Superpermutation minimisation: Difference between revisions
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Thundergnat (talk | contribs) m →{{header|Raku}}: use correct syntax highlighter |
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=={{header|Phix}}==
{{trans|C}}
<!--<lang Phix>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">nMax</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">8</span><span style="color: #0000FF;">:</span><span style="color: #000000;">12</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- Aside: on desktop/Phix, strings can be modified in situ, whereas
-- JavaScript strings are immutable, and the equivalent code
-- in p2js.js ends up doing excessive splitting and splicing
-- hence nMax has to be significantly smaller in a browser.</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">superperm</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">count</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">pos</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">factSum</span><span style="color: #0000FF;">(</span><span style="color: #004080;">int</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">f</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">i</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">(</span><span style="color: #004080;">int</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">n</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">superperm</span><span style="color: #0000FF;">[</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">-</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">count</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">count</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">pos</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">superperm</span><span style="color: #0000FF;">[</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">superPerm</span><span style="color: #0000FF;">(</span><span style="color: #004080;">int</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">chars</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">pos</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
<span style="color: #000000;">superperm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">chars</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">factSum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">superperm</span><span style="color: #0000FF;">!=</span><span style="color: #008000;">""</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">7</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- (I estimate it would take at least 5 days to validate
-- superPerm(12), feel free to try it on your own time)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">chars</span><span style="color: #0000FF;">),</span><span style="color: #000000;">superperm</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">nMax</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">superPerm</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">superperm</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">></span><span style="color: #000000;">40</span> <span style="color: #008080;">then</span> <span style="color: #000000;">superperm</span><span style="color: #0000FF;">[</span><span style="color: #000000;">20</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">20</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"..."</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"superPerm(%2d) len = %d %s (%s)\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">superperm</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</lang>-->
{{out}}
<pre>
Line 1,313 ⟶ 1,320:
I also tried prefixing res with any longer overlap at the start, but it just made things worse.<br>
Uses factSum() from above, and compares that with these results (which are always worse for >3).
<!--<lang Phix>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">factSum</span><span style="color: #0000FF;">(</span><span style="color: #004080;">int</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">f</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">i</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">superPerm</span><span style="color: #0000FF;">(</span><span style="color: #004080;">int</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">chars</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">perms</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">f</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">perms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">chars</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">perms</span><span style="color: #0000FF;">[$]</span>
<span style="color: #000000;">perms</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">perms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">perms</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">best</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bi</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">perms</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">perms</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">pi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">perms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">],</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">=</span><span style="color: #000000;">k</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">m</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">></span><span style="color: #000000;">best</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">best</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">k</span>
<span style="color: #000000;">bi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #000000;">perms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bi</span><span style="color: #0000FF;">],</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (sanity check)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">perms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bi</span><span style="color: #0000FF;">][</span><span style="color: #000000;">best</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">perms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bi</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">perms</span><span style="color: #0000FF;">[$]</span>
<span style="color: #000000;">perms</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">perms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">lr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">fsn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">factSum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">op</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"<"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"="</span><span style="color: #0000FF;">,</span><span style="color: #008000;">">"</span><span style="color: #0000FF;">}[</span><span style="color: #7060A8;">compare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fsn</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #008000;">", "</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">):</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"superPerm(%d) len = %d (%s%d%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">op</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fsn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">7</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (note: 8 takes 65x longer than 7)</span>
<span style="color: #000000;">superPerm</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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