Unsort: remembering a permutation and undoing it.
- by dreeves
Suppose I have a function f that takes a vector v and returns a new vector with the elements transformed in some way.
It does that by calling function g that assumes the vector is sorted.
So I want f to be defined like so:
f[v_] := Module[{s, r},
s = Sort[v]; (* remember the permutation applied in order to sort v *)
r = g[s];
Unsort[r] (* apply the inverse of that permutation *)
]
What's the best way to do the "Unsort"?
Or could we get really fancy and have this somehow work:
answer = Unsort[g[Sort[v]]];
ADDED: Let's make this concrete with a toy example.
Suppose we want a function f that takes a vector and transforms it by adding to each element the next smallest element, if any.
That's easy to write if we assume the vector is sorted, so let's write a helper function g that makes that assumption:
g[v_] := v + Prepend[Most@v, 0]
Now for the function we really want, f, that works whether or not v is sorted:
f[v_] := (* remember the order;
sort it;
call g on it;
put it back in the original order;
return it
*)
