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Implementing Dijkstra Algorithm in Go

I didn’t go through Computer Science, had a very early dropout. Since I started working in the tech space, I cared a lot about RESTful APIs, preventing systems to fail. Algorithms and data structures always seemed daunting and terrifying.

After picking up the Grokking Algorithms book and giving up three times, I finally decided to put some real effort into it. And it’s being an amazing adventure, I can’t recommend it enough!

Chapter 7 is all about the famous Dijkstra Algorithm: finding the shortest path for a vertice in a graph. A bunch of pomodoros later, I got it. The code below is as commented as possible, to solidify the knowledge in my head and help others as well. I also wrote unit tests and the answers to the book’s exercises here.

I won’t go in much detail explaining the theory behind it, other resources do a better job I’d be capable of. Start with this quick video, take a look at Brilliant’s article and, of course, read the already mentioned book if you can.

It probably can be improved, as everything can. I think this is a nice balance between “working” and “readable”. If you have any nice tips to contribute, please leave it in the comments ✨

Well, here it is, the Dijkstra Algorithm in Go:

package main

import (
	"fmt"
	"sort"
	"strconv"
)

type Graph struct {
	Edges []*Edge
	Nodes []*Node
}

type Edge struct {
	Parent *Node
	Child  *Node
	Cost   int
}

type Node struct {
	Name string
}

const Infinity = int(^uint(0) >> 1)

// AddEdge adds an Edge to the Graph
func (g *Graph) AddEdge(parent, child *Node, cost int) {
	edge := &Edge{
		Parent: parent,
		Child:  child,
		Cost:   cost,
	}

	g.Edges = append(g.Edges, edge)
	g.AddNode(parent)
	g.AddNode(child)
}

// AddNode adds a Node to the Graph list of Nodes, if the the node wasn't already added
func (g *Graph) AddNode(node *Node) {
	var isPresent bool
	for _, n := range g.Nodes {
		if n == node {
			isPresent = true
		}
	}

	if !isPresent {
		g.Nodes = append(g.Nodes, node)
	}
}

// String returns a string representation of the Graph
func (g *Graph) String() string {
	var s string

	s += "Edges:\n"
	for _, edge := range g.Edges {
		s += edge.Parent.Name + " -> " + edge.Child.Name + " = " + strconv.Itoa(edge.Cost)
		s += "\n"
	}
	s += "\n"

	s += "Nodes: "
	for i, node := range g.Nodes {
		if i == len(g.Nodes)-1 {
			s += node.Name
		} else {
			s += node.Name + ", "
		}
	}
	s += "\n"

	return s
}

// Dijkstra implements THE Dijkstra algorithm
// Returns the shortest path from startNode to all the other Nodes
func (g *Graph) Dijkstra(startNode *Node) (shortestPathTable string) {

	// First, we instantiate a "Cost Table", it will hold the information:
	// "From startNode, what's is the cost to all the other Nodes?"
	// When initialized, It looks like this:
	// NODE  COST
	//  A     0    // The startNode has always the lowest cost to itself, in this case, 0
	//  B    Inf   // the distance to all the other Nodes are unknown, so we mark as Infinity
	//  C    Inf
	// ...
	costTable := g.NewCostTable(startNode)

	// An empty list of "visited" Nodes. Everytime the algorithm runs on a Node, we add it here
	var visited []*Node

	// A loop to visit all Nodes
	for len(visited) != len(g.Nodes) {

		// Get closest non visited Node (lower cost) from the costTable
		node := getClosestNonVisitedNode(costTable, visited)

		// Mark Node as visited
		visited = append(visited, node)

		// Get Node's Edges (its neighbors)
		nodeEdges := g.GetNodeEdges(node)

		for _, edge := range nodeEdges {

			// The distance to that neighbor, let's say B is the cost from the costTable + the cost to get there (Edge cost)
			// In the first run, the costTable says it's "Infinity"
			// Plus the actual cost, let's say "5"
			// The distance becomes "5"
			distanceToNeighbor := costTable[node] + edge.Cost

			// If the distance above is lesser than the distance currently in the costTable for that neighbor
			if distanceToNeighbor < costTable[edge.Child] {

				// Update the costTable for that neighbor
				costTable[edge.Child] = distanceToNeighbor
			}
		}
	}

	// Make the costTable nice to read :)
	for node, cost := range costTable {
		shortestPathTable += fmt.Sprintf("Distance from %s to %s = %d\n", startNode.Name, node.Name, cost)
	}

	return shortestPathTable
}

// NewCostTable returns an initialized cost table for the Dijkstra algorithm work with
// by default, the lowest cost is assigned to the startNode – so the algorithm starts from there
// all the other Nodes in the Graph receives the Infinity value
func (g *Graph) NewCostTable(startNode *Node) map[*Node]int {
	costTable := make(map[*Node]int)
	costTable[startNode] = 0

	for _, node := range g.Nodes {
		if node != startNode {
			costTable[node] = Infinity
		}
	}

	return costTable
}

// GetNodeEdges returns all the Edges that start with the specified Node
// In other terms, returns all the Edges connecting to the Node's neighbors
func (g *Graph) GetNodeEdges(node *Node) (edges []*Edge) {
	for _, edge := range g.Edges {
		if edge.Parent == node {
			edges = append(edges, edge)
		}
	}

	return edges
}

// getClosestNonVisitedNode returns the closest Node (with the lower cost) from the costTable
// **if the node hasn't been visited yet**
func getClosestNonVisitedNode(costTable map[*Node]int, visited []*Node) *Node {
	type CostTableToSort struct {
		Node *Node
		Cost int
	}
	var sorted []CostTableToSort

	// Verify if the Node has been visited already
	for node, cost := range costTable {
		var isVisited bool
		for _, visitedNode := range visited {
			if node == visitedNode {
				isVisited = true
			}
		}
		// If not, add them to the sorted slice
		if !isVisited {
			sorted = append(sorted, CostTableToSort{node, cost})
		}
	}

	// We need the Node with the lower cost from the costTable
	// So it's important to sort it
	// Here I'm using an anonymous struct to make it easier to sort a map
	sort.Slice(sorted, func(i, j int) bool {
		return sorted[i].Cost < sorted[j].Cost
	})

	return sorted[0].Node
}

func main() {
	a := &Node{Name: "a"}
	b := &Node{Name: "b"}
	c := &Node{Name: "c"}
	d := &Node{Name: "d"}
	e := &Node{Name: "e"}
	f := &Node{Name: "f"}
	g := &Node{Name: "g"}

	graph := Graph{}
	graph.AddEdge(a, c, 2)
	graph.AddEdge(a, b, 5)
	graph.AddEdge(c, b, 1)
	graph.AddEdge(c, d, 9)
	graph.AddEdge(b, d, 4)
	graph.AddEdge(d, e, 2)
	graph.AddEdge(d, g, 30)
	graph.AddEdge(d, f, 10)
	graph.AddEdge(f, g, 1)

	fmt.Println(graph.Dijkstra(a))
}

The output will be:

Distance from a to a = 0
Distance from a to c = 2
Distance from a to b = 3
Distance from a to d = 7
Distance from a to e = 9
Distance from a to g = 18
Distance from a to f = 17

I’m so happy 😌

@edit: The code above is the version 1. Due community contributions (thanks!), it improved! Get the latest version here.


The cover image used is from the book Grokking Algorithms. All rights reserved to Manning Publications.

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