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MathGroup Archive 2005

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combinations problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58563] combinations problem
  • From: hrocht at mail15.com
  • Date: Thu, 7 Jul 2005 05:35:54 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

hi
at first here is my program
<< DiscreteMath`Combinatorica`
lst1 = Table[i, {i, 100}]
Do[
  lst2 = Table[Random[Integer, {1, 300}], {i, 100}];
  lst3 = Transpose[{lst1, lst2}];
  a = KSubsets[lst3, 2];
  num = 0; Do[
       If[
      Abs(a[[i]][[1]][[2]] - a[[i]][[1]][[1]]) == 
          Abs(a[[i]][[2]][[2]] - a[[i]][[2]][[1]]) || (a[[i]][[1]]
[[2]] + 
              a[[i]][[1]][[1]]) == (a[[i]][[2]][[2]] + a[[i]][[2]]
[[1]]), 
      num++;]
      , {i, 1, 4950}];
  If[num > 40, Print[num]; Print[lst2]];
  , {j, 1, 2000}]

lst3 will have each element in lst2 together with its ordering
such as :
Take[lst3, {1, 3}]
{{1, 48}, {2, 295}, {3, 74}}
if we take all the possible combinations in lst3 taken in pairs as in
a = KSubsets[lst3, 2]   
one sublist may be for a[[1]]
{{1, 6}, {29, 34}}
the length of "a" will be 4950 which is number of possible 
combinations for 100 elements taken in pairs.
the mission is to count the sublists such as
{{1, 6}, {29, 34}}  in which  abs[1-6]=abs[29-34]
or the sublists such as 
{{1, 206}, {35, 172}}
in wich 1+206=35+172
and what is the biggest possible number for such sublists when we 
supply our random or carefully designed lst2 ?
in the program above we want to display only the lst2 wich will give 
num>40
how  could i make my program more speedy and more efficient?
thanks
Anton


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