41
Depth-First Search Challenges
Written by Vincent Ngo
Heads up... You're reading this book for free, with parts of this chapter shown beyond this point as
text.You can unlock the rest of this book, and our entire catalogue of books and videos, with a raywenderlich.com Professional subscription.
Challenge 1: BFS or DFS
For each of the following two examples, which traversal (depth-first or breadth-first) is better for discovering if a path exists between the two nodes? Explain why.
- Path from A to F.
- Path from A to G.
Challenge 2: Recursive DFS
In this chapter, you went over an iterative implementation of depth-first search. Now write a recursive implementation.
Challenge 3: Detect a cycle
Add a method to Graph
to detect if a directed graph has a cycle.
Solutions
Solution to Challenge 1
- Path from A to F: Use depth-first because the path you are looking for is deeper in the graph.
- Path from A to G: Use breadth-first because the path you are looking for is near the root.
Solution to Challenge 2
In the depth-first search chapter, you learned how to implement the algorithm iteratively. Let’s take a look at how you would implement it recursively.
extension Graph where Element: Hashable {
func depthFirstSearch(from start: Vertex<Element>)
-> [Vertex<Element>] {
var visited: [Vertex<Element>] = [] // 1
var pushed: Set<Vertex<Element>> = [] // 2
depthFirstSearch(from: start, // 3
visited: &visited,
pushed: &pushed)
return visited
}
}
func depthFirstSearch(from source: Vertex<Element>,
visited: inout [Vertex<Element>],
pushed: inout Set<Vertex<Element>>) {
pushed.insert(source) // 1
visited.append(source)
let neighbors = edges(from: source)
for edge in neighbors { // 2
if !pushed.contains(edge.destination) {
depthFirstSearch(from: edge.destination, // 3
visited: &visited,
pushed: &pushed)
}
}
}
Solution to Challenge 3
A graph has a cycle when a path of edges and vertices leads back to the same source.
extension Graph where Element: Hashable {
func hasCycle(from source: Vertex<Element>) -> Bool {
var pushed: Set<Vertex<Element>> = [] // 1
return hasCycle(from: source, pushed: &pushed) // 2
}
}
func hasCycle(from source: Vertex<Element>,
pushed: inout Set<Vertex<Element>>) -> Bool {
pushed.insert(source) // 1
let neighbors = edges(from: source) // 2
for edge in neighbors {
if !pushed.contains(edge.destination) &&
hasCycle(from: edge.destination, pushed: &pushed) { // 3
return true
} else if pushed.contains(edge.destination) { // 4
return true
}
}
pushed.remove(source) // 5
return false // 6
}