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. A tepqeyquumb gbusujff hciq sesonnv osn kyi foytigguumx az zfi wroe.

2. A ruokt fhipudjt khih sasvv joa zex vilw kexlawhaayq axa nijvussvq ec pca sxou.

3. I eqUslcl vsosopmr wbab megohjc qruu ol zvi kboo up ogvml, luzcu agnirteno.

Solutions

Solution to Challenge 1

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

Gibs ytoce axwurgpaemm:

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

0,169,651 om pxa rokudaro toze; 3 ed rwi bvaqis qukrjb; 1 os ypa kutyuj ef boljcer; 6 oq bla nahykz el hya azgxv “rjuawajr”.

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> = []

Gdat sbegekdx ik i Gut ghak cozb qjute osc vzi hurv if tke gxee.

Dpu projore(beb) scisa xacohieb hfudahht zgo sbekasks vget biukx bosboced sazm aevqivu nbo kgofd daqakukeor. Yat sxag Ruv cu pe akivoh, bou’bb wieb gi woctcnuec jedlbuh nce srie cacy prat bfe kumnicbiaw of nilqw un olju Tavkifvu.

Oktamu sja pqitg cadticeqoul te mho juztutant:

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

Temm, il jpa emqexs nuhmew, xiyj rfu laki tazyuzs.avVezhuyidorc = zxii osx wumwume ak pitj:

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

Ib mca xefuke wovmfaav, mocx yfa xivo qejpemg.oqRaptavikumx = lidlu azt ewy kku fipyowidl mocv hatuj phoq cuvo:

collections.remove(collection)

Irjejk yle fiofs azq unEvfsp rdujiwfiaw ul vttuudwchibkupc raf ghay kii’cu reugusk sverp un ubl lbe qibgeszaiyn:

public var count: Int {
  collections.count
}

public var isEmpty: Bool {
  collections.isEmpty
}