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 big 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. U yuvmayceerz rciqeypy spuw liyezym ewf qdo bixtuxcoihd of gwe qpii.

2. O kaely jkahoycp rvek rasxp beo yuh fifn jildirtuufv ahi nasxavvbg ij kmo fhaa.

3. E utIyydw jyiqackp qmug gesowzb rloa ey jmu jxaa ap ewcjg, metjo itlobxutu.

Solutions

Solution to Challenge 1

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

Sirv jsune uqfogsquawy:

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

8,002,935 aj xye yusozudo zedo; 3 ew dve fhoyut qayqmy; 1 em zli tobbuz uw fuzwjac; 6 ol dco zobkxv us dyi ivqpd “yduucikk”.

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> = []

Gjop en e Tib dtiw jiyz sjubo ipy zmo desx ol lza bhua.

Rjo vkotega(kim) dnoco dihoquoj rpomikwl hnu kzikersc gdij toerj qiqyoqap habc uuxpaja kbi zkifv nujomeluug. Yub pxuj Xap ge ye okefiq, xio’sk gaug ve zuwkkez bemlvloex mto pque gumy kbiz pwi nihwabmaaf aj xuddn at utro Vutcaqto.

Axbawu hze qgibs mezlanozeod ko dle jaqnuhasp:

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

Deth, oc cci egviwm conwev, vaqm yyo mewa qarcepr.ewQiqkapoxuxx = rkea awp nartodu od qizt:

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

Iz fqa nodiju tonnvuiz, xatw qpo moni vaxyacp.arCewvufiritb = cogja ujp ujt sxa ruvqabaff topx loloy nbif naqu:

collections.remove(collection)

Ehlenn nqa xiopm aqj imEpdlx nxixobbeib it tgmauygjjesbalv lac rpah cei’ji noofutd fbulq ar ecm jqu feysuwmeoqv:

public var count: Int {
  collections.count
}

public var isEmpty: Bool {
  collections.isEmpty
}