Filter out sublist in Mathematica

Question

I am a newbie user in mathematica. Here is my problem:

For example, I have a nested list:

 lst = {{1, 0, 0}, {0, 1, 1}, {2, 0, 1}, {1}, {0,3}}

I want to only output those sublist whose elements are 0 or 1. The above list's output should be:

{{1, 0, 0}, {0, 1, 1}, {1}}

I can get the list that satisfies my conditions with this:

lst /. x:{(1 | 0) ..} :> x

But how can I get the converse of the pattern? like this:

 lst /. x:NOT{(1 | 0) ..} :> Sequence[]

So that i can get the result in one stroke.

thanks!

Answer 1

This is a nice application for some/every:

some[f_, l_List] :=                          (* whether f applied to some     *)
  Scan[If[f[#], Return[True]]&, l] === True  (*  element of list is True.     *)

every[f_, l_List] :=                         (* similarly, And @@ f/@l        *)
  Scan[If[!f[#], Return[False]]&, l]===Null  (*  (but with lazy evaluation).  *)

So first make a function that checks a sublist for all zeroes/ones:

chk[lst_] := every[#==0||#==1&, lst]

Then filter your list-of-lists for sublists that pass the test:

Select[lst, chk]

Or, as a one-liner:

Select[lst, every[#==0||#==1&, #]&]