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<title>Data/Graph/Inductive/Query/Indep.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>-- (c) 2000 - 2002 by Martin Erwig [see file COPYRIGHT]</span>
<a name="line-2"></a><span class='hs-comment'>-- | Maximum Independent Node Sets</span>
<a name="line-3"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span><span class='hs-varop'>.</span><span class='hs-conid'>Inductive</span><span class='hs-varop'>.</span><span class='hs-conid'>Query</span><span class='hs-varop'>.</span><span class='hs-conid'>Indep</span> <span class='hs-layout'>(</span>
<a name="line-4"></a> <span class='hs-varid'>indep</span>
<a name="line-5"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>indepSize</span>
<a name="line-6"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-7"></a>
<a name="line-8"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span><span class='hs-varop'>.</span><span class='hs-conid'>Inductive</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span>
<a name="line-9"></a>
<a name="line-10"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Arrow</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'>***</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-11"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Function</span> <span class='hs-layout'>(</span><span class='hs-varid'>on</span><span class='hs-layout'>)</span>
<a name="line-12"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span> <span class='hs-layout'>(</span><span class='hs-varid'>maximumBy</span><span class='hs-layout'>)</span>
<a name="line-13"></a>
<a name="line-14"></a><span class='hs-comment'>-- -----------------------------------------------------------------------------</span>
<a name="line-15"></a>
<a name="line-16"></a><a name="indep"></a><span class='hs-comment'>-- | Calculate the maximum independent node set of the specified</span>
<a name="line-17"></a><span class='hs-comment'>-- graph.</span>
<a name="line-18"></a><span class='hs-definition'>indep</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>DynGraph</span> <span class='hs-varid'>gr</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>gr</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Node</span><span class='hs-keyglyph'>]</span>
<a name="line-19"></a><span class='hs-definition'>indep</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fst</span> <span class='hs-varop'>.</span> <span class='hs-varid'>indepSize</span>
<a name="line-20"></a>
<a name="line-21"></a><a name="indepSize"></a><span class='hs-comment'>-- | The maximum independent node set along with its size.</span>
<a name="line-22"></a><span class='hs-definition'>indepSize</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>DynGraph</span> <span class='hs-varid'>gr</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>gr</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>[</span><span class='hs-conid'>Node</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span> <span class='hs-conid'>Int</span><span class='hs-layout'>)</span>
<a name="line-23"></a><span class='hs-definition'>indepSize</span> <span class='hs-varid'>g</span>
<a name="line-24"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>isEmpty</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span>
<a name="line-25"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>l1</span> <span class='hs-varop'>></span> <span class='hs-varid'>l2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>il1</span>
<a name="line-26"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>il2</span>
<a name="line-27"></a> <span class='hs-keyword'>where</span>
<a name="line-28"></a> <span class='hs-varid'>vs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>nodes</span> <span class='hs-varid'>g</span>
<a name="line-29"></a> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>snd</span> <span class='hs-varop'>.</span> <span class='hs-varid'>maximumBy</span> <span class='hs-layout'>(</span><span class='hs-varid'>compare</span> <span class='hs-varop'>`on`</span> <span class='hs-varid'>fst</span><span class='hs-layout'>)</span>
<a name="line-30"></a> <span class='hs-varop'>.</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-conid'>(,)</span> <span class='hs-varop'>=<<</span> <span class='hs-varid'>deg</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>vs</span>
<a name="line-31"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>g'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>match</span> <span class='hs-varid'>v</span> <span class='hs-varid'>g</span>
<a name="line-32"></a> <span class='hs-varid'>il1</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>l1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>indepSize</span> <span class='hs-varid'>g'</span>
<a name="line-33"></a> <span class='hs-varid'>il2</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>l2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>v</span><span class='hs-conop'>:</span><span class='hs-layout'>)</span> <span class='hs-varop'>***</span> <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>indepSize</span> <span class='hs-layout'>(</span><span class='hs-varid'>delNodes</span> <span class='hs-layout'>(</span><span class='hs-varid'>neighbors'</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-varid'>g'</span><span class='hs-layout'>)</span>
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