I've been reading Eric Lippert's blog for a while now (it's excellent, you should check it out) and In the comments of one of his posts, he mentions that he had no intention indexing a sequence of numbers but rather only enumerate them.
What is the difference between enumeration and indexing, I've searched everywhere ? During my searches I've become even more confused when Iteration was brought into the equation ? Can someone please explain those 3 concepts, maybe even throw in an example ? Before you mark this as a dupe, I've already seen some questions on "Iterator vs Enumerator", however I've yet so see a proper explanation (hence the question). I appreciate your help.
In the comment to the article Eric replied to an observation that since the size of a permutation grows exponentially, it would quickly outgrow numbers representable with 32 bits. Eric's reply was that he has no intention of indexing permutations, by which he meant defining a numbering scheme to obtain a sequential number of a permutation. That is why, he said, overflowing 32 bits was not one of his concerns: his approach allowed to enumerate, or simply "produce", all permutations in some order, as opposed to providing a way to get N-th permutation according to some numbering scheme.
Contrast this to a problem discussed in a question about producing N-th permutation without going through all the preceding ones: here, the author wants to index, or give numbers to, permutations, so the size of an integer is of a concern to them.
Here is an example of indexing permutations discussed in the question linked above:
1 ABC
2 ACB
3 BAC
4 BCA
5 CAB
6 CBA
This indexing scheme lets you answer two questions:
BCA? (it's 4)X, say, 5? (it's CAB)This problem could be somewhat harder than enumerating all permutations, because you need to produce a numbering scheme.