# How can I extract multiple spans from a list?

I know in Mathematica, I can do

A = Range[100];
B = A[[50 ;; 60]]


B will then contain the 50th through 60th elements of A.

Now, what if I wanted B to take 10th through 40th plus 60th through 80th. Can I do so in one expression such as

B = A[[10 ;; 40 + 60 ;; 80]]


Apparently the above code doesn't work. But I don't want to generate a separate list to do so. Is there a short-cut or elegant way of combining two or more spans in one Part expression?

I hope ;; is treated as range. Also, typeing Part, i.e., [[]], really takes a lot of time to type. I wish Mathematica 10 will shorten it to < > or ( ).

## 3 Answers

list = CharacterRange["A", "Z"];
spans = {3 ;; 6, 10 ;; 16};

list[[Join @@ Range @@@ spans]]
(* {"C","D","E","F","J","K","L","M","N","O","P"} *)

spans2 = {3 ;; 6, 10 ;; 16 ;; 2};
list[[Join @@ Range @@@ spans2]]
(* {"C","D","E","F","J","L","N","P"} *)


Or, of course, Part[list,Join @@ Range @@@ spans].

NOTE: this works only for some forms of Span with explicit indices; it fails for cases like ;;-1;; or ;;;; or ;;All;;...

list = Range[100];
subranges = {10 ;; 20, 30 ;; 40};

subRanges = Module[{l = ConstantArray[0, Length@#]},
(l[[#]] = 1) & /@ #2;
Pick[#, l, 1]] &;

subRanges[list, subranges]

(* {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40} *)


You could just use

Join @@ (list[[#]] & /@ subranges)


for the same result.

See also Undocumented form for Extract, it might be useful here.

Here is an example using the undocumented form of Extract (just to have that answer here) uncovered by rasher and linked in his answer.

lis = Range[100];

Rest @ Extract[lis, {{0}, {10 ;; 40}, {60 ;; 80}}]


Which gives:

{
{10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40},
{60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,
79, 80}
}

• Why the {0} in Extract[lis, {{0}, ...?
– a06e
Commented Sep 22, 2015 at 14:30
• @becko, Without it the undocumented form will not work. I think you can also use an empty list {} in place of {0}. Also note that this will not work in version 10+. Commented Sep 22, 2015 at 15:51
• Yes, it doesn't work in version 10.1.
– a06e
Commented Sep 22, 2015 at 16:02