f(f(n)) = -n

Originally from stackoverflow
While working on this puzzle, became confused, but this can be simplified if we first write the state diagram and then the code. The state diagram should consider odd/even and +ve/-ve numbers.
A simple control flow can be as follows:
A: 1 → 2
B: 2 → -1
C: -1 → -2
D: -2 → 1
E: 1 → 2

Notice that E and A are same.
Once we have this,

if n is +ve:
   if n is odd : return n+1
   if n is even : return -1* (n-1)
else if n is -ve:
   if n is odd : return n-1
   if n is even : return -1 * (n+1)

We get the highest rated solution on stackoverflow.