A knight piece in chess can only make L-shaped moves. Specifically, it can only move x steps to the right and y steps up if (x,y) is one of:
(-1,-2) ( 1,-2) (-1, 2) ( 1, 2)
(-2,-1) ( 2,-1) (-2, 1) ( 2, 1)
(For this problem, assume the board extends infinitely in all directions, so a knight may always make eight moves from any starting point.) A knight starting from (0,0) can reach any square, but it may have to take a roundabout route. For instance, to reach the square (0,1) requires three steps:
2, 1
-1, 2
-1, -2
(Notice that the x's add up to 0, and the y's add up to 1.) Write a program, that, given a square (x,y), returns how many moves it takes a knight to reach that square starting from (0,0).
3 7
4
Optional: also output one route the knight could take to reach this square.
This challenge was suggested by /u/Cosmologicon, a well-known moderator of this sub. Many thanks! This one was hiding in the archives ...