Teeko

teeko.md

One of the problems in the "2016 International APL Problem Solving Competition (General Computing Category)" was as follows

Write an APL function named 'winner' which

• takes a right argument of a 5x5 character matrix representing a Teeko board
• if there is a winner, returns the appropriate character for the winner, otherwise returns the character representing an unoccupied space

The competition was won by Joshua David and he briefly goes over his solution in this video, but elides most of the details.

A winner can be 4 in a row - either horizontally, vertically, or diagonally - or a square cluster of 4. Below is my attempt at writing this winner function in both J and BQN.

At the time of writing, I have only been toying around with J for a few months, and only about a week with BQN, so there's likely to better ways to solve this (particularly with BQN).

J Solution

Winner =. {{
    board   =. y
    filler  =. {. ; (\: #@>) </.~ , board
    players =. filler -.~ ~. , board

    Four    =. +./ @ 4 = +/"1 @ (players =/ ])

    row     =. Four    board
    col     =. Four |: board
    quad    =. Four ,/ (2 2) ,;._3 board
    diagL   =. Four |: /.    board
    diagR   =. Four |: /. |. board

    result =. 1 ,~ +./"1 (row ,. col ,. quad ,. diagR ,. diagL)

    {. result # (players , filler)
}}

([: (; Winner) 5 5 $ ])@> cutLF 0 : 0
......XXXX.OO....OO......
.O....O.X.XO.X..O..X.....
.......XX.OOXX..OO.......
.......XX..OOXX.OO.......
......X...OOX...OOX.....X
.........O...O...OXX.OXX.
..XX.XX..........OO..OO..
)

BQN Solution

Winner ← {
  board   ← 𝕩
  filler  ← ⌈´⊸=∘⊒⊸/ ⥊ board
  players ← ¬∘∊⟜filler⊸/ ⍷ ∾´ ⥊ board

  Four    ← ∨´˘ 4 =˘ +´⎉1 ∘ (players =⌜ ⊣)
  Quads   ← ∾˝·⥊⎉2 2‿2⊸↕
  Diags   ← 4↑ 1⌽·∾˝ 4⊸↕⎉1 ∘ (⍉ ¯1 ⌽˘ ↕∘≠ ⌽˘ ⊢)

  row     ← Four         board
  col     ← Four       ⍉ board
  quad    ← Four Quads   board
  diagR   ← Four Diags   board
  diagL   ← Four Diags ⌽ board

  result  ← 1 ∾˜ ∨˝ ∾˘ ⟨col,row,quad,diagR,diagL⟩

  ⊑ result / players ∾ filler
}

{
  •Out ((⥊ "  "⊸∾∘∾⟜(@+10)˘) ∾ "result: " ∾ Winner) 5‿5 ⥊ 𝕩
  •Out 9 ⥊ "="
}¨ ⟨
  "......XXXX.OO....OO......",
  ".O....O.X.XO.X..O..X.....",
  ".......XX.OOXX..OO.......",
  ".......XX..OOXX.OO.......",
  "......X...OOX...OOX.....X",
  ".........O...O...OXX.OXX.",
  "..XX.XX..........OO..OO..",
⟩