knight.ts

const range = (start: number, end: number) =>
  Array.from({ length: end - start + 1 }, (v, k) => k + start);

/* Monad */
const ret = <T>(x: T): T[] => [x];
const bind = <T>(xs: T[], f: (v: T) => T[]): T[] => xs.map(f).flat();
const fail = <T>(_: T): T[] => [];

/* Knight problem */
type KnightPos = [number, number];

const moveKnight = (pos: KnightPos): KnightPos[] =>
  bind(ret(pos), ([c, r]: KnightPos): KnightPos[] => [
    [c + 2, r - 1],
    [c + 2, r + 1],
    [c - 2, r - 1],
    [c - 2, r + 1],
    [c + 1, r - 2],
    [c + 1, r + 2],
    [c - 1, r - 2],
    [c - 1, r + 2],
  ]).filter(
    ([c, r]: KnightPos) => range(1, 8).includes(c) && range(1, 8).includes(r)
  );

const in3 = (start: KnightPos): KnightPos[] =>
  [1, 2, 3].reduce((result) => bind(result, moveKnight), ret(start));

const canReachIn3 = (start: KnightPos, [c, r]: KnightPos): boolean =>
  in3(start).some(([sc, sr]) => sc == c && sr == r);

console.log(canReachIn3([6, 2], [6, 1])); // true
console.log(canReachIn3([6, 2], [7, 3]));  // false

moveKnight :: KnightPos –> [KnightPos]
moveKnight (c,r) = do
 (c',r') <– [(c+2,r-1),(c+2,r+1),(c-2,r-1),(c-2,r+1)
              ,(c+1,r-2),(c+1,r+2),(c-1,r-2),(c-1,r+2)
              ]
   guard (c' `elem` [1..8] && r' `elem` [1..8])
   return (c',r')

in3 :: KnightPos –> [KnightPos]
in3 start = do
   first <– moveKnight start
   second <– moveKnight first
   moveKnight second

-- or

in3 start = return start >>= moveKnight >>= moveKnight >>= moveKnight

canReachIn3 :: KnightPos –> KnightPos –> Bool
canReachIn3 :: KnightPos –> KnightPos –> Bool canReachIn3 start end = end `elem` in3 start

(6, 2) `canReachIn3` (6, 1)

https://www.typescriptlang.org/play/?target=99&jsx=0&ssl=22&ssc=6&pln=22&pc=12#code/MYewdgzgLgBATgQzAcwKYwLwwBTQXKALhjAFcBbAI1TgBoZUwATYsqmgSkwD4AoGGAEE4iAJ4A6AGZwQ5bAG8YAG0bIoAC2KMmMALQw8BGAGoYARhgBfetgBu9ANZcM3GA5MGo+KBwDcvXgB6ACoYAFlwBB1gwN5QSFg4VFgsAB4AFW5sAA9idI48gG0AXR4YQuzi-3joGEoAS2ZMGAys7Igi4vpJYjs851d0koKYIdKXGHbxcgQAB2xJDiklBChsPzjwWskEeqVm1uwAfX7OspL-INCAaTB65HVYWZlKFXIYGN4oUVn0W-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