Combining heads of lists so that you can create a nested list from two sublists

Question

I have a list such as list = {1,4,3,4,6,3,1,2,3,4 ... } and a range, say, range = Range[20000].

I want to obtain the following output:

{{0,1}, {1,4}, {2,3}, {3,4}, {4,6}, ... {nth element of list, nth element of range}}

where n is basically Range[Length[list]].

The general question here would be how can I create a list from the $a_i$th index of list a, the $b_k$th index of list b and so on.

I would have tried MapThread but I'm trying to use the Histogram3D function so I needed this "nice" list.

Answer 1

You can do

Transpose@{ Range@20000 - 1, yourList }

Or more generally if yourList is of varying length

Transpose@{ Range@First@Dimensions@yourList - 1, yourList }

Extracting a part of the list, say from index i to index j can be done with Partor Take

newList = Transpose@{ yourList, Range@First@Dimensions@yourList };
newList[[i;;j]]
(* or *)
Take[newList,{i,j}]

Answer 2

I believe that MapIndexed is the most canonical method:

list = {1, 4, 3, 4, 6, 3, 1, 2, 3, 4};

MapIndexed[{#2[[1]] - 1, #} &, list]

{{0, 1}, {1, 4}, {2, 3}, {3, 4}, {4, 6}, {5, 3}, {6, 1}, {7, 2}, {8, 3}, {9, 4}}

However, Transpose and Range is faster when list is a packed array.

Answer 3

If you've just started learning Mathematica, also check out the Table function, which has many applications:

Table[{i - 1, list[[i]]}, {i, 1, 20}]

   {{0, 1}, {1, 4}, {2, 3}, {3, 4}, {4, 6}, ... }