XProfan

English

p.specht

Info: in the Pascal´schen Dreieck begins The Zeilenzählung (n) with 0. The shape one "Quadratischen Polynoms" (Potenz 2) is therefore in the 3. row of supra to find, the 2. Term (k=2) but in the 2. slot!

Compile Mark Separation

proc BinKoeff :parameters n&,k&

    case n&=0:return 0.0
    case k&=0:return 1.0
    case (2*k&)>n&:k&=n&-k&
    declare r!,z&:z&=n&-k&:r!=z&+1

    Whileloop k&,2,-1

        r!=r!*(&Loop+z&)
        case r!>10^200:return -1.0
        r!=r!/&Loop

    endwhile

    return r!

endproc

Computer: Gerät, daß es in Mikrosekunden erlaubt, 50.000 Fehler zu machen, zB 'daß' statt 'das'...

05/10/21 ▲

Vollständiges Quote

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p.specht

nCr-Algorithmus (appendix To supra):
--------------------
an effiziente Berechnung the Binomialkoeffizienten is into most scientific Taschenrechnern by the nCr-Algorithmus realized - otherwise would there with N=70 already Overflow given! nCr should "n Choose r" hot, The english Bezeichnung ours "N over k" or. "k from N".
fountain: Wikipedia

Compile Mark Separation

Window Title "Binomialkoeffizient gem. ´n Choose r´ = nCr-Algorithmus"
'https://de.wikipedia.org/wiki/Binomialkoeffizient#Algorithmus_zur_effizienten_Berechnung
Window Style 24:Cls:declare N&,k&
Repeat:print "\n n =",:input N&:print " k =",:input k&
print "\n Binom_nCr(n,k) = ";stature$("%g",Binom_nCr(N&,k&))

Until &Loop'= 0

proc Binom_nCr :parameters N&,k&

case k&=0:return 1:case N&<=0:return 0
var P!=1:case (2*k&)>N&:k&=N&-k&

whileloop k&'with nCr zurück only Ganzzahlen on:

    P!=P!*(N&-k&+&Loop)/&Loop

endwhile

return P!

endproc