Rare numbers: Difference between revisions
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for over 30% of the run time. Improvements welcome: run p -d test, examine the list.asm produced from this source, and discuss or
make suggestions on [[User_talk:Petelomax|my talk page]].
<!--<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;">maxDigits</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;">10</span><span style="color: #0000FF;">:</span><span style="color: #000000;">15</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">COEFF</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">TDXA</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">TDXB</span> <span style="color: #000080;font-style:italic;">-- struct term = {atom coeff, integer idxa, idxb}
-- (see allTerms below)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">nd</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- number of digits</span>
<span style="color: #000000;">count</span> <span style="color: #000080;font-style:italic;">-- of solutions found earlier, for lower nd</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">rares</span> <span style="color: #000080;font-style:italic;">-- (cleared after sorting/printing for each nd)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">to_atom</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- convert digits array to an atom value</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</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;">digits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">10</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">-- psq eliminates 52 out of 64 of numbers fairly cheaply, which translates
-- to approximately 66% of numbers, or around 10% off the overall time.
-- NB: only tested to 9,007,199,254,740,991, then again I found no more new
-- bit patterns after just 15^2.</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">psq</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">int_to_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">#02030213</span><span style="color: #0000FF;">,</span><span style="color: #000000;">32</span><span style="color: #0000FF;">)&</span> <span style="color: #000080;font-style:italic;">-- #0202021202030213 --> bits,</span>
<span style="color: #7060A8;">int_to_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">#02020212</span><span style="color: #0000FF;">,</span><span style="color: #000000;">32</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- in 32/64-bit compatible way.</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">isSquare</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- determine if n is a perfect square or not</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">psq</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">63</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: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">fnpr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">nmr</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- generate (n+r) candidates from (n-r) candidates</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dis</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">digits</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- (the precise why of how this populates digits has eluded me...)</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">candidates</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: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">di</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: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">a</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">d</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">d</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">le</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">di</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">d</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">[</span><span style="color: #000000;">le</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">le</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">dx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">le</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">[</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">[</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">10</span>
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">[</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">a</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">d</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">d</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">npr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nmr</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">to_atom</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">))*</span><span style="color: #000000;">2</span> <span style="color: #000080;font-style:italic;">-- (npr == 'n + r')</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">isSquare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">npr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">rares</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">to_atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- (note this gets overwritten by sorted set:)</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;">"working... %2d: %,d\r"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rares</span><span style="color: #0000FF;">),</span><span style="color: #000000;">rares</span><span style="color: #0000FF;">[$]})</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: #008080;">else</span>
<span style="color: #000000;">di</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">di</span><span style="color: #0000FF;">)</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;">dis</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">di</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
<span style="color: #000000;">fnpr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">level</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nmr</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">)</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;">procedure</span> <span style="color: #000000;">fnmr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- generate (n-r) candidates with a given number of digits.</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">list</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">nmr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (nmr == 'n - r')</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;">terms</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">nmr</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">COEFF</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nmr</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">isSquare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nmr</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">candidates</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: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">])-</span><span style="color: #000000;">1</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">dis</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">l</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;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">candidates</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">10</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;">dmd</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">])-</span><span style="color: #000000;">1</span>
<span style="color: #000000;">dis</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">dis</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- (above generates dis of eg {1,4,7,9} for nd=7, which as far
-- as I (lightly) understand it scans for far fewer candidate
-- pairs than a {9,9,9,9} would, or something like that.)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">di</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dis</span><span style="color: #0000FF;">))</span>
<span style="color: #000080;font-style:italic;">-- (di is the current "dis-scan", eg {0,0,0,0} to {1,4,7,9})</span>
<span style="color: #000000;">fnpr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nmr</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">di</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dis</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">candidates</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">candidates</span><span style="color: #0000FF;">)</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: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">list</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">candidates</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">fnmr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">level</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;">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;">constant</span> <span style="color: #000000;">dl</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">9</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- all differences (-9..+9 by 1)</span>
<span style="color: #000000;">zl</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- zero difference (0 only)</span>
<span style="color: #000000;">el</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- even differences (-8 to +8 by 2)</span>
<span style="color: #000000;">ol</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- odd differences (-9..+9 by 2)</span>
<span style="color: #000000;">il</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</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: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- all integers (0..9 by 1)</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">start</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #000080;font-style:italic;">-- terms of (n-r) expression for number of digits from 2 to maxdigits</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">allTerms</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">pow</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">maxDigits</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #000000;">pow</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pow</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">tdxa</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tdxb</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">tdxa</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">tdxb</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tdxa</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tdxb</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- {COEFF,TDXA,TDXB}</span>
<span style="color: #000000;">p1</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">10</span>
<span style="color: #000000;">p2</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span>
<span style="color: #000000;">tdxa</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">tdxb</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #000000;">allTerms</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">allTerms</span><span style="color: #0000FF;">,</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000080;font-style:italic;">--/*
--(This is what the above loop creates:)
--pp(allTerms,{pp_Nest,1,pp_StrFmt,3,pp_IntCh,false,pp_IntFmt,"%d",pp_FltFmt,"%d",pp_Maxlen,148})
<nowiki>{{</nowiki>{9,0,1<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>99,0,2<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>999,0,3}, {90,1,2<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>9999,0,4}, {990,1,3<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>99999,0,5}, {9990,1,4}, {900,2,3<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>999999,0,6}, {99990,1,5}, {9900,2,4<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>9999999,0,7}, {999990,1,6}, {99900,2,5}, {9000,3,4<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>99999999,0,8}, {9999990,1,7}, {999900,2,6}, {99000,3,5<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>999999999,0,9}, {99999990,1,8}, {9999900,2,7}, {999000,3,6}, {90000,4,5<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>9999999999,0,10}, {999999990,1,9}, {99999900,2,8}, {9999000,3,7}, {990000,4,6<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>99999999999,0,11}, {9999999990,1,10}, {999999900,2,9}, {99999000,3,8}, {9990000,4,7}, {900000,5,6<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>999999999999,0,12}, {99999999990,1,11}, {9999999900,2,10}, {999999000,3,9}, {99990000,4,8}, {9900000,5,7<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>9999999999999,0,13}, {999999999990,1,12}, {99999999900,2,11}, {9999999000,3,10}, {999990000,4,9}, {99900000,5,8}, {9000000,6,7<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>99999999999999,0,14}, {9999999999990,1,13}, {999999999900,2,12}, {99999999000,3,11}, {9999990000,4,10}, {999900000,5,9}, {99000000,6,8<nowiki>}}</nowiki>}
--*/
-- map of first minus last digits for 'n' to pairs giving this value</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">fml</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({},</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (aka 0..9)
-- (fml == 'first minus last')</span>
<span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">}}</span>
<span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">}}</span>
<span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}}</span>
<span style="color: #000080;font-style:italic;">-- fml[6] = <nowiki>{{</nowiki>8, 3<nowiki>}}</nowiki> -- (um? - needs longer lists, & that append(lists[4],dl) below)</span>
<span style="color: #000000;">fml</span><span style="color: #0000FF;">[</span><span style="color: #000000;">7</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">}}</span>
<span style="color: #000080;font-style:italic;">-- sequence lists = <nowiki>{{</nowiki>{0<nowiki>}}</nowiki>,<nowiki>{{</nowiki>1<nowiki>}}</nowiki>,<nowiki>{{</nowiki>4<nowiki>}}</nowiki>,<nowiki>{{</nowiki>5<nowiki>}}</nowiki>,<nowiki>{{</nowiki>6<nowiki>}}</nowiki>}</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">lists</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}},{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}},{{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">}},{{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}}</span>
<span style="color: #000080;font-style:italic;">-- map of other digit differences for 'n' to pairs giving this value</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">dmd</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({},</span><span style="color: #000000;">19</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (aka -9..+9, so add 10 when indexing dmd)
-- (dmd == 'digit minus digit')</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">tens</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tens</span><span style="color: #0000FF;">+</span><span style="color: #000000;">10</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">ones</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">dmd</span><span style="color: #0000FF;">[</span><span style="color: #000000;">d</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dmd</span><span style="color: #0000FF;">[</span><span style="color: #000000;">d</span><span style="color: #0000FF;">],</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">tens</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ones</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">d</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;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000080;font-style:italic;">--/*
--(This is what the above loop creates:)
--pp(dmd,{pp_Nest,1,pp_StrFmt,3,pp_IntCh,false})
<nowiki>{{</nowiki>{0,9<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>0,8}, {1,9<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>1,0}, {2,1}, {3,2}, {4,3}, {5,4}, {6,5}, {7,6}, {8,7}, {9,8<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>2,0}, {3,1}, {4,2}, {5,3}, {6,4}, {7,5}, {8,6}, {9,7<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>3,0}, {4,1}, {5,2}, {6,3}, {7,4}, {8,5}, {9,6<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>4,0}, {5,1}, {6,2}, {7,3}, {8,4}, {9,5<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>5,0}, {6,1}, {7,2}, {8,3}, {9,4<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>6,0}, {7,1}, {8,2}, {9,3<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>7,0}, {8,1}, {9,2<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>8,0}, {9,1<nowiki>}}</nowiki>,
<nowiki>{{</nowiki>9,0<nowiki>}}</nowiki>}
--*/</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</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;">"digits time nth rare numbers:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">nd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">nd</span> <span style="color: #0000FF;"><=</span> <span style="color: #000000;">maxDigits</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">rares</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">allTerms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nd</span><span style="color: #0000FF;">=</span><span style="color: #000000;">4</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">zl</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span><span style="color: #000000;">ol</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">],</span><span style="color: #000000;">el</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- lists[4] = append(lists[4],dl) -- if fml[6] = <nowiki>{{</nowiki>8, 3<nowiki>}}</nowiki>
-- lists[5] = append(lists[5],ol) -- ""
-- lists[4] = append(lists[4],ol) -- else</span>
<span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]),</span><span style="color: #000000;">ol</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- else</span>
<span style="color: #008080;">elsif</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">)></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</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;">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;">lists</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">--
<span style="color: #000000;">lists</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;">append</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]),</span><span style="color: #000000;">dl</span><span style="color: #0000FF;">)</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: #004080;">sequence</span> <span style="color: #000000;">indices</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">t</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;">terms</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">term</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">t</span><span style="color: #0000FF;">]</span>
<span style="color: #000080;font-style:italic;">-- (we may as well make this 1-based while here)</span>
<span style="color: #000000;">indices</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">indices</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">term</span><span style="color: #0000FF;">[</span><span style="color: #000000;">TDXA</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">term</span><span style="color: #0000FF;">[</span><span style="color: #000000;">TDXB</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;">for</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;">lists</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">list</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lists</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">candidates</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">list</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">fnmr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">candidates</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">indices</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fml</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dmd</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;">for</span>
<span style="color: #000080;font-style:italic;">-- (re-)output partial results for this nd-set in sorted order:
-- rares = sort(rares)</span>
<span style="color: #000000;">rares</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rares</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;">rares</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</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;">"%12s %2d: %,19d \n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">" %2d %5s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">nd</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">elapsed_short</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">start</span><span style="color: #0000FF;">)})</span>
<span style="color: #000000;">nd</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</lang>-->
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