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Length of monotonic sequencies

  • To: mathgroup at
  • Subject: [mg33579] Length of monotonic sequencies
  • From: merkat <cabanc at>
  • Date: Mon, 1 Apr 2002 02:02:13 -0500 (EST)
  • Sender: owner-wri-mathgroup at


I want to get the lengths of the monotonic rising and falling  parts
in a list l. 
for this I can use:

Drop[RotateRight[l] - l, 1];
% /. x_ /; x > 0 -> 1  ;
% /. x_ /; x < 0 -> -1  ;
Length /@ %

I want to include the case of no change in the sequence values which
makes the seqence longer. (flat progression) 
I further want to relax the condition of monotonicity by allowing
shallow drops in the sequences.

for a drop of one unit:
{ 2,3,2,3,4,3,5,3,4,3,7}  gives {7,4} 

for a drop of 2 units:
{2,3,4,2,5,6,5,1}              gives {7,1} 
how can the code be written for an arbitrary drop? 


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