When to use indexed variables

Question

Still learning the fundamentals of the language I would like to ask you what advantages there might be in writing something like:

a[1] = 2;
a[2] = 4;
a[3] = "x";

It seems to me that it is always better to write

a = {2, 4, "x"};

Do you know about any practical constructs where indexed variables would offer an advantage?

Answer 1

Indexed variables can be used in symbolic calculations. They're useful when the number of variables used needs to be changed programmatically.

Here's an example:

vars = Array[a, 3]
(* {a[1], a[2], a[3]} *)

Minimize[vars.vars, vars]
(* {0, {a[1] -> 0, a[2] -> 0, a[3] -> 0}} *)

They can also be used to emulate sparse arrays, as described here.