reorg and add code for second edition

09_dijkstras_algorithm/lua/01_dijkstras_algorithm.lua

@@ -0,0 +1,72 @@
+-- the graph
+local graph = {}
+graph["start"] = {}
+graph["start"]["a"] = 6
+graph["start"]["b"] = 2
+
+graph["a"] = {}
+graph["a"]["fin"] = 1
+
+graph["b"] = {}
+graph["b"]["a"] = 3
+graph["b"]["fin"] = 5
+
+graph["fin"] = {}
+
+-- the costs table
+local infinity = math.huge
+local costs = {}
+costs["a"] = 6
+costs["b"] = 2
+costs["fin"] = infinity
+
+-- the parents table
+local parents = {}
+parents["a"] = "start"
+parents["b"] = "start"
+parents["fin"] = nil
+
+local processed = {}
+
+local function find_lowest_cost_node(costs)
+    local lowest_cost = math.huge
+    local lowest_cost_node = nil
+    -- Go through each node.
+    for node, cost in pairs(costs) do
+        -- If it's the lowest cost so far and hasn't been processed yet...
+        if cost < lowest_cost and not processed[node] then
+            -- ... set it as the new lowest-cost node.
+            lowest_cost = cost
+            lowest_cost_node = node
+        end
+    end
+    return lowest_cost_node
+end
+
+-- Find the lowest-cost node that you haven't processed yet.
+local node = find_lowest_cost_node(costs)
+-- If you've processed all the nodes, this while loop is done.
+while node ~= nil do
+    local cost = costs[node]
+    -- Go through all the neighbors of this node.
+    local neighbors = graph[node]
+    for n, n_cost in pairs(neighbors) do
+        local new_cost = cost + n_cost
+        -- If it's cheaper to get to this neighbor by going through this node...
+        if costs[n] > new_cost then
+            -- ... update the cost for this node.
+            costs[n] = new_cost
+            -- This node becomes the new parent for this neighbor.
+            parents[n] = node
+        end
+    end
+    -- Mark the node as processed.
+    processed[node] = true
+    -- Find the next node to process, and loop.
+    node = find_lowest_cost_node(costs)
+end
+
+print("Cost from the start to each node:")
+for key, value in pairs(costs) do
+    print(key .. ": " .. value)
+end