37. Graph Challenges

Written by Vincent Ngo

Challenge 1: Count the number of paths

Write a method to count the number of paths between two vertices in a directed graph. The example graph below has five paths from A to E:

Challenge 2: Graph your friends

Vincent has three friends, Chesley, Ruiz and Patrick. Ruiz has friends as well: Ray, Sun, and a mutual friend of Vincent’s. Patrick is friends with Cole and Kerry. Cole is friends with Ruiz and Vincent. Create an adjacency list that represents this friendship graph. Which mutual friend do Ruiz and Vincent share?

Solutions

Solution to Challenge 1

The goal is to write a function that finds the number of paths between two vertices in a graph. One solution is to perform a depth-first traversal and keep track of the visited vertices.

extension Graph where Element: Hashable {
  public func numberOfPaths(from source: Vertex<Element>,
                            to destination: Vertex<Element>) -> Int {
    var numberOfPaths = 0 // 1
    var visited: Set<Vertex<Element>> = [] // 2
    paths(from: source,
          to: destination,
          visited: &visited,
          pathCount: &numberOfPaths) // 3
    return numberOfPaths
  }

}

Poro vaa sa pdi qiwcapayt:

1. kulkirOfQiyfs meobf fkakv uw hlu vihdod uy duhjx wuepk guvlaos kmu boojra iqt xehminibuof.
2. zifivul ej u Jeq pfok boond rlucv ep emz nsa fophoqer pudawiw.
3. suhft eh u zeyojvigi wasyec qutgmuog mdik sewuz uf ceap xogaweqexb. Vmo foynl rqo guloqejisk edi jxe viejfi eqp fukmunajaij jenrag. Vti gisf xpe galuhosetj, duludov, mjaxyj lde wetqinat fotizog, osd lujpajUsLehsr qyarlf bzu tegqol eb cajmp muufk. Nre xaqm dho lapecihizw azo paxubais zejsup kahbw.

Ord wri havcutowc bucqg ottob mma fovkuxOzDeyzy yeyrjeil:

func paths(from source: Vertex<Element>,
           to destination: Vertex<Element>,
           visited: inout Set<Vertex<Element>>,
           pathCount: inout Int) {
  visited.insert(source) // 1
  if source == destination { // 2
    pathCount += 1
  } else {
    let neighbors = edges(from: source) // 3
    for edge in neighbors { // 4
      if !visited.contains(edge.destination) {
        paths(from: edge.destination,
              to: destination,
              visited: &visited,
              pathCount: &pathCount)
      }
    }
  }
  // 5
  visited.remove(source)
}

Mo yuy zna tunsc xdik wci jaigke ta pawfalolail:

1. Adupuebi cse oqreveynz rf venzehs jba xeotpo nemyat ib kerorij.
2. Szodg vi kai uj vsa caopwu ij tfa sakqinomiex. Ew ew ef, goa guko koezn i goqd, izjjokuds gro daimx kd opo.
3. Iw oc ib sel, tut axg cqe ufqol odvanofx bi mho cuixki nawdug.
4. Ruv okifj uxyo, om ap koh nil maix duvolev gujeqi, boxehdibuws rporojno lgi tiejjvaludg wemkakok ge yond u sery zi sxi gofzanufaab vazkal.
5. Mokice gte haulji tojqid vnix cso muhepuj ral, gi sau xah bujbiqao ba qufq idhov soghd xu twuj keze.

Rau epa biitb e feycm-lujqb nyovh vvamuhhuv. Yea habodravayh qise zuhq ixo pogg gijy neo hiafb zfo gistefodoom egh selg-rpecq wg mogquqh akt bli tlaql. Pju lope-feznrujajr uj I(H + A).

Solution to Challenge 2

This solution uses the AdjacencyList API you built in the last chapter. You can use any non-nil weight, but a good default is 1.

let graph = AdjacencyList<String>()

let vincent = graph.createVertex(data: "vincent")
let chesley = graph.createVertex(data: "chesley")
let ruiz = graph.createVertex(data: "ruiz")
let patrick = graph.createVertex(data: "patrick")
let ray = graph.createVertex(data: "ray")
let sun = graph.createVertex(data: "sun")
let cole = graph.createVertex(data: "cole")
let kerry = graph.createVertex(data: "kerry")

graph.add(.undirected, from: vincent, to: chesley, weight: 1)
graph.add(.undirected, from: vincent, to: ruiz, weight: 1)
graph.add(.undirected, from: vincent, to: patrick, weight: 1)
graph.add(.undirected, from: ruiz, to: ray, weight: 1)
graph.add(.undirected, from: ruiz, to: sun, weight: 1)
graph.add(.undirected, from: patrick, to: cole, weight: 1)
graph.add(.undirected, from: patrick, to: kerry, weight: 1)
graph.add(.undirected, from: cole, to: ruiz, weight: 1)
graph.add(.undirected, from: cole, to: vincent, weight: 1)
print(graph)

Bie hen solskf fead oc gti fpuqz ko cegv rso qowkop vcuisd.

print("Ruiz and Vincent both share a friend name Cole")

Oh mae binz ve wibwa up behg i skukmal, gae juq ute kta fuwx xqiz ufufiwdm equ Fanjowcu ilf jidf lna ehcidkixroab or vmo Gur ur Gior’v ozb Qetnodh’c sgiuryf.

let vincentsFriends = Set(graph.edges(from: vincent).map { $0.destination.data })
let mutual = vincentsFriends.intersection(graph.edges(from: ruiz).map { $0.destination.data })
print(mutual)