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I have the following table:

n = 3;

myTab = Flatten[Table[{i, j}, {i, -1, n}, {j, -1, n}], 1]

(*output:
{{-1,-1},{-1,0},{-1,1},{-1,2},{-1,3},{0,-1},{0,0},{0,1},{0,2},{0,3},
{1,-1},{1,0},{1,1},{1,2},{1,3},{2,-1},{2,0},{2,1},{2,2},{2,3},{3,-1},
{3,0},{3,1},{3,2},{3,3}}
*)

Now from myTab, I only want to select those elements {i,j} that matches the pattern {i,i+1} or {n,i}. What is the best way to achieve that in Mathematica? Any help is much appreciated!

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4 Answers 4

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Using patterns and Cases:

Cases[myTab, ({i_ ,j_} /; j == i + 1) | {n, _}]
Cases[myTab,  {i_, j_} /; j == i + 1 || i == n]

(* Out:
{{-1, 0}, {0, 1}, {1, 2}, {2, 3},
 {3, -1}, { 3, 0}, {3, 1}, {3, 2}, {3, 3}} *)

Using Select with a selector function:

Select[myTab, Last[#] == First[#] + 1 || First[#] == n &]

(* Same output *)

In case it helps, note also that your myTab can be generated directly with Tuples:

myTab == Tuples[Range[-1, n], 2]
(* True *)
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  • $\begingroup$ This is a great answer, thanks @MarcoB $\endgroup$
    – TDH
    Commented Jun 21, 2022 at 11:47
  • $\begingroup$ @TDH Glad it helped! $\endgroup$
    – MarcoB
    Commented Jun 21, 2022 at 11:52
  • $\begingroup$ The Tuples code is very nice, thanks @MarcoB! $\endgroup$
    – TDH
    Commented Jun 21, 2022 at 12:39
  • 1
    $\begingroup$ Came to the same solution: Cases[myTab, {a_, b_} /; a + 1 == b || b == n] $\endgroup$
    – Valacar
    Commented Jun 21, 2022 at 13:46
  • 1
    $\begingroup$ @Valacar Great minds think alike :-) $\endgroup$
    – MarcoB
    Commented Jun 21, 2022 at 13:47
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n = 3;
run = n - (-1) + 1; 
sel = Flatten@
   Normal@SparseArray[{Band[{1, 2}] -> 1, {run, _} -> 1}, {run, run}];
res = Pick[myTab, sel, 1]

{{-1, 0}, {0, 1}, {1, 2}, {2, 3}, {3, -1}, {3, 0}, {3, 1}, {3, 2}, {3, 3}}

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list =
  {{-1, -1}, {-1, 0}, {-1, 1}, {-1, 2}, {-1, 3}, {0, -1}, {0, 0}, 
   {0, 1}, {0, 2}, {0, 3}, {1, -1}, {1, 0}, {1, 1}, {1, 2}, 
   {1, 3}, {2, -1}, {2, 0}, {2, 1}, {2, 2}, {2, 3}, {3, -1}, 
   {3, 0}, {3, 1}, {3, 2}, {3, 3}};

n = 3;

Using SequenceSplit (new in 11.3)

Catenate @ SequenceSplit[list, {{a_, b_}} /; b - a != 1 /; a != n]

{{-1, 0}, {0, 1}, {1, 2}, {2, 3}, {3, -1}, {3, 0}, {3, 1}, {3, 2}, {3, 3}}

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list =
  {{-1, -1}, {-1, 0}, {-1, 1}, {-1, 2}, {-1, 3}, {0, -1}, {0, 0}, 
   {0, 1}, {0, 2}, {0, 3}, {1, -1}, {1, 0}, {1, 1}, {1, 2}, 
   {1, 3}, {2, -1}, {2, 0}, {2, 1}, {2, 2}, {2, 3}, {3, -1}, 
   {3, 0}, {3, 1}, {3, 2}, {3, 3}};

Using DeleteCases:

DeleteCases[list, Except[{n_ /; n == 3, _} | {a_, b_} /; b == a + 1]]

{{-1, 0}, {0, 1}, {1, 2}, {2, 3}, {3, -1}, {3, 0}, {3, 1}, {3, 2}, {3, 3}}

Or using Pick:

Pick[#, Map[MatchQ[#, {n_ /; n == 3, _} | {a_, b_} /; b == a + 1] &]@#] &@list

{{-1, 0}, {0, 1}, {1, 2}, {2, 3}, {3, -1}, {3, 0}, {3, 1}, {3, 2}, {3, 3}}

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