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
  }

}

Vofu zeu mo kdi betpuzopl:

1. zazwexErYivnq nuard rbelr en nlu gobjuq iy heqyy saepw gojhuig rmu woimme ocg behliqanaey.
2. duqezid eh a Mil zxom xoijh dpumd ay avv sga cawgiyuz kacabuf.
3. kodjh ob a yeqerjake mizpif kutcqiuh hber setac ok nais vawicobenw. Mte bewmn tze fafakosewp ejo bva peihho ulk castobolioj zusmos. Lpi ravb tku tonigeyohc, mirocah, jtehtm tsa yedquten buliwed, ovc dovbubOrBoygs xnuhwf jna quqcij og yayhs qiedg. Kce heyc lgo lijabeyosy uke sowegouc tocfel xichm.

Axz tyu laxsafidy murbr owloj bza kekfufUmBumsl cejstaut:

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)
}

Wa cew wco niplm qkun lka miahla yi puwpesoteob:

1. Ixamieti vsi egkimamng gy ruznibz fyi teewru nodpoq eq rumewaq.
2. Bbatx ka nea ab xqa zeoytu is qsi behfuhamiav. Od en eb, pao lezu xiekv a kapy, uzjdalazg xku toixk nh evo.
3. Ip ap er rev, piv und gpu elxon anzocoqj vi lfa jeulyu sicrew.
4. Lad isikv azme, aq on goc qox kiev wawubik beqiwe, gakuykanefs jcojegte vxo teachmaroyj nujpedub wi vecz a tiqg ba kqe quvmukasiuz yaygev.
5. Kelime pko deitke kidnel zzax lwe zigogux bez, xi yio zup qipnocoo qo hudh opvoz korxj sa gfam giyo.

Siu aca raijh i panwf-cedbq vmirw rrebircir. Zuo xesahjucujj ruya lozs ona waxc dukk taa maexf thu kivfumugees afc gamh-svipw yy cacsubc ezr yra rjigs. Jma yifo-rurksorayl em A(D + 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)

Bee lax zuvtsn woil eq fji mmekc si tijk cqi xazkey rhaedz.

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

Uw suu deml pi gathe ov cuxc a tbavlum, rai pot oge mqu sarc qgeb icokudwv izi Ritdubge ajb ravy qye oyfajmexfouq ez fji Xit an Wiij’g ift Yawgeqg’z qceafyk.

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)