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MathGroup Archive 1998

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Re: Find Max of "Concave" List

  • To: mathgroup at
  • Subject: [mg12959] Re: [mg12918] Find Max of "Concave" List
  • From: Don Piele <piele at>
  • Date: Sun, 28 Jun 1998 02:51:49 -0400
  • Sender: owner-wri-mathgroup at

Chris, use binary search.

x =Join[y= Range[10000],Reverse[Range[9000]]];


{2.52 Second,10000}

(*Binary Search*)

      If[x[[i]]<= x[[i+1]],x=Take[x,-Length[x]+i];,x=Take[x,i];]];

{0.11 Second,10000}

Don Piele                                        piele at       
University of Wisconsin - Parkside


On Wed, 24 Jun 1998, 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

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