Factor-perfect numbers: Difference between revisions

Content added Content deleted
(→‎{{header|Wren}}: Changed to Erdos method for factor counting - another huge speed-up > 30x.)
m (→‎{{header|Phix}}: replaced my beloved g() with the even faster cached erdosFactorCount().)
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=={{header|Phix}}==
=={{header|Phix}}==
{{libheader|Phix/online}}
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/fpn.htm here]. Note that my routine names of f(), m(), and g() match my detailed understanding of what I'm doing here perfectly.
You can run this online [http://phix.x10.mx/p2js/fpn.htm here] (expect a blank screen for ~30s).
<!--<syntaxhighlight lang="phix">(phixonline)-->
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo/rosetta/factor-perfect_numbers.exw
--</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">get_factor_set</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</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: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</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: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">x</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: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</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: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span> <span style="color: #008080;">in</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span> <span style="color: #008080;">in</span> <span style="color: #000000;">get_factor_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">&</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">&</span><span style="color: #000000;">x</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;">for</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">N</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">48</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">N</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">48</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">rN</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</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;">rN</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_factor_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">jbm</span><span style="color: #0000FF;">(</span><span style="color: #004080;">bool</span> <span style="color: #000000;">munge</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">jbm</span><span style="color: #0000FF;">(</span><span style="color: #004080;">bool</span> <span style="color: #000000;">munge</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">munge</span> <span style="color: #008080;">then</span> <span style="color: #000000;">rN</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rN</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;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">munge</span> <span style="color: #008080;">then</span> <span style="color: #000000;">rN</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rN</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;">if</span>
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<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;">"%d sequences using second definition:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jbm</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</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;">"%d sequences using second definition:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jbm</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">g</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">efc_cache</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">new_dict</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">factors</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;">f</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">erdosFactorCount</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">d</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;">l</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">divs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</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;">l</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: #004080;">integer</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span> <span style="color: #008080;">in</span> <span style="color: #000000;">divs</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">d</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: #000000;">1</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">node</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">efc_cache</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">by</span> <span style="color: #000000;">k</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">erdosFactorCount</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">j</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">l</span> <span style="color: #008080;">and</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">x</span> <span style="color: #008080;">do</span> <span style="color: #000000;">j</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: #7060A8;">setd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">efc_cache</span><span style="color: #0000FF;">)</span>
⚫
<span style="color: #008080;">else</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">></span><span style="color: #000000;">l</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">x</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_by_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">node</span><span style="color: #0000FF;">,</span><span style="color: #000000;">efc_cache</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">d</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: #000000;">d</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">r</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: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">4</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">4</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"1"</span><span style="color: #0000FF;">}</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"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;">res</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">7</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">while</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: #7060A8;">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;">9</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">g</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: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">erdosFactorCount</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: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</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;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #7060A8;">progress</span><span style="color: #0000FF;">(</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">progress</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;">"Found %d: %s (%s)\n"</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: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</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: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t</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;">"Found %d: %s (%s)\n"</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: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</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: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">wait_key</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
<!--</syntaxhighlight>-->
{{out}}
{{out}}
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{12,4} {16,3} {24,2} {48}
{12,4} {16,3} {24,2} {48}


Found 7: 0 1 48 1280 2496 28672 29808 (1.2s)
Found 9: 0 1 48 1280 2496 28672 29808 454656 2342912 (1 minute and 9s)
</pre>
</pre>
Unfortunately it takes 4 minutes 13 seconds to find 9 under p2js, so I've limited that to 8 (as mentioned above, ~30s)
It takes about 6s under p2js, and 4&half; minutes to get the eighth, and 2 hours, 23 minutes and 6s to get the ninth (2342912) on desktop/Phix, compared to 13s for 7 and 39:18 for 8 in Julia (9th not tried), and since python took 2:20 for 7 I didn't even bother trying 8.


=={{header|Python}}==
=={{header|Python}}==
Retrieved from "https://rosettacode.org/wiki/Factor-perfect_numbers"