# 41 Depth-First Search Challenges Written by Vincent Ngo

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### 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 is said to have a cycle when there is a path of edges and vertices leading 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
}
``````

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