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