# Dijkstra's Algorithm

Jun 18 2019, 4:25 PM PST

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.

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

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.