       Re: Find Max of "Concave" List

• To: mathgroup at smc.vnet.net
• Subject: [mg13000] Re: Find Max of "Concave" List
• From: Tobias Oed <tobias at physics.odu.edu>
• Date: Sun, 28 Jun 1998 02:52:21 -0400
• Organization: Old Dominion University
• References: <6mqcvs\$3bt@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Chris Farr wrote:

> I have a one-dimensional list which is concave.  That is, if you did a
> ListPlot on the list you would have a concave curve.
>
> Given the concavity, when finding the max, it is inefficient to use
> Max[] which does a comparison on all elements of the list.
>
> Is there an elegant way to exploit the concavity when performing a
> Max[]?  That is, the algorithm should stop when the next element in the
>  list is lower then the previous element.  This would limit the number
> of  comparisons.
>
> Thanks,
>
> Chris Farr

maybe something like

l={1,2,3,4,3,2,1}

e=First[l]

Catch[Scan[If[#<e,Throw[e],e=#]&,Rest[l]]]

```

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