Fixed points or 3-colorings of functions without fixed points

[chadbrewbaker]

Felix Dilke put in a request for fixed points of an endofunction, or a 3-coloring of an endofunction such that x and f(x) do not have the same color.

fixedPoints :: (a->a) -> [a] -> [a]

threeColoring :: (a->a) -> [a] -> [ [a],[a],[a]]
threeColoring f set
| (length $ fixedPoints f set) == 0 = []
| otherwise = -- split into connected components. 3 color cycles, greedy color tree branches

[chadbrewbaker]

If memory serves Munro had a few algorithms in that vein which could be nice to have features, Succinct Representations of Permutations and Functions