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Re: why do recursive function calculations take so long in Mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43575] Re: why do recursive function calculations take so long in Mathematica?
  • From: "Steve Luttrell" <luttrell at _removemefirst_westmal.demon.co.uk>
  • Date: Sun, 21 Sep 2003 05:42:15 -0400 (EDT)
  • References: <bkhbk7$7lr$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

You need to memorise the intermediate results thus:

dr[0, 0] := 0; dr[n_, n_] := 0;
dr[n_, 0] := 1; dr[n_, k_] := dr[n, k] = dr[n, k - 1] + dr[n - 1, k];

--
Steve Luttrell
West Malvern, UK

"G Feigin" <g.feigin at verizon.net> wrote in message
news:bkhbk7$7lr$1 at smc.vnet.net...
> I defined the following simple recursive function:
>
> dr[0,0] := 0; dr[n_,n_]:= 0;
> dr[n_,0]:=1;dr[n_,k_]:=dr[n,k-1]+dr[n-1,k];
>
> To evaluate dr[16,15] takes about 5 minutes on a Pentium class
> machine, an absurdly long time.  Why? And what can I do to speed
> things up?  By the way,
> if I perform the recursion in an Excel spreadsheet on the same
> machine, the calculation time is practically instantaneous.
>
> Please reply by email.
>



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