Re: programming problem about elements taken

*To*: mathgroup at smc.vnet.net*Subject*: [mg72472] Re: programming problem about elements taken*From*: Peter Pein <petsie at dordos.net>*Date*: Sun, 31 Dec 2006 04:58:58 -0500 (EST)*References*: <en5evt$l12$1@smc.vnet.net>

Barrow schrieb: > Dear all, > I have a list of numbers (A),in fact, they are numbers distributed > over [0,1]. Given parameter \epsilon, I have to choose elements from A > such that their distances are larger than \epsilon, so the elements are > "distringuishable". My goal is to find the maximum number of elements > from A to meet the above "distinct criterion". > How to do it with the functions build-in in mathematica ?? > Thanks in advence. Sincerely Barrow > Hi Barrow, the first method coming to my mind has been the use of ReplaceRepeated, but for long lists this lasts far too long: A=Table[Random[],{2000}]; epsilon=1.*^-4; Timing[Length[ r1=A//.{x___,c_,y___}/;Min[Abs[c-{x,y}]]<epsilon:>{x,y} ]] --> {22.125 Second,1650} It is sufficient to compare element k with elements k+1,...,n: selectDistinguishable[a_List,eps_]:= Pick[a,Min[Abs[a[[#]]-Drop[a,#]]]>eps&/@Range[Length[a]]] Timing[Length[ r2=selectDistinguishable[A,epsilon] ]] --> {0.11 Second,1650} _Much_ better :-) r1===r2 --> True hth, Peter