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<pre><a name="line-1"></a><span class='hs-comment'>-- (c) 2000-2005 by Martin Erwig [see file COPYRIGHT]</span>
<a name="line-2"></a><span class='hs-comment'>-- | Minimum-Spanning-Tree Algorithms </span>
<a name="line-3"></a>
<a name="line-4"></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'>MST</span> <span class='hs-layout'>(</span>
<a name="line-5"></a> <span class='hs-varid'>msTreeAt</span><span class='hs-layout'>,</span><span class='hs-varid'>msTree</span><span class='hs-layout'>,</span>
<a name="line-6"></a> <span class='hs-comment'>-- * Path in MST</span>
<a name="line-7"></a> <span class='hs-varid'>msPath</span>
<a name="line-8"></a><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-9"></a>
<a name="line-10"></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-11"></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'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>RootPath</span>
<a name="line-12"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</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'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Heap</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>H</span>
<a name="line-13"></a>
<a name="line-14"></a>
<a name="line-15"></a><a name="newEdges"></a><span class='hs-definition'>newEdges</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>LPath</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Context</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'>H</span><span class='hs-varop'>.</span><span class='hs-conid'>Heap</span> <span class='hs-varid'>b</span> <span class='hs-layout'>(</span><span class='hs-conid'>LPath</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-16"></a><span class='hs-definition'>newEdges</span> <span class='hs-layout'>(</span><span class='hs-conid'>LP</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varid'>l</span><span class='hs-layout'>,</span><span class='hs-varid'>v</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>-></span><span class='hs-conid'>H</span><span class='hs-varop'>.</span><span class='hs-varid'>unit</span> <span class='hs-varid'>l</span> <span class='hs-layout'>(</span><span class='hs-conid'>LP</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>v</span><span class='hs-layout'>,</span><span class='hs-varid'>l</span><span class='hs-layout'>)</span><span class='hs-conop'>:</span><span class='hs-varid'>p</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
<a name="line-17"></a>
<a name="line-18"></a><a name="prim"></a><span class='hs-definition'>prim</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Graph</span> <span class='hs-varid'>gr</span><span class='hs-layout'>,</span><span class='hs-conid'>Real</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>H</span><span class='hs-varop'>.</span><span class='hs-conid'>Heap</span> <span class='hs-varid'>b</span> <span class='hs-layout'>(</span><span class='hs-conid'>LPath</span> <span class='hs-varid'>b</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-conid'>LRTree</span> <span class='hs-varid'>b</span>
<a name="line-19"></a><span class='hs-definition'>prim</span> <span class='hs-varid'>h</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>H</span><span class='hs-varop'>.</span><span class='hs-varid'>isEmpty</span> <span class='hs-varid'>h</span> <span class='hs-varop'>||</span> <span class='hs-varid'>isEmpty</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-20"></a><span class='hs-definition'>prim</span> <span class='hs-varid'>h</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span>
<a name="line-21"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>match</span> <span class='hs-varid'>v</span> <span class='hs-varid'>g</span> <span class='hs-keyword'>of</span>
<a name="line-22"></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'>p</span><span class='hs-conop'>:</span><span class='hs-varid'>prim</span> <span class='hs-layout'>(</span><span class='hs-conid'>H</span><span class='hs-varop'>.</span><span class='hs-varid'>mergeAll</span> <span class='hs-layout'>(</span><span class='hs-varid'>h'</span><span class='hs-conop'>:</span><span class='hs-varid'>newEdges</span> <span class='hs-varid'>p</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>g'</span>
<a name="line-23"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Nothing</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'>prim</span> <span class='hs-varid'>h'</span> <span class='hs-varid'>g'</span>
<a name="line-24"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>p</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>LP</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>v</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-varid'>h'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>H</span><span class='hs-varop'>.</span><span class='hs-varid'>splitMin</span> <span class='hs-varid'>h</span>
<a name="line-25"></a>
<a name="line-26"></a><a name="msTreeAt"></a><span class='hs-definition'>msTreeAt</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Graph</span> <span class='hs-varid'>gr</span><span class='hs-layout'>,</span><span class='hs-conid'>Real</span> <span class='hs-varid'>b</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-varid'>gr</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>LRTree</span> <span class='hs-varid'>b</span>
<a name="line-27"></a><span class='hs-definition'>msTreeAt</span> <span class='hs-varid'>v</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>prim</span> <span class='hs-layout'>(</span><span class='hs-conid'>H</span><span class='hs-varop'>.</span><span class='hs-varid'>unit</span> <span class='hs-num'>0</span> <span class='hs-layout'>(</span><span class='hs-conid'>LP</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>v</span><span class='hs-layout'>,</span><span class='hs-num'>0</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'>g</span>
<a name="line-28"></a>
<a name="line-29"></a><a name="msTree"></a><span class='hs-definition'>msTree</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Graph</span> <span class='hs-varid'>gr</span><span class='hs-layout'>,</span><span class='hs-conid'>Real</span> <span class='hs-varid'>b</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-conid'>LRTree</span> <span class='hs-varid'>b</span>
<a name="line-30"></a><span class='hs-definition'>msTree</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>msTreeAt</span> <span class='hs-varid'>v</span> <span class='hs-varid'>g</span> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>v</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>matchAny</span> <span class='hs-varid'>g</span>
<a name="line-31"></a>
<a name="line-32"></a><a name="msPath"></a><span class='hs-definition'>msPath</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>LRTree</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Node</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Node</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Path</span>
<a name="line-33"></a><span class='hs-definition'>msPath</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>joinPaths</span> <span class='hs-layout'>(</span><span class='hs-varid'>getLPathNodes</span> <span class='hs-varid'>a</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>getLPathNodes</span> <span class='hs-varid'>b</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<a name="line-34"></a>
<a name="line-35"></a><a name="joinPaths"></a><span class='hs-definition'>joinPaths</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Path</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Path</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Path</span>
<a name="line-36"></a><span class='hs-definition'>joinPaths</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>joinAt</span> <span class='hs-layout'>(</span><span class='hs-varid'>head</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span>
<a name="line-37"></a>
<a name="line-38"></a><a name="joinAt"></a><span class='hs-definition'>joinAt</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Node</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Path</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Path</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Path</span>
<a name="line-39"></a><span class='hs-definition'>joinAt</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-varid'>v</span><span class='hs-conop'>:</span><span class='hs-varid'>vs</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span><span class='hs-conop'>:</span><span class='hs-varid'>ws</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>v</span><span class='hs-varop'>==</span><span class='hs-varid'>w</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>joinAt</span> <span class='hs-varid'>v</span> <span class='hs-varid'>vs</span> <span class='hs-varid'>ws</span>
<a name="line-40"></a><span class='hs-definition'>joinAt</span> <span class='hs-varid'>x</span> <span class='hs-varid'>p</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>reverse</span> <span class='hs-varid'>p</span><span class='hs-varop'>++</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-varid'>q</span><span class='hs-layout'>)</span>
<a name="line-41"></a>
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