Greedy algorithm for Egyptian fractions: Difference between revisions
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{{libheader|Phix/mpfr}}
The sieve copied from Go
<!--<lang Phix>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">egyptian</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">num</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">denom</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">num</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">denom</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">mpz_cmp_si</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: #000000;">0</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">mpz_cdiv_q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">result</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"1/"</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">mpz_neg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_mod</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;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_neg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</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: #0000FF;">=</span> <span style="color: #7060A8;">mpz_free</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: #008080;">return</span> <span style="color: #000000;">result</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">efrac</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">num</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">denom</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">fraction</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d/%d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span><span style="color: #000000;">denom</span><span style="color: #0000FF;">}),</span>
<span style="color: #000000;">prefix</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">num</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">denom</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">whole</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">num</span><span style="color: #0000FF;">/</span><span style="color: #000000;">denom</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">num</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">whole</span><span style="color: #0000FF;">*</span><span style="color: #000000;">denom</span>
<span style="color: #000000;">prefix</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;">whole</span><span style="color: #0000FF;">)</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;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">egyptian</span><span style="color: #0000FF;">(</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">denom</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;">"%s -> %s%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">fraction</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prefix</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: #000000;">efrac</span><span style="color: #0000FF;">(</span><span style="color: #000000;">43</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">efrac</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">121</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">efrac</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2014</span><span style="color: #0000FF;">,</span><span style="color: #000000;">59</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">maxt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">maxd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">maxts</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">maxds</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">maxda</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">98</span> <span style="color: #008080;">to</span> <span style="color: #000000;">998</span> <span style="color: #008080;">by</span> <span style="color: #000000;">900</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (iterates just twice!)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sieve</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</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: #0000FF;">),</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- to eliminate duplicates</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;">r</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">d</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: #008080;">to</span> <span style="color: #000000;">r</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;">sieve</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: #004600;">false</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">term</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d/%d"</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: #004080;">sequence</span> <span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">egyptian</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: #004080;">integer</span> <span style="color: #000000;">nterms</span> <span style="color: #0000FF;">=</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;">if</span> <span style="color: #000000;">nterms</span><span style="color: #0000FF;">></span><span style="color: #000000;">maxt</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">maxt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nterms</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">nterms</span><span style="color: #0000FF;">=</span><span style="color: #000000;">maxt</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">maxts</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">", "</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">term</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">mlen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">[$])-</span><span style="color: #000000;">2</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">mlen</span><span style="color: #0000FF;">></span><span style="color: #000000;">maxd</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">maxd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mlen</span>
<span style="color: #000000;">maxds</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">term</span>
<span style="color: #000000;">maxda</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[$]</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">mlen</span><span style="color: #0000FF;">=</span><span style="color: #000000;">maxd</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">maxds</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">", "</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">term</span>
<span style="color: #008080;">end</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">r</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9999</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</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;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">][</span><span style="color: #000000;">d</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</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;">if</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: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nfor proper fractions with 1 to %d digits\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</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;">"Largest number of terms is %d for %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">maxt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxts</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">maxda</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">maxda</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">..$]</span> <span style="color: #000080;font-style:italic;">-- (strip the "1/")</span>
<span style="color: #000000;">maxda</span><span style="color: #0000FF;">[</span><span style="color: #000000;">6</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"..."</span> <span style="color: #000080;font-style:italic;">-- (show only first/last 5 digits)</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;">"Largest size for denominator is %d digits (%s) for %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">maxd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxda</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxds</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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