Partition function P: Difference between revisions
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=={{header|Phix}}== |
=={{header|Phix}}== |
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{{libheader|Phix/mpfr}} |
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Not exactly super-fast, but this sort of stuff is not really what Phix does best. |
Not exactly super-fast, but this sort of stuff is not really what Phix does best. |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">function</span> <span style="color: #000000;">partDiffDiff</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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return (n+1)/(1+and_bits(n,1)) |
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<span style="color: #008080;">return</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;">and_bits</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> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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sequence pd = {1} |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">pd</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> |
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function partDiff(integer n) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">partDiff</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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while n>length(pd) do |
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<span style="color: #008080;">while</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pd</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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pd &= pd[$] + partDiffDiff(length(pd)) |
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<span style="color: #000000;">pd</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">pd</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">partDiffDiff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pd</span><span style="color: #0000FF;">))</span> |
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end while |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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return pd[max(1,n)] |
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<span style="color: #008080;">return</span> <span style="color: #000000;">pd</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">max</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> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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include mpfr.e |
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<span style="color: #008080;">include</span> <span style="color: #7060A8;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> |
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sequence pn = {mpz_init(1)} |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">pn</span> <span style="color: #0000FF;">=</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> |
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function partitionsP(integer n) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">partitionsP</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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mpz res = mpz_init(1) |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">res</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> |
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while n>length(pn) do |
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<span style="color: #008080;">while</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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integer nn = length(pn)+1 |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">nn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span> |
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mpz psum = mpz_init(0) |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">psum</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> |
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for i=1 to nn do |
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<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;">nn</span> <span style="color: #008080;">do</span> |
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integer pd = partDiff(i) |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">pd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">partDiff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> |
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if pd>nn then exit end if |
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<span style="color: #008080;">if</span> <span style="color: #000000;">pd</span><span style="color: #0000FF;">></span><span style="color: #000000;">nn</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> |
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integer sgn = iff(remainder(i-1,4)<2 ? 1 : -1) |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">sgn</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">remainder</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: #0000FF;">,</span><span style="color: #000000;">4</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: #0000FF;">:</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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mpz pnmpd = pn[max(1,nn-pd)] |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">pnmpd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pn</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nn</span><span style="color: #0000FF;">-</span><span style="color: #000000;">pd</span><span style="color: #0000FF;">)]</span> |
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if sgn=-1 then |
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<span style="color: #008080;">if</span> <span style="color: #000000;">sgn</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> |
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mpz_sub(psum,psum,pnmpd) |
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<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">psum</span><span style="color: #0000FF;">,</span><span style="color: #000000;">psum</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pnmpd</span><span style="color: #0000FF;">)</span> |
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else |
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<span style="color: #008080;">else</span> |
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<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">psum</span><span style="color: #0000FF;">,</span><span style="color: #000000;">psum</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pnmpd</span><span style="color: #0000FF;">)</span> |
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end if |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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pn = append(pn,psum) |
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<span style="color: #000000;">pn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">psum</span><span style="color: #0000FF;">)</span> |
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end while |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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return pn[max(1,n)] |
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<span style="color: #008080;">return</span> <span style="color: #000000;">pn</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">max</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> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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atom t0 = time() |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span> |
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integer n=6666 |
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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;">6666</span> |
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printf(1,"p(%d) = %s (%s)\n",{n,mpz_get_str(partitionsP(n)),elapsed(time()-t0)})</lang> |
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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;">"p(%d) = %s (%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">partitionsP</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</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;">t0</span><span style="color: #0000FF;">)})</span> |
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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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p(6666) = 193655306161707661080005073394486091998480950338405932486880600467114423441282418165863 (0.8s) |
p(6666) = 193655306161707661080005073394486091998480950338405932486880600467114423441282418165863 (0.8s) |
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</pre> |
</pre> |
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=={{header|Picat}}== |
=={{header|Picat}}== |