Programming Puzzle: Game Button Sequence Recognizer

So just yesterday, I did a live coding interview. Looking back, the problem I was presented with was very simple, but true to my usual nervous self, I over-analzyed the problem — completely missing the point and needlessly complicating things. In an effort to redeem myself, I thought about the problem again and even went out as to write tests for it, in both Ruby and Haskell. If you want to have a crack at the problem yourself, be conservative about scrolling down the page! Without further ado, I present the problem to you.

The Problem

You are a game engine API writer. You need to implement a mechanism that allows your developers to store and retrieve game moves based on the input to the game engine. The two functions for this mechanism should be named register() and on_button().

register() should take a named button sequence, and store it into the database of all named sequences. A single named sequence might look like this: (["down", "forward", "punch"], "hadoken").

on_button() should take a single key, and then return all named sequences that match the ones in the database. E.g., on_button("punch") should return "hadoken" if the previous two inputs were "down" and "forward".

Some Constraints

Multiple Sequences

Because our API is flexible, we allow multiple named sequences with the same sequence. Thus, you can expect something like this:

register(["up", "punch"], "uppercut")
register(["up", "punch"], "uppercut_2")
on_button("up")        # no result
on_button("punch")     # ["uppercut", "uppercut_2"]

. You don’t have to worry about multiple named sequences with the same sequence and also the same name — we will worry about this “exact duplicate” situation in a later version of our API.

Input History

You might have noticed that on_button() depends on the input history of whatever buttons were previously entered into the game. Because of this, you can alternatively write an on_buttons() function (plural with an “s”) that takes the history of buttons as input; this way you don’t have to silently depend on the global state of input history.

My Nervous-Wreck Solution

I decided to use pure Haskell code in the actual interview. The code I wrote had the general idea, but it was a big failure because it performed a naive, custom search without any thought given to data structures. I actually went back and revised the code to make it compile and work after the interview was over; here it is in all its glory:

import Data.List

type ButtonSeqDB = [(ButtonSeq, Name)]
type ButtonSeq = [String]
type Name = String

-- Default DB of button sequences.
buttonSeqDB :: ButtonSeqDB
buttonSeqDB =
  [ (["down", "forward", "punch"], "hadoken")
  , (["forward", "punch"], "charger")
  , (["up", "punch"], "uppercut")
  ]

register :: ButtonSeq -> Name -> ButtonSeqDB -> ButtonSeqDB
register sequence name db
  | null sequence = db
  | alreadyExists = db
  | otherwise = (sequence, name) : db
  where
  alreadyExists = elem (sequence, name) db

onButtons :: ButtonSeq -> ButtonSeqDB -> [Name]
onButtons buttonHist db = map snd
  . fst
  . foldl step ([], db)
  $ reverse buttonHist
  where
  step acc@(foundSoFar, dbRem) button
    | null remaining = acc
    | otherwise =
      ( foundSoFar ++ entriesComplete
      , dbRem'
      )
    where
    remaining = filter ((==button) . last . fst)
      $ filter (not . null . fst) dbRem
    dbRem' = map (\(a, b) -> (init a, b)) remaining
    entriesComplete = filter (null . fst) dbRem'

. I have to admit, the step function in onButtons is essentially unreadable. But it does work:

$ ghci code/toy/game-button-seq/interview_ver.hs
GHCi, version 7.8.4: http://www.haskell.org/ghc/  :? for help
Loading package ghc-prim ... linking ... done.
Loading package integer-gmp ... linking ... done.
Loading package base ... linking ... done.
[1 of 1] Compiling Main             ( code/toy/game-button-seq/interview_ver.hs, interpreted )
Ok, modules loaded: Main.
*Main> onButtons ["down", "down", "forward", "punch"] buttonSeqDB
["charger","hadoken"]

.

Anyway, I will explain the behavior of the code. The first thing to notice is that we feed into step the reversed list of buttonHist, so that we examine the button press history, from newest to oldest. So we look at the just-pressed-button, then the one before that, and the one before, etc, backwards up the history.

As we look at each button, we use it to filter out all known sequences. This filtering is done in remaining, where we check the last button of every known sequence, and see if that matches the current button. That’s what the line filter ((==button) . last . fst) does; the sister line filter (not . null . fst) dbRem is just there to prevent calling last on an empty list.

After we’re done checking, we modify the entire sequence database db, such that we only care about the first \(N - 1\) buttons in the sequence. This way, on the next iteration, we can rest assured that checking against the “last” button in a sequence is not always the same button. In subsequent runs of step, we have dbRem’s sequences slowly get reduced down to nothing as we keep chopping off all sequences’ last button. Keep in mind that we feed the filtered, matching entries of db back into subsequent runs of step, so that effectively we’re only working with matching sequences. Once we reach down to no buttons, we label these named sequences as entriesComplete, and append it into foundSoFar.

Analysis

Obviously, this code has many problems. First, it is virtually unreadable. Readability is important, and the code feels very counter-intuitive — it is marvelously complex when the problem statement sounds so simple.

Second, the fact that we have to bring in and mutate dbRem, which is a copy of the original given ButtonSeqDB type, seems wasteful. We’re wasting a lot of CPU cycles here.

Ruby Solution Using Hashes

So on the day after (that is, today as of the time of this writing), I thought about the problem again and realized we can use hashes. It is a very simple approach, with far less lines of code. I even wrote some tests for it. Here is the implementation below.

module GameButtonSeq
  # button_seq = ["down", "forward", "punch"]
  # name = "hadoken"
  # button_seq_db = a hash of {sequence => name}, but a sequence can have
  # multiple names if that sequence already exists.
  def GameButtonSeq.register(button_seq, name, button_seq_db)
    # If the sequence already exists, simply add the new name to the old name,
    # and store it as a list of names.
    if button_seq_db.key?(button_seq)
      button_seq_db[button_seq] = [name] + button_seq_db[button_seq]
    else
      button_seq_db[button_seq] = [name]
    end

    button_seq_db
  end

  def GameButtonSeq.on_buttons(button_seq, button_seq_db)
    found = []
    # We search the entire button_seq_db hash for the full length of N buttons
    # first, then N - 1 buttons, then N - 2 buttons, until the search input
    # becomes 0. Meanwhile, we collect any and all matches that come our way.
    # The point is to search based on the *last* input button, as this is the
    # "current" button that should "finish" whatever combination/move we were
    # trying to do.
    while button_seq.size > 0
      if button_seq_db.key?(button_seq)
        found << button_seq_db[button_seq]
      end
      # Discard oldest button press, and search again. Even if we have a match,
      # it's important to search for other matches, too.
      button_seq.shift
    end

    # Clean up, so that we get ["foo", "bar"] instead of [["foo"], ["bar"]].
    found.flatten
  end

  def GameButtonSeq.add_hist(button_hist, button_name)
    button_hist + [button_name]
  end
end

And here is the test suite for it. You can run it with ruby test_hash_ver.rb.

require 'minitest/autorun'
require_relative './hash_ver.rb'

class TestPuz < Minitest::Test

  def setup
    @db = GameButtonSeq.register(["down", "forward", "punch"], "hadoken", {})
    @db = GameButtonSeq.register(["forward", "punch"], "charger", @db)
    @db = GameButtonSeq.register(["up", "punch"], "uppercut", @db)

    # Aside: We can easily limit the size of button_hist[] by forcefully always
    # saving only the last N key presses, with N determined by the longest
    # button sequence.
    @button_hist = []

    @button_hist = GameButtonSeq.add_hist(@button_hist, "down")
    @button_hist = GameButtonSeq.add_hist(@button_hist, "down")
    @button_hist = GameButtonSeq.add_hist(@button_hist, "down")
    @button_hist = GameButtonSeq.add_hist(@button_hist, "forward")
    @button_hist = GameButtonSeq.add_hist(@button_hist, "punch")
  end

  def test_button_seq_multiple_names_entered
    db2 = GameButtonSeq.register(["up", "punch"], "uppercut_2", @db)
    button_hist2 = GameButtonSeq.add_hist(@button_hist, "up")
    button_hist2 = GameButtonSeq.add_hist(button_hist2, "punch")
    assert_equal ["uppercut_2", "uppercut"],
      GameButtonSeq.on_buttons(button_hist2, db2)
  end

  def test_button_seq_no_sequence_found
    # Add an unrecognized button.
    button_hist2 = GameButtonSeq.add_hist(@button_hist, "back")
    assert_equal [],
      GameButtonSeq.on_buttons(button_hist2, @db)
  end

  def test_button_seq_one_sequence_found
    button_hist2 = GameButtonSeq.add_hist(@button_hist, "up")
    button_hist2 = GameButtonSeq.add_hist(button_hist2, "punch")
    assert_equal ["uppercut"],
      GameButtonSeq.on_buttons(button_hist2, @db)
  end

  def test_button_seq_multiple_sequences_found
    assert_equal ["hadoken", "charger"],
      GameButtonSeq.on_buttons(@button_hist, @db)
  end
end

Analysis

The key insight was when I realized that you could indeed use a hash even though we have the requirement that multiple, identical button sequences can have different names. The trick is to simply store the value as not a single name, but an array of possible names. This is reflected in the GameButtonSeq.register method.

The heart of on_buttons() is a single while loop that checks the given button history against the database; we reduce the button sequence by 1 button on each iteration to check against shorter matches as well. That’s what the button_seq.shift is for.

Haskell Solution Using Hashes

Inspired by the Ruby solution, I rewrote a Haskell version — with tests to boot! Here is the implementation.

module GameButtonSeq where

import qualified Data.Map as M
import Data.Maybe

-- The database stores a list of Name values, because multiple sequences can
-- have the same name, in which case we store just one instance of the sequence,
-- but a list of multiple Name values.
type ButtonSeqDB = M.Map ButtonSeq [Name]
type ButtonSeq = [String]
type Name = String

-- If a button sequence is already given some set of names, add the current
-- given name into that list of names..
register :: (ButtonSeq, Name) -> ButtonSeqDB -> ButtonSeqDB
register (buttonSeq, name) db = case M.lookup buttonSeq db of
  Just names -> M.insert buttonSeq (name:names) db
  Nothing -> M.insert buttonSeq [name] db

-- Input `buttonSeq` is a list of buttons pressed, from oldest to newest, so
-- that the head of the list contains the oldest button.
onButtons :: ButtonSeq -> ButtonSeqDB -> [Name]
onButtons buttonHist db = concatMap extractNames buttonHists
  where
  buttonHists = take (length buttonHist) $ iterate tail buttonHist
  extractNames bHist = case M.lookup bHist db of
    Just names -> names
    Nothing -> []

onButtons2 :: ButtonSeq -> ButtonSeqDB -> [Name]
onButtons2 buttonHist db = concat $ mapMaybe (flip M.lookup db) buttonHists
  where
  buttonHists = take (length buttonHist) $ iterate tail buttonHist

The file is named GameButtonSeq because of Haskell naming conventions for files containing module code. And here is the test for it.

module Main where

import qualified Data.Map as M
import Test.Tasty
import Test.Tasty.HUnit
import Test.Tasty.QuickCheck as QC

import GameButtonSeq

main :: IO ()
main = defaultMain tests

tests :: TestTree
tests = testGroup "Tests" [qcProps, unitTests]

qcProps :: TestTree
qcProps = testGroup "(checked by QuickCheck)"
  [ QC.testProperty "GameButtonSeq (empty DB cannot produce matches)" $
    \buttonHist -> onButtons (buttonHist :: ButtonSeq) M.empty == []
  ]

unitTests :: TestTree
unitTests = testGroup "Unit tests"
  [ testCase "GameButtonSeq (entry of multiple sequences with same name)" $
    (onButtons ["up", "punch"]
    $ register (["up", "punch"], "uppercut_2") buttonSeqDB)
      @?=
      ["uppercut_2", "uppercut"]
  , testCase "GameButtonSeq (no sequence found)" $
    onButtons
      ["down", "down", "forward", "punch", "down"]
      buttonSeqDB
      @?=
      []
  , testCase "GameButtonSeq (one sequences found)" $
    onButtons
      ["down", "down", "up", "punch"]
      buttonSeqDB
      @?=
      ["uppercut"]
  , testCase "GameButtonSeq (multiple sequences found)" $
    onButtons
      ["down", "down", "forward", "punch"]
      buttonSeqDB
      @?=
      ["hadoken", "charger"]
  ]
  where
  -- Default DB of button sequences.
  buttonSeqDB :: M.Map ButtonSeq [Name]
  buttonSeqDB = M.fromList
    [ (["down", "forward", "punch"], ["hadoken"])
    , (["forward", "punch"], ["charger"])
    , (["up", "punch"], ["uppercut"])
    ]

Analysis

This Haskell version uses the standard Data.Map module, which provides an efficient, basic hash data structure. What we first do is expand buttonHist to all of the cases we are interested in — namely, all of the subsequences of concern. E.g., given a list like ["up", "down", "right", "left"], buttonHists becomes:

[ ["up", "down", "right", "left"]
,       ["down", "right", "left"]
,               ["right", "left"]
,                        ["left"]
]

(spaces added for readability). What we do is reduce the initial input list into all of the “sublist” combinations of \(N\) buttons, \(N - 1\) buttons, \(N - 2\) buttons, etc.

The next step is to simply look at each sublist with concatMap, calling extractNames; we treat each sublist as a key, and look for it in our db hash. We then simply concatenate the results.

The onButtons2 is an alternate version which uses mapMaybe to reduce it down to just two lines of code.

Conclusion

I cringe as I look back at the half-baked code I wrote during the interview. Even the working, compilable version that I wrote after the interview remains ugly and hard to reason about. I can picture my interviewer being grossed out by my ugly, hacky version wondering if I even know what hashes are…

The moral of the story is to think carefully about the most obvious data structure to use, before embarking on writing a solution — no matter how trivial it seems. For myself, I was nervous and did not realize how simple the problem actually was until the day after when I rewrote the solution in Ruby. It was so simple and straightforward that I even wrote some test cases for it¹.

I hope you had some fun writing out your own solutions. Happy hacking!

Copyright (C) 2013-2023 Linus Arver. All rights reserved.