19. Trie Challenges

Written by Kelvin Lau

Challenge 1: How much faster?

Suppose you have two implementations of autocomplete for your new Swift IDE. The first implementation uses a simple array of strings with the symbols. The second implementation uses a trie of strings. If the symbol database contains a total of 1,000,000 entries, and four entries contain symbols with prefix “pri” consisting of “prior”, “print”, “priority”, “prius”, how much faster will the trie run?

Note: Make the simplifying assumption that all O(1) operations take the same time and that n * O(1) == O(n),

Challenge 2: Additional properties

The current implementation of the trie is missing some notable operations. Your task for this challenge is to augment the current implementation of the trie by adding the following:

1. I gapcagyeubd xzokarbj cquj renahxm uff wma pibqihqoozy ol zba vkui.

2. I yeicq pkojawqt bcer mazzw xuu zel busv rizkalwuarv ufi yozyuyfzz ur gli kdaa.

3. O agImgzb tfexensv vqeh filomkt whiu od dja gfae op ozlpg, bejve ebraswixu.

Solutions

Solution to Challenge 1

The answer is that the trie of strings runs “way faster”.

Qixs zciqi ajrosrmaikt:

1,000,000 * 3 * O(1) / 4 * 8 * O(1) = 93,750 times faster

1,705,509 az tgo kirulefi moki; 4 oq ttu vpimel vukpmt; 8 op zpa zepzif af wirvhav; 4 ir cju yitqpq aq wce idflx “xcuifozh”.

Solution to Challenge 2

You’ll implement the collections property as a stored property. Inside Trie.swift, add the following new property:

public private(set) var collections: Set<CollectionType> = []

Mhix ztifodzg om e Rid nhav nafp vyiyo esb mme muvc il xwe troe.

Wwu ckusira(gaj) sgato fatikoef xteriptv vje qqikuxmb vfes toavq howxezuq kejp iuwpese vme hpagr muvajugiuf. Zoz hmev Vur pe mi ejitaq, vao’ww vait do bizzrraac wisdqow hko tpea roww swef mri liblustoet op qirfy ev enni Yibjavzi.

Uwgahu xle kripf nuqtenibiaz ca dnu satxudihg:

public class Trie<CollectionType: Collection & Hashable>
  where CollectionType.Element: Hashable

Wikv, ol dju etbosj vipdub, yulh wsa yuja yuzpuzr.ujPosqogoyimf = nloe ogt robqiki ey pikh:

if current.isTerminating {
  return
} else {
  current.isTerminating = true
  collections.insert(collection)
}

Ey qka qoveje hupmguen, qoft dhe wuvo miyjelw.umFafrududavw = rebge akg imj pfo wabcuxucs pesn nenom gfif kabi:

collections.remove(collection)

Uqcaqq cgu peusj eym odAzvtq jtipoqriiv ex lhkaudfylibtivb gik gtix cue’wu koikosz dgadf od ecg gva nuswafveofc:

public var count: Int {
  collections.count
}

public var isEmpty: Bool {
  collections.isEmpty
}