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Stirling numbers of the second kind: Difference between revisions

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Stirling numbers of the second kind (view source)

Revision as of 18:06, 11 June 2021

9,832 bytes added ,  2 years ago
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→‎{{header|Phix}}: added syntax colouring the hard way
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{{libheader|Phix/mpfr}}
{{trans|Go}}
<!--<lang Phix>include mpfr.e(phixonline)-->
<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>
constant lim = 100,
lim1 = lim+1,
<span style="color: #008080;">constant</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</span><span style="color: #0000FF;">,</span>
last = 12
<span style="color: #000000;">lim1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lim</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
sequence s2 = repeat(0,lim1)
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">12</span>
for n=1 to lim1 do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s2</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;">lim1</span><span style="color: #0000FF;">)</span>
s2[n] = mpz_inits(lim1)
<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;">lim1</span> <span style="color: #008080;">do</span>
mpz_set_si(s2[n][n],1)
<span style="color: #000000;">s2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lim1</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">],</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
mpz {t, m100} = mpz_inits(2)
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
for n=1 to lim do
<span style="color: #004080;">mpz</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m100</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
for k=1 to n do
<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;">lim</span> <span style="color: #008080;">do</span>
mpz_set_si(t,k)
<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;">n</span> <span style="color: #008080;">do</span>
mpz_mul(t,t,s2[n][k+1])
<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
mpz_add(s2[n+1][k+1],t,s2[n][k])
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s2</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;">1</span><span style="color: #0000FF;">])</span>
end for
<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s2</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>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
printf(1,"Stirling numbers of the second kind: S2(n, k):\n n k:")
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
for i=0 to last do
<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;">"Stirling numbers of the second kind: S2(n, k):\n n k:"</span><span style="color: #0000FF;">)</span>
printf(1,"%5d ", i)
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">last</span> <span style="color: #008080;">do</span>
end for
<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;">"%5d "</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
printf(1,"\n--- %s\n",repeat('-',last*10+5))
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
for n=0 to last do
<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;">"\n--- %s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">last</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">5</span><span style="color: #0000FF;">))</span>
printf(1,"%2d ", n)
<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;">last</span> <span style="color: #008080;">do</span>
for k=1 to n+1 do
<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 "</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
mpfr_printf(1,"%9Zd ", s2[n+1][k])
<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;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
end for
<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;">"%9s "</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])})</span>
printf(1,"\n")
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for
<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;">"\n"</span><span style="color: #0000FF;">)</span>
for k=1 to lim1 do
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
mpz s100k = s2[lim1][k]
<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;">lim1</span> <span style="color: #008080;">do</span>
if mpz_cmp(s100k,m100) > 0 then
<span style="color: #004080;">mpz</span> <span style="color: #000000;">s100k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">lim1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
mpz_set(m100,s100k)
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s100k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m100</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">></span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
end if
<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s100k</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
printf(1,"\nThe maximum S2(100,k): %s\n",shorten(mpz_get_str(m100)))</lang>
<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;">"\nThe maximum S2(100,k): %s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m100</span><span style="color: #0000FF;">)))</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
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