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April 27, 2019

A while ago I wrote Dijkstra’s algorithm in Python, and I figured I’d convert it to Kotlin to test my Kotlin skills, since it’s a language I’m interacting with a lot at work these days.

Dijkstra’s algorithm answers the question – What is the shortest path from a start vertex to every other vertex in the graph? It hinges on the observation that any subpath of a shortest path must also be a shortest path (I encourage you to think about why). Here is my favorite explanation of it, and here is a useful visualization.

My code is more focused on education, mirroring the way I learned it originally at GT. To speed it up, you can make the operation of getting the next vertex to explore (`v`

, in the code) done with a min heap.

Some other good implementations to compare with are Rosetta code, and the one in Kotlin Algorithm Club (what an awesome project!).

So, first let’s write a Graph class, so the algorithm has something to act upon.

data class Graph<T>(val vertices: Set<T>,val edges: Map<T, Set<T>>,val weights: Map<Pair<T, T>, Int>)

Without going too much into the details of initialization and providing a simple API, this is essentially my Graph class (on Github I add an additional constructor).

Now, let’s actually take a look at the algorithm.

fun <T> dijkstra(graph: Graph<T>, start: T): Map<T, T?> {val S: MutableSet<T> = mutableSetOf() // a subset of vertices, for which we know the true distanceval delta = graph.vertices.map { it to Int.MAX_VALUE }.toMap().toMutableMap()delta[start] = 0val previous: MutableMap<T, T?> = graph.vertices.map { it to null }.toMap().toMutableMap()while (S != graph.vertices) {val v: T = delta.filter { !S.contains(it.key) }.minBy { it.value }!!.keygraph.edges.getValue(v).minus(S).forEach { neighbor ->val newPath = delta.getValue(v) + graph.weights.getValue(Pair(v, neighbor))if (newPath < delta.getValue(neighbor)) {delta[neighbor] = newPathprevious[neighbor] = v}}S.add(v)}return previous.toMap()}fun <T> shortestPath(shortestPathTree: Map<T, T?>, start: T, end: T): List<T> {fun pathTo(start: T, end: T): List<T> {if (shortestPathTree[end] == null) return listOf(end)return listOf(pathTo(start, shortestPathTree[end]!!), listOf(end)).flatten()}return pathTo(start, end)}

Definitely enjoy coding in Kotlin, it provides a lot of good API’s for functional programming.

Here’s the test:

@Testfun shouldCalculateCorrectShortestPaths() {val weights = mapOf(Pair("A", "B") to 2,Pair("A", "C") to 8,Pair("A", "D") to 5,Pair("B", "C") to 1,Pair("C", "E") to 3,Pair("D", "E") to 2)val start = "A"val shortestPathTree = dijkstra(Graph(weights), start)Assert.assertEquals(listOf(start, "B", "C"), shortestPath(shortestPathTree, start, "C"))Assert.assertEquals(listOf(start, "B", "C", "E"), shortestPath(shortestPathTree, start, "E"))Assert.assertEquals(listOf(start, "D"), shortestPath(shortestPathTree, start, "D"))}

If you’d like to run the code, clone the git repo and get started using gradle.

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