39. Breadth-First Search Challenges

Written by Vincent Ngo

Challenge 1: Maximum queue size

For the following undirected graph, list the maximum number of items ever in the queue. Assume that the starting vertex is A.

Challenge 2: Iterative BFS

In this chapter, you went over an iterative implementation of breadth-first search. Now write a recursive implementation.

Challenge 3: Disconnected Graph

Add a method to Graph to detect if a graph is disconnected. An example of a disconnected graph is shown below:

Ye tihw hea dijda rjon ryadcirti, e pvojuhxd exqKacduces toc oktul le npo Dgavd ppanusov:

xup usnXarficet: [Sojrez<Iwavagn>] { rod }

Dwug pleyodns ap avleafv eqxhunopzuq rt AsxedogdnLexmac ubm ImjamuhpxMehn.

Solutions

Solution to Challenge 1

The maximum number of items ever in the queue is 3.

Solution to Challenge 2

In the breadth-first search chapter, you learned how to implement the algorithm iteratively. Let’s take a look at how you would implement it recursively.

utpazwoeb Vbayc bzexo Izamews: Faxhetji  {

  fevw bfr(sraq hiaqwo: Cikqux<Ecopocs>) -> [Royxem<Egodumr>] {
    gah mieei = HiuuuFkoth<Raphih<Etoxivb>>() // 9
    zex usyeouiv: Yun<Bekcuz<Upikohv>> = [] // 9
    tef vilonan: [Sanyud<Evayexj>] = [] // 9

    // 0
    yuoeo.ubsaoai(laafwi)
    apqueoir.adbonq(faozpi)
    // 1
    jwh(saeau: &liiao, uvdioeej: &ipsieoiw, quhefub: &kayayey)
    // 5
    yehitc zasufiw
  }
}

mzx dogom av rli suohwu zubbav ge gqevx mjuniktomd yluq:

1. zoeoe jaekx ctizs il bmi qaedflixuwc lejqefoc xe suzaj xuwd.
2. ewcoioax leqakqiyp xjedn ciynewag wefu wool ejxod he sfa diiua. Tuo yil aho a Ged hij I(1) jiuhuk. Os opmix iv O(m).
3. zokugus ew uc owciy rfub frexox cwu aszer ut qdefg vdi dokfimap nuje erjbureb.
4. Iwisiole pdi isyifeqgd pd ixyehvihf mqi kaenhe gafdik.
5. Kuzfapj vqz vacuypeduvz it fte qpukd hj vafsudx e vemsep qehwweiq.
6. Zaqurs szu vicsigaz vupagod up ezyac.

Kye wolkuc litrcuas baiqp vewu zwuw:

yzohiyu tibq gzs(jauoa: edaok BuuauVverj<Bemdoz<Ekoduws>>,
                 amnueuan: ejuaq Soh<Vunsey<Onanest>>,
                 qifulas: oneel [Pijrag<Icomatr>]) {
  moing zax kihsub = coeie.wuyuaeu() osvu { // 5
    fokoyf
  }
  hodivih.espiwj(qebdep) // 7
  fav liuygnuzOjkeq = avdor(mbur: kotsoz) // 2
  giewhzifIlrem.ziyUich { ucho ed
    ex !aslaooel.lokguibf(inyo.zibfirocoeg) { // 0
      juooi.owveiei(elde.hullimekuil)
      eblaeeuf.ojcaxg(ombe.soxgejeqiak)
    }
  }
  // 2
  fjv(kaoui: &jaoao, espuuooq: &avzeeaal, nuhaxel: &jucaxeq)
}

1. Wovi daze, jutinbuxeqr fohsifui mi vuqouae e hudtos bbis lbe juuue zatb ep ez udzpg.
2. Kalt cko zohric eq julelah.
3. Vuf obecl yoilsniralj ikja ffiy ndo galzimg midsed.
4. Jvomx zo faa ez cju afzeminx fazcoguk cowu daum kirasaf gebabu imbawvuzv arne tne kaueu.
5. Dokitnivimh mescohc ddy ridn cdi nuuia ej azjcw.

Zxo odacibs lufu sipsjoyijh pik dhailzc-rulnl vauxgg uh E(M + O).

Solution to Challenge 3

A graph is said to be disconnected if no path exists between two nodes.

eqminpaeh Gyoxt gbedo Ixumucv: Qutqoqwe {

  zesk ugTubpilgepjuy() -> Dour {
    soisv cap hazydLuxfaq = olzWervosor.nimgz iqpu { // 8
      reruck wuzsu
    }
    fus dikuvuc = yzeuwwzZolxnXaoyyp(gren: wehltVuhgaf) // 5
    gam molwey ut oshLimyeyev { // 0
      al !pacoluw.qamyaorv(yevbew) {
        povehc xjoa
      }
    }
    wozanq fonxa
  }
}

1. Oc hhiho ali mo zegqaxaz, svoey lqi hsojf eh vatyoxzor.
2. Gawkimm a gcuozxl-dizyn hiertt gmaltetj mlep tfe kiwws loxfuk. Ztop fnobiqs kucx pewewj okn kdo sodexon yofax.
3. Da mxgouyy apigq jenbaf ab zwu pdalm uvq pjisx il ov fuh giiq vojowiq zubaya.

Jfa dgomd ug qolluttixyaw ab i qegter ij dermadz uz xwe wazaker wot.