Question

I have two list operations which I would like to ask for help. The way I implemented them is not very elegant, so I want to learn from you experts.

1) Suppose I have two lists, one is like {{0,2,4},{1,3,2},{2,0,4}} and the other is {{1,3,7},{2,4,6},{3,1,9}}. I want to either based on the value, or based on some criterion to filter through the first list, and then get the corresponding elements in the second. For example, based on value which is non-zero, I want to get {{3,7},{2,4,6},{3,9}}. Based on the condition greater than 2, I want to get {{7},{4},{9}}.

2) I have a list such as {{{1,2},{1,1}},{{1,3},{2,4}},{{1,2},{2,3}},{{1,4},{3,3}}}. I want to form {{{1,2},{{1,1},{2,3}}},{{1,3},{{2,4}}},{{1,4},{{3,3}}}. That is, I want to group those second lists if the first element is the same. How can I do this in a beautiful way?

Many thanks.

Answer 1

For the first part, you want Pick:

In[27]:= Pick[{{1,3,7},{2,4,6},{3,1,9}},{{0,2,4},{1,3,2},{2,0,4}},_?Positive]
Out[27]= {{3,7},{2,4,6},{3,9}}

In[28]:= Pick[{{1,3,7},{2,4,6},{3,1,9}},{{0,2,4},{1,3,2},{2,0,4}},_?(#>2&)]
Out[28]= {{7},{4},{9}}

For the second question, GatherBy gets you most of the way there:

In[29]:= x = GatherBy[{{{1, 2}, {1, 1}}, {{1, 3}, {2, 4}}, {{1, 2}, 
    {2, 3}}, {{1, 4}, {3, 3}}}, First]

Out[29]= {{{{1, 2}, {1, 1}}, {{1, 2}, {2, 3}}}, {{{1, 3}, 
    {2, 4}}}, {{{1, 4}, {3, 3}}}}

And then you can apply a rule to clean things up a bit:

In[30]:= x /. l:{{a_, _}..} :> {a, Last /@ l}

Out[30]= {{{1, 2}, {{1, 1}, {2, 3}}}, {{1, 3}, {{2, 4}}},
    {{1, 4}, {{3, 3}}}}