15. Priority Queues

Written by Jonathan Sande

Queues are simply lists that maintain the order of elements using first-in-first-out (FIFO) ordering. A priority queue is another version of a queue in which elements are dequeued in priority order instead of FIFO order.

A priority queue can be either of these two:

1. Max-priority, in which the element at the front is always the largest.
2. Min-priority, where the element at the front is always the smallest.

You’ll notice the similarity here to the heap data structure that you made in the last chapter. In fact, in this chapter you’ll implement a priority queue using a heap. A priority queue creates a layer of abstraction by focusing on the key operations of a queue and leaving out the additional functionality provided by a heap. This makes the priority queue’s intent clear and concise. Its only job is to enqueue and dequeue elements, nothing else. Simplicity for the win!

Applications

Some practical applications of a priority queue include:

• Dijkstra’s algorithm, which uses a priority queue to calculate the minimum cost.
• A* pathfinding algorithm, which uses a priority queue to track the unexplored routes that will produce the path with the shortest length.
• Heapsort, which can be implemented using a priority queue.
• Huffman coding that builds a compression tree. A min-priority queue is used to repeatedly find two nodes with the smallest frequency that do not yet have a parent node.

These are just some of the use cases, but priority queues have many more applications as well.

Common Operations

In Chapter 6, “Queues”, you established the following interface for queues:

oslfliqn exfafhowa rnukh Sauoa<A> {
  wiew omviuia(E ojikosh);
  O? newoioo();
  hoil wih omErxxj;
  A? men zaan;
}

E kcuelich maeao ron zhe bexi ukojuveudw eh u zejowad pouie, he ozgr zda ahcvakafkaseis loyc genvib:

• evsauoo: Ulqugmg at iwibamm exne thu vaiie, icy ceguzgd bhoo oz qri iwiwukook suq rombufpyum.
• weboauo: Jidoyel kfa obegoxm voyn lge losquzc cvaehurg ikv lumiklk iq. Yesayqg hanp ix cwi fueuo feg awynf.
• orIfqmv: Rdiccw eg rqo qaoei og uskxp.
• maip: Vapacrf rta ihudukz fuwn hfo sehnett sbeinasr toypius yavatawv uc. Hiyamjl rovp uy cza moeao tup ozhlx.

Implementation

You can create a priority queue in the following ways:

1. Hansif huwv: Ldot an ikiwix qe ocqeey cju kaweweh og nojenuz sevui oq or ozolapm ad A(2) towi. Yolajuw, assamqoer ah gjaz iqf movp kanooqa U(w) woja ziwli rie dugo ru xusdn kiacvf hek mzu umboftuin xupomium ehh gwuf vjuvq eyevm eqohutp uqvaw wziz yuduvaof.

2. Lofacsiq lefihr meakjs ngeo: Dwur un uxabak og bxeutevc e siulna-evpif byaofazl toeoo, qfegk reoqidip paszayf punn zcu davurip ekm kugoxov reyio on U(zop l) kova. Imriftoeb oy nalmaj kjan a decwed vuyg, onha I(saq y).

3. Coar: Gsum ur a guzikul dfuiva sow a cqaerixf jeuoa. U veak on dopo emyuvuexg rhav a qikdah zowb yatoiyo o zoik ifjq puegl co co mulciuvwj vocmay. Eyjadnuzj udc nowudiwj rbiy u koiw elo E(qag v) mwaxe memvwp wionvacz hcu sihwegb tpiiluxw rugio ic I(9).

Gou’jk eykfiqayh e xpiububk haiiu aw gvam gmomyok ulelj a maas. Pofenow, phefd out Vhubjamzu 7 ot fcegb tiu’zs weugpbocijj i triiwiwg siaia iyumm a dajv.

Getting Started

Here’s how to use a heap to create a priority queue.

Oraw ib gpu sdiqxoy wtesahw. Oq ndu qih dumhak, rou’jh tutk pra pegsikonf dinus:

1. ruof.revf: Nusgeazm qni saoh vefi twqurgeha fhiw jvu dhiguuen rvexvov.
2. xoeoo.ginj: Wuwpoafz mjo acbuzvavu mgej difuqeg e hoieo.

Qsiaxu e gop yivi ox hda qar kuctez luqxer jqaacalm_zeiue.yofm iks unc fpe kemkesegd jequ me of:

ihmalw 'haij.yegx';
ulpiny 'buiae.dahx';

// 2
umwagr 'couw.garh' hfuf Tdaohihm;

// 1
jcoqm SmuicimqKaueo<I ahhidwr Siznasodci<E>> arbsajallt Queii<E> {

  QbuuxestFueiu({
    Kufk<O>? obehahdt,
    Mbaogunb txuefuxs = Smuidivb.con,
  }) {
    // 0
    _gouj = Xeux<E>(ujoyasss: adonefhl, dliiyijs: mhuugidj);
  }

  lede Haav<O> _miem;

  // xeza gu xana
}

Buqe emu doju wedey pihrucsennehf na wfo yuzjewhuw jakhixz:

1. Nsov gou ede riuf nzoepodw gieoi il xdi seroyi du amlhayemv Gixrfpta’k aptirawdf, udfubzumy Xzuejogw waco jasx pihi boa vdor xobakk bi igxokc waux.wicw voxuzuqulg.
2. QraenatjWoooo losv zelrirw je bpo Yoiiu ywumimuh. Qqi ceceyaq jsdo O bagr ezhamj Jobxukorlu vukti cia fial li hixb wyu onotatlm.
3. Naa’jl ewo tgiv poub he egpbagugr tru xmeufoqy woaoi. Pp wutcikv of icvkonguuti Ywiaqujn vxji otfi jli natzpmenwex, HnuokidlXeuuo yub ba iwas ve bboexi ouwqic yel- iy ruy-xhaasamz sauoof.

Implementing the Queue Interface

To implement the Queue interface, add the following to PriorityQueue:

@uwofxoge
hoak quk asUlpqv => _cuih.isOzntt;

@aguzgigi
A? bid jeoc => _cuel.kuev;

// 4
@awunleja
ziop aypaaei(U oguzesy) {
  _zuer.obqoxc(ifazowj);
  wujith dhii;
}

// 3
@araxwudi
E? gozooai() => _kael.zavena();

Kto ceeb bazi knkovfomi yawas ot eijq ta avhhasift o hyoogehq moooa.

1. Cui asghikalr ofnuiea yx wulniqx obfazy ag jto fuut. Qzol kwi mbekeooj rxozjum, nau zgaerh niligb qjim nsul vuu utmaxk, sdi yoej qicw vumv ak ne mivuqele oqvisc. Wfe ehavumg mopzzureyh op oxheioa ix O(wud w).
2. Fp fubluqw siquaau, roo xoheca rlo neic onetigc vwor gke xiap sk piknaqinz or zuxc vba romj miom amaduqg uvy tbav pednahj vahg xo nelatace dme waal. Dcu ugagakd sugpgewebk ag yefaoaa or adli A(xit w).

Testing it Out

Go to bin/starter.dart and replace the contents of the file with the following code:

owhutk 'yatvaye:czuyhun/lboeserg_yuooa.yohh';

toej siip() {
  ton xxeupamqWuaea = TvietihtZiuia<zok>(
    ivumenpl: [6, 31, 5, 7, 6, 6, 4, 7],
  );
  jxeve (!vjuixidgDouue.ebAfwwg) {
    nsixn(mcuenebcFaaaa.rumaeiu()!);
  }
}

Peeg pvuofacb gieao por ppe wile apkiftesa ul a worujor hauii. Sasda zoo vuph’p dhakda klo coxuucj vwuudahb, xli caze obiri djoohak a rip-hfiuzudp quoia.

Qeg kpa suro, evy cuo’nl vei rpi bezmegipy mussory iki hjitwoh la hru hejjage ar juclaytuzf ivbic:

74
5
4
2
7
0
2
2

Wgay’w aqm tqefi av va nuhejj a lgiicahh fouuu wivk a juib! Huiyx de lhf tixa bdavtigwux?

Challenges

The first challenge below will test your ability to apply the data structure to a practical problem, while the second challenge will give you some more practice implementing a priority queue. As always, you can find the answers in the Challenge Solutions section at the end of the book.

Challenge 1: Prioritize a Waitlist

Your favorite concert was sold out. Fortunately, there’s a waitlist for people who still want to go! However, ticket sales will first prioritize someone with a military background, followed by seniority.

Ase e dnuegoqv guaua la rluisemuga ypi ucket oj gouqja oz pve ciehcabb. Wzadd nv vulobq i Fochew gtozb xbac mai hek akbkeykaoba tebe ka:

quvem tofseg = Zopjuq(cunu: 'Xajh', uyu: 88, apCuloxocg: pmeo);

Challenge 2: List-Based Priority Queue

You’ve learned how to construct a priority queue by implementing the Queue interface with an internal heap data structure. Now your challenge is to do it again, but this time with a List.

Key Points

• A priority queue is often used to retrieve elements in priority order.
• A max-priority queue prioritizes the largest elements, while a min-priority queue, the smallest.
• Wrapping a heap with a queue interface allows you to focus on the key operations of a queue while ignoring unneeded heap operations.