StackOverflow2013

Note that there are some explanatory texts on larger screens.

plurals

PO
text
Body
copied!<p>The following will build a binary tree, and then analyze it and extract the results:</p> <pre><code>Clear[intParts]; intParts[num_, elems_List] /; Total[elems] < num := p[]; intParts[num_, {fst_, rest___}] /; fst < num := {p[fst, intParts[num - fst, {rest}]], intParts[num, {rest}]}; intParts[num_, {fst_, rest___}] /; fst > num := intParts[num, {rest}]; intParts[num_, {num_, rest___}] := {pf[num], intParts[num, {rest}]}; Clear[nextPosition]; nextPosition = Compile[{{pos, _Integer, 1}}, Module[{ctr = 0, len = Length[pos]}, While[ctr < len && pos[[len - ctr]] == 1, ++ctr]; While[ctr < len && pos[[len - ctr]] == 2, ++ctr]; Append[Drop[pos, -ctr], 1]], CompilationTarget -> "C"]; Clear[getPartitionsFromTree, getPartitions]; getPartitionsFromTree[tree_] := Map[Extract[tree, #[[;; -3]] &@FixedPointList[nextPosition, #]] &, Position[tree, _pf, Infinity]] /. pf[x_] :> x; getPartitions[num_, elems_List] := getPartitionsFromTree@intParts[num, Reverse@Sort[elems]]; </code></pre> <p>For example, </p> <pre><code>In[14]:= getPartitions[200,Prime~Array~150]//Short//Timing Out[14]= {0.5,{{3,197},{7,193},{2,5,193},<<4655>>,{3,7,11,13,17,19,23,29,37,41}, {2,3,5,11,13,17,19,23,29,37,41}}} </code></pre> <p>This is not insanely fast, and perhaps the algorithm could be optimized further, but at least the number of partitions does not grow as fast as for <code>IntegerPartitions</code>.</p> <p>Edit:</p> <p>It is interesting that simple memoization speeds the solution up about twice on the example I used before:</p> <pre><code>Clear[intParts]; intParts[num_, elems_List] /; Total[elems] < num := p[]; intParts[num_, seq : {fst_, rest___}] /; fst < num := intParts[num, seq] = {p[fst, intParts[num - fst, {rest}]], intParts[num, {rest}]}; intParts[num_, seq : {fst_, rest___}] /; fst > num := intParts[num, seq] = intParts[num, {rest}]; intParts[num_, seq : {num_, rest___}] := intParts[num, seq] = {pf[num], intParts[num, {rest}]}; </code></pre> <p>Now, </p> <pre><code>In[118]:= getPartitions[200, Prime~Array~150] // Length // Timing Out[118]= {0.219, 4660} </code></pre>

Querying!

Guidance

An individual column

Larger individual text columns get their own page to allow for proper reading.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload