In-place interleaving of the two halves of a string

Question

Given a string of even size, say:

abcdef123456

How would I interleave the two halves, such that the same string would become

Answer 1

Generically that problem is quite hard -- and it reduces to finding permutation cycles. The number and length of those varies quite a lot depending on the length.

The first and last cycles are always degenerate; the 10 entry array has 2 cycles of lengths 6 and 2 and the 12 entry array has a single cycle of length 10.

Withing a cycle one does:

 for (i=j; next=get_next(i) != j; i=next) swap(i,next);

Even though the function next can be implemented as some relatively easy formula of N, the problem is postponed to do book accounting of what indices have been swapped. In the left case of 10 entries, one should [quickly] find the starting positions of the cycles (they are e.g. 1 and 3).