Re: Extracting information from lists

*To*: mathgroup at smc.vnet.net*Subject*: [mg63356] Re: Extracting information from lists*From*: "dkr" <dkrjeg at adelphia.net>*Date*: Sun, 25 Dec 2005 02:19:34 -0500 (EST)*References*: <dojefh$fmb$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Tony, The following extracts the positions of the first elements of runs of all integers, provided the integer has at least one run whose length exceeds one. Thus if In[1]:= egList={1,1,2,2,2,1,2,3,1,1,1,3,2,2}; the extracted positions will be {1,3,6,7,9,13}, corresponding to the beginning of the runs of 1 and 2. In[2]:= s1={First[#],Length[#]}&/@Split[egList] Out[2]= {{1,2},{2,3},{1,1},{2,1},{3,1},{1,3},{3,1},{2,2}} The first element of each sublist gives the integer involved in the run, and the second element gives the length of the run. In[3]:= s2=FoldList[#1+Last@#2&,1,Most@s1] Out[3]= {1,3,6,7,8,9,12,13} s2 gives the positions of the first elements of all runs, including those corresponding to integers (in this case the integer 3) which don't have any runs exceeding one in length. In[6]:= s3=Cases[s1,{a_,b_Integer}/;b>1:>a]//Union Out[6]= {1,2} s3 contains each integer which has a maximal run exceeding one in length. In[8]:= Pick[s2,s1,{a_Integer,_}/;MemberQ[s3,a]] Out[8]= {1,3,6,7,9,13} Finally we pick only those positions in s2 which correpond to integers having a maximal run exceeding one in length. Putting it all together: In[9]:= fn[x:{__Integer}]:=Module[{s1,s2,s3}, s1={First[#],Length[#]}&/@Split[x]; s2=FoldList[#1+Last@#2&,1,Most@s1]; s3=Cases[s1,{a_,b_Integer}/;b>1:>a]//Union; Pick[s2,s1,{a_Integer,_}/;MemberQ[s3,a]] ]; In[10]:= fn[egList] Out[10]= {1,3,6,7,9,13} In[11]:= fn[{7,9,1,6,8,1,1,6,5,1,1,1,8,7,6,1,1,1,1,7}] Out[11]= {3,6,10,16} In[12]:= fn[{1,2,3}] Out[12]= {} dkr