# 37 Graph Challenges Written by Vincent Ngo

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### 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
}

}
``````
``````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)
}
``````

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