Partition function P: Difference between revisions
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The [https://mathworld.wolfram.com/PartitionFunctionP.html Partition Function P]
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The successive numbers in the above equation have the differences: 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, 7, 15, 8 ...
This task may be of popular interest because [https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg Mathologer] made the video, [https://www.youtube.com/watch?v=iJ8pnCO0nTY The hardest "What comes next?" (Euler's pentagonal formula)], where he asks the programmers among his viewers to calculate P(666). The video
In Wolfram Language, this function has been implemented as PartitionsP.
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<pre>[1,2,3,5,7,11,15,22,30,42,56,77,101,135]</pre>
Using gojq 0.12.11, `partitions(6666)` yields (in about 12 minutes (u+s) on a 3GHz machine):
jq's built-in integer precision is insufficient for computing ``partitions(6666)``, but more as a test▼
of the BigInt.jq library for jq than anything else, here are the results of using it in conjunction▼
193655306161707661080005073394486091998480950338405932486880600467114423441282418165863
▲
▲of the BigInt.jq library for jq
with a trivially-modified version of the ''partitions'' implementation above. That is, after
modifying the lines that refer to "p" (or ".p"), we see that ''partitions(6666)'' yields:
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"193655306161707661080005073394486091998480950338405932486880600467114423441282418165863"
=== Recursive ===
{{trans|Julia}} with memoization
<syntaxhighlight lang="jq">def partDiffDiff($n):
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In [4]: %timeit partitions(6666)
215 ms ± 1.84 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
</pre>
=={{header|Quackery}}==
<code>0 partitions</code> returns <code>1</code> as per [https://oeis.org/A000041 oeis.org/A000041 (Partitions of n)].
This is a naive recursive solution, so computing the partitions of 6666 would take a hideously long time.
<syntaxhighlight lang="Quackery"> [ 1 swap
dup 0 = iff drop done
[ 2dup = iff [ 2drop 1 ] done
2dup > iff [ 2drop 0 ] done
2dup dip 1+ recurse
unrot over - recurse + ] ] is partitions ( n --> n )
say "Partitions of 0 to 29" cr
30 times [ i^ partitions echo sp ]
</syntaxhighlight>
{{out}}
<pre>Partitions of 0 to 29
1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 1575 1958 2436 3010 3718 4565
</pre>
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{{libheader|Wren-big}}
Although it may not look like it, this is actually a decent time for Wren which is interpreted and the above module is written entirely in Wren itself.
<syntaxhighlight lang="
var p = []
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