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Evaluate binomial coefficients: Difference between revisions
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The task is to compute ANY binomial coefficient(s), but these REXX examples are limited to 100k digits.
===idiomatic===
<lang rexx>/*REXX program calculates binomial coefficients (
numeric digits 100000 /*be able to handle gihugeic numbers. */
parse arg n k . /*obtain N and K from the C.L. */
say 'combinations('n","k')=' comb(n,k) /*display the number of combinations. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
comb: procedure; parse arg x,y; return !(x) % (!(x-y) * !(y))
!: procedure; !=1; do j=2 to arg(1); !=!*j; end /*j*/; return !</lang>▼
▲!: procedure; !=1; do j=2 to arg(1); !=!*j; end; return !</lang>
'''output''' when using the input of: <tt> 5 3 </tt>
<pre>
combinations(5,3)= 10
</pre>
'''output''' when using the input of: <tt> 1200 120 </tt>
<pre>
combinations(1200,120)= 1004576581793084916475353119318331966507299414258370667602185866686463289093457468590558508056798211449853806741873396451735444387513582540860551330127062642417424083600
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This REXX version takes advantage of reducing the size (product) of the numerator, and also,
<br>only two (factorial) products need be calculated.
<lang rexx>/*REXX program calculates binomial coefficients (
numeric digits 100000 /*be able to handle gihugeic numbers. */
parse arg n k . /*obtain N and K from the C.L. */
say 'combinations('n","k')=' comb(n,k) /*display the number of combinations. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
comb: procedure; parse arg x,y; return pfact(x-y+1, x) % pfact(2, y)
/*──────────────────────────────────────────────────────────────────────────────────────*/
pfact: procedure; !=1;
'''output''' is identical to the 1<sup>st</sup> REXX version.
It is (around average) about ten times faster than the 1<sup>st</sup> version for <code> 200,20 </code> and <code> 100,10</code>.
<br>For <code>100,80 </code> it is about 30% faster. <br>
=={{header|Ring}}==
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