Problem

Dijkstra’s Algorithm is a shortest path tree pathfinding algorithm. It compares the distance that has been traveled from the start node to the current node to find the shortest path.

Solution

local function Dijkstra(start, finish, nodes)
	-- Create a closed and open set
	local open = {}
	local closed = {}

	-- Attach data to all nodes without modifying them
	local data = {}
	for _, node in pairs(nodes) do
		data[node] = {
			distance = math.huge,
			previous = nil
		}
	end

	-- The start node has a distance of 0 and starts in the open set
	open[start] = true
	data[start].distance = 0

	while true do
		-- Pick the nearest open node
		local best = nil
		for node in pairs(open) do
			if not best or data[o].distance < data[best].distance then
				best = o
			end
		end
 
		--at the finish - stop looking
		if best == finish then break end
 
		--all nodes traversed - finish not found! No connection between start and finish
		if not best then return end
 
		--calculate a new score for each neighbour
		for _, neighbor in ipairs(best:neighbors()) do
			--provided it's not already in the closed set
			if not closed[neighbor] then
				local newdist = data[best].distance + best:distanceTo(neighbor)
				if newdist < data[neighbor].distance then
					data[neighbor].distance = newdist
					data[neighbor].previous = best
					open[neighbor] = true -- add newly discovered node to set of open nodes
				end
			end
		end
 
		--move the node to the closed set
		closed[best] = true
		open[best] = nil
	end
 
	--walk backwards to reconstruct the path
	local path = {}
	local at = finish
	while at ~= start do
		table.insert(path, 0, at)
		at = data[at].previous
	end
 
	return path
end

Discussion

Based on the function above, Dijkstra’s Algorithm works as follows:

1. It adds a starting node to the closed set.
2. For every node in the closed set, it finds all the adjacent nodes and adds the distance traveled from the parent node to the distance to the next node. If there are two nodes in the closed set that share a neighbor, it gives the neighboring node the shorter distance.
3. It finds the node with the shortest distance.
4. It adds the node to closed set. If node is the goal, the process ends. Otherwise, it repeats from step 2.