I'm having trouble understanding a concept in my book which is about finding a good structure to represent a union-find datastructure. Here we define a structure -referred to as collection- $V$ as such a datastructure:
A collection $V$ is a bitvector (bitvector is an array of $l = (n/b) + 1$ longs) where bit $i$ ($0 \le i \lt b$) of word $j$ ($0 \le j \lt l$) is 1 only if the element $j * b + 1$ is in the collection $V$.
($n$ is the amount of elements, $b$ is how many bits are represented in a long)
So i was thinking of figuring this out with an example, let's say we have collection $V$:
[ 1 | 3 | 6 | ... | l ]
1 = 001 3 = 011 6 = 110
Does that mean elements with the number (assuming we have given each element a number):
1 * 64 + 1 = 65
3 * 64 + 1 = 193
3 * 64 + 2 = 194
6 * 64 + 2 = 386
6 * 64 + 3 = 387
are in the collection $V$ ?
If this is completely wrong, could someone please give me a decent example of such a collection $V$, or point out where i'm wrong, or why my example can't be such a collection?
(also, i couldn't give this any sensible tag since i can't create tags yet)