*To*: mathgroup@smc.vnet.net*Subject*: [mg12108] Re: Pattern matching more than once*From*: villegas@wolfram.com*Date*: Sat, 25 Apr 1998 01:30:38 -0400*Organization*: Deja News - The Leader in Internet Discussion*References*: <6hjqaa$2kj@smc.vnet.net>

> Input: Two lists, from some universal set > Output: Many "spliced" lists obtained from the input. > > e.g. {{a,b,c},{d,e,f}} --> {{a,b,c},{d,e,f}} (no common element) > > {{a,b,c},{d,b,f}} --> {{a,b,c},{d,b,f},{a,b,f},{d,b,c}} > > {{a,b,c,d,e},{f,b,g,d,h}} --> > {{a,b,c,d,e},{a,b,c,d,h},{a,b,g,d,e},{a,b,g,d,h}, > {f,b,c,d,e},{f,b,c,d,h},{f,b,g,d,e},{f,b,g,d,h}} The common elements act as separators to split each list into several sublists that don't contain the common elements. For instance, if X, Y, and Z are the common elements, then {a, b, X, c, Y, d, e, Z, f} ===> {{a, b}, {c}, {d, e}, {f}} If there are n common elements, each of the two lists, call them S and T, falls apart into (n + 1) sublists: S = {S0, S1, S2, ..., Sn} T = {T0, T1, T2, ..., Tn} Now you can form any spliced list you want: take either S0 or T0, followed by either S1 or T1, followed by either S2 or T2, ..., followed by either Sn or Tn. For instance, {S0, T1, T2, S3, T4, ..., T(n-1), Sn} Forming all possible combinations like this is just the Cartesian product of the sets: {S0, T0} x {S1, T1} x {S2, T2} x ... x {Sn, Tn} In Mathematica, the most direct way to do a Cartesian product of lists is with Distribute. A small example: In[37]:= Distribute[{{S0, T0}, {S1, T1}, {S2, T2}}, List, List] Out[37]= {{S0, S1, S2}, {S0, S1, T2}, {S0, T1, S2}, {S0, T1, T2}, {T0, S1, S2}, {T0, S1, T2}, {T0, T1, S2}, {T0, T1, T2}} The only thing left to do with this result is to re-insert the common elements. Here is one way to implement the Cartesian product idea. Interleave[subLists_, commonElements_] /; (Length[commonElements] == Length[subLists] - 1) := Drop[ Join @@ MapThread[Sequence, {subLists, List /@ Append[commonElements, Null]}] -1 ] SpliceChains[chain1_, chain2_] := Module[{commonElements, commonPos1, commonPos2, subChains1, subChains2}, commonElements = Intersection[chain1, chain2]; commonPos1 = Flatten @ Position[chain1, Alternatives @@ commonElements, {1}, Heads -> False]; commonPos2 = Flatten @ Position[chain2, Alternatives @@ commonElements, {1}, Heads -> False]; subChains1 = Apply[ Take[chain1, {#1 + 1, #2 - 1}] &, Partition[Join[{0}, commonPos1, {0}], 2, 1], {1} ]; subChains2 = Apply[ Take[chain2, {#1 + 1, #2 - 1}] &, Partition[Join[{0}, commonPos2, {0}], 2, 1], {1} ]; Distribute[Transpose[{subChains1, subChains2}], List, List, List, Interleave[{##}, commonElements] & ] ] Here are a few small examples: In[4]:= SpliceChains[{1, 2, x, 5, 6}, {3, x, 7, 8}] Out[4]= {{1, 2, x, 5, 6}, {1, 2, x, 7, 8}, {3, x, 5, 6}, {3, x, 7, 8}} In[5]:= SpliceChains[{1, 2, x, 5, 6}, {x, 7, 8}] Out[5]= {{1, 2, x, 5, 6}, {1, 2, x, 7, 8}, {x, 5, 6}, {x, 7, 8}} In[6]:= SpliceChains[{x, 5, 6}, {3, x}] Out[6]= {{x, 5, 6}, {x}, {3, x, 5, 6}, {3, x}} In[7]:= SpliceChains[{x, y}, {x, y}] Out[7]= {{x, y}, {x, y}, {x, y}, {x, y}, {x, y}, {x, y}, {x, y}, {x, y}} In[8]:= SpliceChains[{1, 2, x, 6, 7, y, 11, 12, z, 16, 17}, {3, 4, x, 8, 9, y, 13, 14, z, 18, 19}] Out[8]= {{1, 2, x, 6, 7, y, 11, 12, z, 16, 17}, {1, 2, x, 6, 7, y, 11, 12, z, 18, 19}, {1, 2, x, 6, 7, y, 13, 14, z, 16, 17}, {1, 2, x, 6, 7, y, 13, 14, z, 18, 19}, {1, 2, x, 8, 9, y, 11, 12, z, 16, 17}, {1, 2, x, 8, 9, y, 11, 12, z, 18, 19}, {1, 2, x, 8, 9, y, 13, 14, z, 16, 17}, {1, 2, x, 8, 9, y, 13, 14, z, 18, 19}, {3, 4, x, 6, 7, y, 11, 12, z, 16, 17}, {3, 4, x, 6, 7, y, 11, 12, z, 18, 19}, {3, 4, x, 6, 7, y, 13, 14, z, 16, 17}, {3, 4, x, 6, 7, y, 13, 14, z, 18, 19}, {3, 4, x, 8, 9, y, 11, 12, z, 16, 17}, {3, 4, x, 8, 9, y, 11, 12, z, 18, 19}, {3, 4, x, 8, 9, y, 13, 14, z, 16, 17}, {3, 4, x, 8, 9, y, 13, 14, z, 18, 19}} Outer can be used instead of Distribute, but there are a couple slight complications such as making sure it doesn't delve beyond level 1 in lists, and flattening to the correct level at the end. Robby Villegas -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/ Now offering spam-free web-based newsreading