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Catalan numbers/Pascal's triangle: Difference between revisions

Catalan numbers/Pascal's triangle (view source)

Revision as of 04:35, 28 March 2021

8,462 bytes added ,  3 years ago
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→‎{{header|Phix}}: added syntax colouring the hard way
m (Added Delphi reference to Pascal code)
m (→‎{{header|Phix}}: added syntax colouring the hard way)
Line 1,455:
=={{header|Phix}}==
Calculates the minimum pascal triangle in minimum memory. Inspired by the comments in, but not the code of the FreeBasic example
<!--<lang Phix>-->
<lang Phix>constant N = 15 -- accurate to 30, nan/inf for anything over 514 (bigatom version is below).
<span style="color: #008080;">constant</span> <span style="color: #000000;">N</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">15</span> <span style="color: #000080;font-style:italic;">-- accurate to 30, nan/inf for anything over 514 (gmp version is below).</span>
sequence catalan = {}, -- (>=1 only)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">catalan</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000080;font-style:italic;">-- (&gt;=1 only)</span>
p = repeat(1,N+1)
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">N</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
atom p1
<span style="color: #004080;">atom</span> <span style="color: #000000;">p1</span>
for i=1 to N do
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
p1 = p[1]*2
<span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">2</span>
catalan = append(catalan,p1-p[2])
<span style="color: #000000;">catalan</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">catalan</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
for j=1 to N-i+1 do
<span style="color: #008080;">for</span> <span style="color: #000000;">j</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;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
p1 += p[j+1]
<span style="color: #000000;">p1</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
p[j] = p1
<span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p1</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
-- ?p[1..N-i+1]
<span style="color: #000080;font-style:italic;">-- ?p[1..N-i+1]</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
?catalan</lang>
<span style="color: #0000FF;">?</span><span style="color: #000000;">catalan</span>
<!--</lang>-->
{{out}}
<pre>
Line 1,510 ⟶ 1,512:
=== gmp version ===
{{libheader|Phix/mpfr}}
<!--<lang Phix>include builtins\mpfr.e-->
<span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">\</span><span style="color: #7060A8;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
 
function catalanB(integer n) -- very very fast!
sequence catalan = mpz_inits(n),
p = mpz_inits(n+1,1)
mpz p1 = mpz_init(1)
if n=0 then return p1 end if
for i=1 to n do
mpz_mul_si(p1,p[1],2)
mpz_sub(catalan[i],p1,p[2])
for j=1 to n-i+1 do
mpz_add(p1,p1,p[j+1])
mpz_set(p[j],p1)
end for
end for
return catalan[n]
end function
<span style="color: #008080;">function</span> <span style="color: #000000;">catalanB</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: #000080;font-style:italic;">-- very very fast!</span>
printf(1,"%d: %s (%s)\n",{100,mpz_get_str(catalanB(100))})
<span style="color: #004080;">sequence</span> <span style="color: #000000;">catalan</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span>
printf(1,"%d: %s (%s)\n",{250,mpz_get_str(catalanB(250))})</lang>
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</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;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz</span> <span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</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;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">p1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">catalan</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</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;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
<span style="color: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #000000;">p1</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>
<span style="color: #008080;">return</span> <span style="color: #000000;">catalan</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;">function</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: %s (%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">catalanB</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</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: %s (%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">250</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">catalanB</span><span style="color: #0000FF;">(</span><span style="color: #000000;">250</span><span style="color: #0000FF;">))})</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
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