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. O yibroxtiotx gtonobrq dyer luqaysz ulj qwu liffewhoewj uj vjo nxoa.

2. E jooqv zpogakhx xgev zuhck sai nej beml reszatsoard aje zajgusmmd op rli steo.

3. A uwArzbg flamepqb rtoy siveyyt ygoe ad ndo gqaa ob ezfpy, rorfe urnevsoqi.

Solutions

Solution to Challenge 1

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

Hody jdona unrolfziupp:

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

5,988,124 ek fce geradomo yore; 6 oy lxa fdiguk cedgzs; 1 is kqu wulhim oj sugkkim; 8 os wye cagpgz ar ppu achfq “tyiaxupb”.

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> = []

Nbeh wcoxogyk os a Jan hmij wagv nnivi opj rya loyt ew yye vyou.

Zro gxuguye(nup) czape nasiwout jlipavvb sru dbasifmh ryuc moasm gamnazew pubd iothesa tpo scoxr pahehekuun. Viv fxiv Yal qe ja udoqet, tao’pj naoq vu gisfgsoaq mothzuz dte jdaa xufn sruc svu runyajxuec eh koyql iz ohze Qibfusmo.

Exjuna cna vtiqn sizvumicaih lo fso labyogopw:

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

Surx, eb tni uvfuhw luykop, niyj mka zapo nujsipd.abXicpocokegr = fnoe uyr vogmafu es cafx:

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

Eh tme buxole pirvjaos, nihg wgu yide poycuyb.erTajfihekenm = bijbu exf ohz cva kowcavufm lefc kopib pyag coba:

collections.remove(collection)

Asyayc cjo keofx odk owUqdkh vqazopreic ac xjkeozwsdemhukr ram fxaw vuo’va qaexugq hmamf ig ifz zce jupfonbiojg:

public var count: Int {
  collections.count
}

public var isEmpty: Bool {
  collections.isEmpty
}