Data commit

Task/Dijkstras-algorithm/Lua/dijkstras-algorithm.lua

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+-- Graph definition
+local edges = {
+    a = {b = 7, c = 9, f = 14},
+    b = {c = 10, d = 15},
+    c = {d = 11, f = 2},
+    d = {e = 6},
+    e = {f = 9}
+}
+
+-- Fill in paths in the opposite direction to the stated edges
+function complete (graph)
+    for node, edges in pairs(graph) do
+        for edge, distance in pairs(edges) do
+            if not graph[edge] then graph[edge] = {} end
+            graph[edge][node] = distance
+        end
+    end
+end
+
+-- Create path string from table of previous nodes
+function follow (trail, destination)
+    local path, nextStep = destination, trail[destination]
+    while nextStep do
+        path = nextStep .. " " .. path
+        nextStep = trail[nextStep]
+    end
+    return path
+end
+
+-- Find the shortest path between the current and destination nodes
+function dijkstra (graph, current, destination, directed)
+    if not directed then complete(graph) end
+    local unvisited, distanceTo, trail = {}, {}, {}
+    local nearest, nextNode, tentative
+    for node, edgeDists in pairs(graph) do
+        if node == current then
+            distanceTo[node] = 0
+            trail[current] = false
+        else
+            distanceTo[node] = math.huge
+            unvisited[node] = true
+        end
+    end
+    repeat
+        nearest = math.huge
+        for neighbour, pathDist in pairs(graph[current]) do
+            if unvisited[neighbour] then
+                tentative = distanceTo[current] + pathDist
+                if tentative < distanceTo[neighbour] then
+                    distanceTo[neighbour] = tentative
+                    trail[neighbour] = current
+                end
+                if tentative < nearest then
+                    nearest = tentative
+                    nextNode = neighbour
+                end
+            end
+        end
+        unvisited[current] = false
+        current = nextNode
+    until unvisited[destination] == false or nearest == math.huge
+    return distanceTo[destination], follow(trail, destination)
+end
+
+-- Main procedure
+print("Directed:", dijkstra(edges, "a", "e", true))
+print("Undirected:", dijkstra(edges, "a", "e", false))