2&#038;camp=217145&#038;creative=399369&#038;creativeASIN=B001F7VI30">ThinkFun 36 Cube</a><img src="http://www.assoc-amazon.com/e/ir?t=&#038;l=as2&#038;o=1&#038;a=B001F7VI30&#038;camp=217145&#038;creative=399369" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" />. It is consists of 36 towers in 6 colors and 6 different sizes and a base plate with 6 by 6 slots to plug in the towers. These slots are of different heights. The goal is to place one towers of every color in each row and column. And the  towers must fit to form a level cube.</p>
<p>After some tries, I came to the conclusion that this puzzle is the work of the devil and that I should not waste more brain cycles on solving it. So I wrote a little python script to solve the puzzle for me.</p>
<p><a onclick="document.getElementById('34cube').style.display='inline';" href="javascript:void(0)">Show sourcecode</a></p>
<div id="34cube" style="display: none;">

<div class="wp_syntax"><div class="code"><pre class="python" style="font-family:monospace;"><span style="color: #808080; font-style: italic;">#!/usr/bin/python</span>
&nbsp;
COLORS = <span style="color: #008000;">dict</span><span style="color: black;">&#40;</span><span style="color: #008000;">zip</span><span style="color: black;">&#40;</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">1</span> <span style="color: #66cc66;">&amp;</span>lt<span style="color: #66cc66;">;&amp;</span>lt<span style="color: #66cc66;">;</span> i <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>, <span style="color: black;">&#40;</span><span style="color: #483d8b;">'P'</span>,<span style="color: #483d8b;">'Y'</span>,<span style="color: #483d8b;">'O'</span>,<span style="color: #483d8b;">'B'</span>,<span style="color: #483d8b;">'R'</span>,<span style="color: #483d8b;">'G'</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>
COLORS<span style="color: black;">&#91;</span><span style="color: #008000;">False</span><span style="color: black;">&#93;</span> = <span style="color: #483d8b;">'X'</span>
&nbsp;
used_towers = <span style="color: black;">&#91;</span><span style="color: #ff4500;">0</span> <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#93;</span>
&nbsp;
cube = <span style="color: black;">&#40;</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">0</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">3</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">4</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">2</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">1</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">5</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>
&nbsp;
solution = <span style="color: black;">&#91;</span><span style="color: black;">&#91;</span><span style="color: #008000;">False</span> <span style="color: #ff7700;font-weight:bold;">for</span> x <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#93;</span> <span style="color: #ff7700;font-weight:bold;">for</span> x <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#93;</span>
used = <span style="color: #008000;">tuple</span><span style="color: black;">&#40;</span><span style="color: #008000;">set</span><span style="color: black;">&#40;</span><span style="color: black;">&#41;</span> <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>
&nbsp;
<span style="color: #ff7700;font-weight:bold;">def</span> test_color<span style="color: black;">&#40;</span>pos, solution, used_towers, color, size<span style="color: black;">&#41;</span>:
 <span style="color: #808080; font-style: italic;">#check if tower of this size and color has already been used</span>
 <span style="color: #ff7700;font-weight:bold;">if</span> color <span style="color: #66cc66;">&amp;</span>amp<span style="color: #66cc66;">;</span> used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span>:
  <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">False</span>
 <span style="color: #808080; font-style: italic;">#check if tower has already been used in row or column:</span>
 <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span>:
  <span style="color: #ff7700;font-weight:bold;">if</span> color == solution<span style="color: black;">&#91;</span>pos/<span style="color: #ff4500;">6</span><span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>i<span style="color: black;">&#93;</span>: <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">False</span>
  <span style="color: #ff7700;font-weight:bold;">if</span> color == solution<span style="color: black;">&#91;</span>i<span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#93;</span>: <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">False</span>
 <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">True</span>
&nbsp;
<span style="color: #ff7700;font-weight:bold;">def</span> print_solution<span style="color: black;">&#40;</span>solution<span style="color: black;">&#41;</span>:
 <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span>:
  <span style="color: #ff7700;font-weight:bold;">print</span> <span style="color: #008000;">zip</span><span style="color: black;">&#40;</span><span style="color: black;">&#40;</span>COLORS<span style="color: black;">&#91;</span>c<span style="color: black;">&#93;</span> <span style="color: #ff7700;font-weight:bold;">for</span> c <span style="color: #ff7700;font-weight:bold;">in</span> solution<span style="color: black;">&#91;</span>i<span style="color: black;">&#93;</span><span style="color: black;">&#41;</span>, <span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span> - s <span style="color: #ff7700;font-weight:bold;">for</span> s <span style="color: #ff7700;font-weight:bold;">in</span> cube<span style="color: black;">&#91;</span>i<span style="color: black;">&#93;</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>
&nbsp;
<span style="color: #ff7700;font-weight:bold;">def</span> solve<span style="color: black;">&#40;</span>pos, solution, used_towers, best<span style="color: black;">&#41;</span>:
 <span style="color: #ff7700;font-weight:bold;">if</span> pos == <span style="color: #ff4500;">36</span>: <span style="color: #ff7700;font-weight:bold;">return</span> best, solution
 size = cube<span style="color: black;">&#91;</span>pos/<span style="color: #ff4500;">6</span><span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#93;</span>
 <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span>:
  color = <span style="color: #ff4500;">1</span> <span style="color: #66cc66;">&amp;</span>lt<span style="color: #66cc66;">;&amp;</span>lt<span style="color: #66cc66;">;</span> i
  <span style="color: #ff7700;font-weight:bold;">if</span> test_color<span style="color: black;">&#40;</span>pos, solution, used_towers, color, size<span style="color: black;">&#41;</span>:
   used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span> = used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span> | color
   solution<span style="color: black;">&#91;</span>pos/<span style="color: #ff4500;">6</span><span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#93;</span> = color
   <span style="color: #ff7700;font-weight:bold;">if</span> pos <span style="color: #66cc66;">&amp;</span>gt<span style="color: #66cc66;">;</span> best:
    <span style="color: #ff7700;font-weight:bold;">print</span> <span style="color: #483d8b;">&quot;#######&quot;</span>, pos + <span style="color: #ff4500;">1</span>, <span style="color: #483d8b;">&quot;towers placed&quot;</span>
    print_solution<span style="color: black;">&#40;</span>solution<span style="color: black;">&#41;</span>
    best = pos
   best, solution = solve<span style="color: black;">&#40;</span>pos+<span style="color: #ff4500;">1</span>, solution, used_towers, best<span style="color: black;">&#41;</span>
   <span style="color: #ff7700;font-weight:bold;">if</span> best <span style="color: #66cc66;">&amp;</span>gt<span style="color: #66cc66;">;</span>= <span style="color: #ff4500;">35</span>:
    <span style="color: #ff7700;font-weight:bold;">return</span> best, solution
   solution<span style="color: black;">&#91;</span>pos/<span style="color: #ff4500;">6</span><span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#93;</span> = <span style="color: #008000;">False</span>
   used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span> = used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span> ^ color
 <span style="color: #ff7700;font-weight:bold;">return</span> best, solution
&nbsp;
solve<span style="color: black;">&#40;</span><span style="color: #ff4500;">0</span>, solution, used_towers, <span style="color: #ff4500;">0</span><span style="color: black;">&#41;</span></pre></div></div>

</div>
<p>My program quickly came up with a correct placement for 34 towers &#8211; but it failed to find the complete solution.</p>
<pre>[('P', 5), ('Y', 3), ('O', 2), ('B', 1), ('R', 4), ('G', 6)]
[('Y', 4), ('O', 1), ('P', 6), ('R', 2), ('G', 5), ('B', 3)]
[('O', 6), ('B', 5), ('R', 3), ('G', 4), ('P', 1), ('Y', 2)]
[('R', 1), ('G', 2), ('Y', 5), ('P', 3), ('B', 6), ('O', 4)]
[('B', 2), ('P', 4), ('G', 1), ('Y', 6), ('O', 3), ('R', 5)]
[('G', 3), ('R', 6), ('B', 4), ('O', 5), ('X', 2), ('X', 1)]</pre>
<p>Legend:<br />
P = Purple, Y = Yellow, O = Orange, B = Blue, R = Red, G = Green, X = Empty<br />
The number is the size of the tower.<br />
As you can see, I didn&#8217;t waste much time on making the output pretty <img src='http://daniel.hepper.net/blog/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /> </p>
<div id="attachment_129" class="wp-caption aligncenter" style="width: 310px"><a href="http://daniel.hepper.net/blog/wp-content/36cube_almost_solved.jpg"><img class="size-medium wp-image-129" title="36cube almost solved" src="http://daniel.hepper.net/blog/wp-content/36cube_almost_solved-300x225.jpg" alt="36cube almost solved" width="300" height="225" /></a><p class="wp-caption-text">So close and yet so far</p></div>
<p>After spending lots of time verifying that my program was working correctly, I became impatient and googled for help. I found an answer, but it revealed to much, taking all the fun.</p>
<p>Therefore, I split my solution into multiple hints. If you are stuck, reveal just one of them at a time and try to figure it out by yourself. It is way more rewarding!</p>
<p>Hint #1 <a onclick="document.getElementById('hint1').style.display='inline';" href="javascript:void(0)">(show)</a>: <span id="hint1" style="display: none;">Your assumptions are probably wrong.<br />
Now go back and try to solve it. I&#8217;m waiting here.</span></p>
<p>Hint #2 <a onclick="document.getElementById('hint2').style.display='inline';" href="javascript:void(0)">(show)</a>: <span id="hint2" style="display: none;">The assumption that all towers of the same size only differ in color is wrong.</span></p>
<p>Hint #3 <a onclick="document.getElementById('hint3').style.display='inline';" href="javascript:void(0)">(show)</a>: <span id="hint3" style="display: none;">There are two towers which do fit on slots where the other towers of the same size do not fit.</span></p>
<p>Hint #4 <a onclick="document.getElementById('hint4').style.display='inline';" href="javascript:void(0)">(show)</a>: <span id="hint4" style="display: none;">The two special towers are the yellow one of heigh 5 and the orange one of height 6.</span></p>
<p>Hint #5 <a onclick="document.getElementById('hint5').style.display='inline';" href="javascript:void(0)">(show)</a>: <span id="hint5" style="display: none;">The yellow tower of height 5 has to go to position (1,2) and the orange tower of height 6 to (3,2) in my coordinate system.</span></p>
<p>Even if you uncovered all hints, the puzzle is still far from solved. You can still tinker with it forever.</p>
<p>Spoiler alert: Don&#8217;t uncover the solution, unless your are really desperate!</p>
<p><strong><a onclick="document.getElementById('solution').style.display='inline';" href="javascript:void(0)">Click to show the 36cube solution.</a></strong></p>
<div id="solution" style="display: none;">After I had found the two culprits, I adjusted my program by changing the array and inserting two special conditions. Within seconds I had a complete solution of the 36 Cube:</p>
<pre>[('P', 5), ('Y', 3), ('B', 2), ('O', 1), ('R', 4), ('G', 6)]
[('B', 4), ('P', 1), ('Y', 5), ('G', 2), ('O', 5), ('R', 3)]
[('R', 6), ('G', 5), ('P', 3), ('Y', 4), ('B', 1), ('O', 2)]
[('G', 1), ('R', 2), ('O', 6), ('B', 3), ('Y', 6), ('P', 4)]
[('Y', 2), ('O', 4), ('R', 1), ('P', 6), ('G', 3), ('B', 5)]
[('O', 3), ('B', 6), ('G', 4), ('R', 5), ('P', 2), ('Y', 1)]</pre>
<div id="attachment_130" class="wp-caption aligncenter" style="width: 310px"><a href="http://daniel.hepper.net/blog/wp-content/36cube_complete_solution.jpg"><img class="size-medium wp-image-130" title="36cube complete solution" src="http://daniel.hepper.net/blog/wp-content/36cube_complete_solution-300x225.jpg" alt="" width="300" height="225" /></a><p class="wp-caption-text">Finally solved</p></div>

<div class="wp_syntax"><div class="code"><pre class="python" style="font-family:monospace;"><span style="color: #808080; font-style: italic;">#!/usr/bin/python</span>
&nbsp;
COLORS = <span style="color: #008000;">dict</span><span style="color: black;">&#40;</span><span style="color: #008000;">zip</span><span style="color: black;">&#40;</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">1</span> <span style="color: #66cc66;">&amp;</span>lt<span style="color: #66cc66;">;&amp;</span>lt<span style="color: #66cc66;">;</span> i <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>, <span style="color: black;">&#40;</span><span style="color: #483d8b;">'P'</span>,<span style="color: #483d8b;">'Y'</span>,<span style="color: #483d8b;">'O'</span>,<span style="color: #483d8b;">'B'</span>,<span style="color: #483d8b;">'R'</span>,<span style="color: #483d8b;">'G'</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>
COLORS<span style="color: black;">&#91;</span><span style="color: #008000;">False</span><span style="color: black;">&#93;</span> = <span style="color: #483d8b;">'X'</span>
&nbsp;
used_towers = <span style="color: black;">&#91;</span><span style="color: #ff4500;">0</span> <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#93;</span>
&nbsp;
<span style="color: #808080; font-style: italic;"># definition with (1,2) and (3,2) switched</span>
cube = <span style="color: black;">&#40;</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">0</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">3</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">4</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">2</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">5</span>,<span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">1</span><span style="color: black;">&#41;</span>,
        <span style="color: black;">&#40;</span><span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">0</span>,<span style="color: #ff4500;">2</span>,<span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">4</span>,<span style="color: #ff4500;">5</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>
&nbsp;
solution = <span style="color: black;">&#91;</span><span style="color: black;">&#91;</span><span style="color: #008000;">False</span> <span style="color: #ff7700;font-weight:bold;">for</span> x <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#93;</span> <span style="color: #ff7700;font-weight:bold;">for</span> x <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#93;</span>
used = <span style="color: #008000;">tuple</span><span style="color: black;">&#40;</span><span style="color: #008000;">set</span><span style="color: black;">&#40;</span><span style="color: black;">&#41;</span> <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>
&nbsp;
<span style="color: #ff7700;font-weight:bold;">def</span> test_color<span style="color: black;">&#40;</span>pos, solution, used_towers, color, size<span style="color: black;">&#41;</span>:
 <span style="color: #808080; font-style: italic;">#check if tower of this size and color has already been used</span>
 <span style="color: #ff7700;font-weight:bold;">if</span> color <span style="color: #66cc66;">&amp;</span>amp<span style="color: #66cc66;">;</span> used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span>:
  <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">False</span>
 <span style="color: #808080; font-style: italic;">#check if tower has already been used in row or column:</span>
 <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span>:
  <span style="color: #ff7700;font-weight:bold;">if</span> color == solution<span style="color: black;">&#91;</span>pos/<span style="color: #ff4500;">6</span><span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>i<span style="color: black;">&#93;</span>: <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">False</span>
  <span style="color: #ff7700;font-weight:bold;">if</span> color == solution<span style="color: black;">&#91;</span>i<span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#93;</span>: <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">False</span>
 <span style="color: #808080; font-style: italic;"># special conditions for the two special towers</span>
 <span style="color: #ff7700;font-weight:bold;">if</span> <span style="color: black;">&#40;</span>pos/<span style="color: #ff4500;">6</span>, pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#41;</span> == <span style="color: black;">&#40;</span><span style="color: #ff4500;">1</span>,<span style="color: #ff4500;">2</span><span style="color: black;">&#41;</span> <span style="color: #ff7700;font-weight:bold;">and</span> color <span style="color: #66cc66;">!</span>= <span style="color: #ff4500;">2</span>: <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">False</span>
 <span style="color: #ff7700;font-weight:bold;">if</span> <span style="color: black;">&#40;</span>pos/<span style="color: #ff4500;">6</span>, pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#41;</span> == <span style="color: black;">&#40;</span><span style="color: #ff4500;">3</span>,<span style="color: #ff4500;">2</span><span style="color: black;">&#41;</span> <span style="color: #ff7700;font-weight:bold;">and</span> color <span style="color: #66cc66;">!</span>= <span style="color: #ff4500;">4</span>: <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">False</span>
 <span style="color: #ff7700;font-weight:bold;">return</span> <span style="color: #008000;">True</span>
&nbsp;
<span style="color: #ff7700;font-weight:bold;">def</span> print_solution<span style="color: black;">&#40;</span>solution<span style="color: black;">&#41;</span>:
 <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span>:
  <span style="color: #ff7700;font-weight:bold;">print</span> <span style="color: #008000;">zip</span><span style="color: black;">&#40;</span><span style="color: black;">&#40;</span>COLORS<span style="color: black;">&#91;</span>c<span style="color: black;">&#93;</span> <span style="color: #ff7700;font-weight:bold;">for</span> c <span style="color: #ff7700;font-weight:bold;">in</span> solution<span style="color: black;">&#91;</span>i<span style="color: black;">&#93;</span><span style="color: black;">&#41;</span>, <span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span> - s <span style="color: #ff7700;font-weight:bold;">for</span> s <span style="color: #ff7700;font-weight:bold;">in</span> cube<span style="color: black;">&#91;</span>i<span style="color: black;">&#93;</span><span style="color: black;">&#41;</span><span style="color: black;">&#41;</span>
&nbsp;
<span style="color: #ff7700;font-weight:bold;">def</span> solve<span style="color: black;">&#40;</span>pos, solution, used_towers, best<span style="color: black;">&#41;</span>:
 <span style="color: #ff7700;font-weight:bold;">if</span> pos == <span style="color: #ff4500;">36</span>: <span style="color: #ff7700;font-weight:bold;">return</span> best, solution
 size = cube<span style="color: black;">&#91;</span>pos/<span style="color: #ff4500;">6</span><span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#93;</span>
 <span style="color: #ff7700;font-weight:bold;">for</span> i <span style="color: #ff7700;font-weight:bold;">in</span> <span style="color: #008000;">range</span><span style="color: black;">&#40;</span><span style="color: #ff4500;">6</span><span style="color: black;">&#41;</span>:
  color = <span style="color: #ff4500;">1</span> <span style="color: #66cc66;">&amp;</span>lt<span style="color: #66cc66;">;&amp;</span>lt<span style="color: #66cc66;">;</span> i
  <span style="color: #ff7700;font-weight:bold;">if</span> test_color<span style="color: black;">&#40;</span>pos, solution, used_towers, color, size<span style="color: black;">&#41;</span>:
   used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span> = used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span> | color
   solution<span style="color: black;">&#91;</span>pos/<span style="color: #ff4500;">6</span><span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#93;</span> = color
   <span style="color: #ff7700;font-weight:bold;">if</span> pos <span style="color: #66cc66;">&amp;</span>gt<span style="color: #66cc66;">;</span> best:
    <span style="color: #ff7700;font-weight:bold;">print</span> <span style="color: #483d8b;">&quot;#######&quot;</span>, pos + <span style="color: #ff4500;">1</span>, <span style="color: #483d8b;">&quot;towers placed&quot;</span>
    print_solution<span style="color: black;">&#40;</span>solution<span style="color: black;">&#41;</span>
    best = pos
   best, solution = solve<span style="color: black;">&#40;</span>pos+<span style="color: #ff4500;">1</span>, solution, used_towers, best<span style="color: black;">&#41;</span>
   <span style="color: #ff7700;font-weight:bold;">if</span> best <span style="color: #66cc66;">&amp;</span>gt<span style="color: #66cc66;">;</span>= <span style="color: #ff4500;">35</span>:
    <span style="color: #ff7700;font-weight:bold;">return</span> best, solution
   solution<span style="color: black;">&#91;</span>pos/<span style="color: #ff4500;">6</span><span style="color: black;">&#93;</span><span style="color: black;">&#91;</span>pos<span style="color: #66cc66;">%</span>6<span style="color: black;">&#93;</span> = <span style="color: #008000;">False</span>
   used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span> = used_towers<span style="color: black;">&#91;</span>size<span style="color: black;">&#93;</span> ^ color
 <span style="color: #ff7700;font-weight:bold;">return</span> best, solution
&nbsp;
solve<span style="color: black;">&#40;</span><span style="color: #ff4500;">0</span>, solution, used_towers, <span style="color: #ff4500;">0</span><span style="color: black;">&#41;</span></pre></div></div>

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