Re: identical rows in tables

*To*: mathgroup at smc.vnet.net*Subject*: [mg97610] Re: identical rows in tables*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Tue, 17 Mar 2009 04:57:10 -0500 (EST)*References*: <gpl5qr$oss$1@smc.vnet.net>

King, Peter R wrote: > I have a table of values > > e.g.{{1, 2, 3, 4, 5, 6, 7, 8}, {1, 4, 6, 2, 8, 3, 7, 5}, {1, 4, 2, 6, 3, > 8, 5, 7}, {1, 3, 2, 5, 4, 7, 6, 8}, {1, 3, 5, 2, 7, 4, 8, 6}, {1, 2, > 4, 3, 6, 5, 8, 7}, {1, 2, 3, 4, 5, 6, 7, 8}} > > and want to check if any rows are identical (so there are none in the above= > - I can remove last or first row which are supposed to be the same). > > But in the following {{1, 2, 3, 4, 5, 6, 7, 8}, {1, 4, 6, 2, 8, 3, 7, 5}, {= > 1, 4, 2, 6, 3, > 8, 5, 7}, {1, 3, 2, 5, 4, 7, 6, 8}, {1, 3, 5, 2, 7, 4, 8, 6}, {1, 8, > 7, 6, 5, 4, 3, 2}, {1, 8, 6, 7, 4, 5, 2, 3}, {1, 3, 2, 5, 4, 7, 6, > 8}, {1, 3, 5, 2, 7, 4, 8, 6},....} > > there is a pair {1, 3, 2, 5, 4, 7, 6, > 8}, {1, 3, 5, 2, 7, 4, 8, 6} which are the same. > > In an ideal world when I print out (in say TableForm) the repeated rows ca= > n be printed in red (or some specified colour) > > These rows are permutations if that makes any difference. The tables can be= > of any size (but always permutations of n numbers) > > as a subsidiary question is there an easy way to convert the tables into nu= > mbers (or strings) eg > > {12345678,14628375,14263857 etc} > > Alternatively is there an easy way to perform permutations on strings of ch= > aracters? > > Many thanks for your help to the multiple questions > ps I am using Mathematica 6.03 > For simply checking whether there are any duplicates, one can use Union[]. table = {{1, 2, 3, 4, 5, 6, 7, 8}, {1, 4, 6, 2, 8, 3, 7, 5}, {1, 4, 2, 6, 3, 8, 5, 7}, {1, 3, 2, 5, 4, 7, 6, 8}, {1, 3, 5, 2, 7, 4, 8, 6}, {1, 2, 4, 3, 6, 5, 8, 7}, {1, 3, 2, 5, 4, 7, 6, 8}, {1, 2, 3, 4, 5, 6, 7, 8}}; Now compare Length@Union[table] and Length[table] If you need to colour repeated elements, you can use Tally to identify them: repeatedElements = Cases[Tally[table], {list_, multiplicity_} /; multiplicity > 1 :> list] colorizeRules = MapIndexed[#1 -> Style[#1, Bold, ColorData[2][First[#2]]] &, repeatedElements] table /. colorizeRules // ColumnForm I hope this helps, Szabolcs P.S. Conversion to strings is easy, but I don't think you can permute strings easily (without converting them back to lists first). StringJoin[ToString /@ {1, 2, 3, 4, 5, 6, 7, 8}] Convert back to a list of characters using Characters[]