43.
Dijkstra’s Algorithm Challenges
Written by Vincent Ngo
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Challenge 1: Step-by-step diagram
Given the following graph, step through Dijkstra’s algorithm to produce the shortest path to every other vertex starting from vertex A. Provide the final table of the paths as shown in the previous chapter.
Challenge 2: Find all the shortest paths
Add a method to class Dijkstra that returns a dictionary of all the shortest paths to all vertices given a starting vertex. Here’s the method signature to get you started:
public func getAllShortestPath(from source: Vertex<T>)
-> [Vertex<T> : [Edge<T>]] {
var pathsDict = [Vertex<T> : [Edge<T>]]()
// Implement Solution Here
return pathsDict
}
Solutions
Solution to Challenge 1
Solution to Challenge 2
This function is part of Dijkstra.swift. To get the shortest paths from the source vertex to every other vertex in the graph, do the following:
public func getAllShortestPath(from source: Vertex<T>)
-> [Vertex<T> : [Edge<T>]] {
var pathsDict = [Vertex<T> : [Edge<T>]]() // 1
let pathsFromSource = shortestPath(from: source) // 2
for vertex in graph.vertices { // 3
let path = shortestPath(to: vertex, paths: pathsFromSource)
pathsDict[vertex] = path
}
return pathsDict // 4
}