found some formula on stackoverflow (no credit due to limited space here)
Maximum recursion depth = ((Stack size) - (Total size of stack frames in call chain up to the recursive function)) / (Stack frame size of recursive function)
though it depends on tail recursion optimization. 8 MB stack size as usual, but tunable on OS.
I have readed somewhere around 800 recursions on gcc and 400 in microsoft visual, but you have to check for yourself.

ah, counts uses a hash to find any item and adds to counts.
The syntax looked just confusing to me.
Looks good.

just map is needed as include; i dont like the solution for big strings; otherwise it looks neat

Considering physics every objects that comes up, will fall down.
Though I guess you might study physics and consider a hamilton system or some funky planet? :)

When you hint to not modify the array, it should not be allowed to modify it.
Otherwise this is a boring one.