2
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Example list below. All elements are in the form {1 or 0, 1 or 0, 1 or 0}, with a least one of the numbers 0 and 1 in the element (so excluding {1,1,1} and {0,0,0})

ListA = {{1, 1, 0}, {1, 1, 0}, {1, 1, 0}, **{0, 1, 1}**, {1, 0, 1}, {1, 0, 1}, {1,
   0, 1}}

I want a command to replace any single lone entry in the sequence to be replaced with the next sequence.

In List A the single lone entry is {0, 1, 1} as before this there are three {1, 1, 0} in a succession and following the single lone entry there are three {1, 0, 1} in a succession. So I want this lone entry to be replaced by {1, 0, 1}.

I want the command to be generic so can handle any combination of lone entries, I believe there will be 6 different scenarios (assuming the element sequence either side of the lone entry are different). Another example of lone entry of {{1, 1, 0}, {1, 1, 0}, {1, 0, 1}, {0, 1, 1}, {0, 1, 1}}

Lone entries at the start and end of the lists can be ignored.

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1
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You may construct a pattern with Longest and utilise it with ReplaceAll.

With

listA = {{1, 1, 0}, {1, 1, 0}, {1, 1, 0}, {0, 1, 1}, {1, 0, 1}, {1, 0, 1}, {1, 0, 1}};
listB = {{1, 1, 0}, {1, 1, 0}, {1, 0, 1}, {0, 1, 1}, {0, 1, 1}};

and

loneEntry = {s : Longest[a_ ..], b_, c___} :> {s, a, c}

Then

listA /. loneEntry
{{1, 1, 0}, {1, 1, 0}, {1, 1, 0}, {1, 1, 0}, {1, 0, 1}, {1, 0, 1}, {1, 0, 1}}
listB /. loneEntry
{{1, 1, 0}, {1, 1, 0}, {1, 1, 0}, {0, 1, 1}, {0, 1, 1}}

Hope this helps.

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Just for kicks:

f[{a__, a__, b__}] := a
f[{a__, b__, b__}] := b
f[{a__, b__, c__}] := c
{First@ListA} ~Join~ Map[f, Partition[ListA, 3, 1]] ~Join~ {Last@ListA}

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

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2
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Written for clarity over efficiency:

ListA =
  {{1, 1, 0}, {1, 1, 0}, {1, 1, 0}, {0, 1, 1}, {1, 0, 1}, {1, 0, 1}, {1, 0, 1}};

Split[ListA]

% //. {a___List, lone : {{__}}, b__List} :> {a, {b}[[1, {1}]], b}

Join @@ %
{{{1, 1, 0}, {1, 1, 0}, {1, 1, 0}}, {{0, 1, 1}}, {{1, 0, 1}, {1, 0, 1}, {1, 0, 1}}}

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

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

Other ideas:

sp = Split[ListA];

lone = Position[sp, {{__}}];
lone = DeleteCases[lone, {Length@sp}];

Scan[(sp[[#]] = sp[[# + 1, {1}]]) &, lone];

Join @@ sp

Or:

fill[{{{__}}, {x_List, ___List}}] := {x}
fill[{a_, b_}] := a

Join @@ Developer`PartitionMap[fill, Split@ListA, 2, 1, 1, {{}}]
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