Walking Distance

type dir = N | S | E | W

Implement the function

val dist : dir list -> float

so that dist dirs, given a list of directions dirs, computes the \(\ell_2\) distance (i.e., "as the crow flies") between the starting point and ending point of the path given by dirs. Note that it doesn't matter where you start, the distance between the starting and ending points will always be the same.

let is_close f1 f2 = Float.abs (f1 -.f2) < 10. ** (-15.)
let _ = assert (is_close (dist [N; N; S; E]) (sqrt 2.))