reorg and add code for second edition

09_dijkstras_algorithm/PowerShell/01_dijkstras_algorithm.ps1

@@ -0,0 +1,80 @@
+$infinity = [float]::PositiveInfinity
+
+# the graph
+$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
+
+$graph["fin"] = @{}
+
+# the costs table
+$costs = [ordered]@{}
+$costs["a"] = 6
+$costs["b"] = 2
+$costs["fin"] = $infinity
+
+# the parents table
+$parents = [ordered]@{}
+$parents["a"] = "start"
+$parents["b"] = "start"
+$parents["fin"] = $null
+
+$processed = New-Object System.Collections.Generic.HashSet[String]
+
+function Find-GRKLowestCostNode
+{
+    param ($costs)
+    $lowest_cost = $infinity
+    $lowest_cost_node = $null
+    # Go through each node.
+    foreach ($node in $costs.GetEnumerator())
+    {
+        $cost = $costs[$node.key]
+        # If it's the lowest cost so far and hasn't been processed yet...
+        if (($cost -lt $lowest_cost) -and ($node.key -notin $processed))
+        {
+            # ... set it as the new lowest-cost node.
+            $lowest_cost = $cost
+            $lowest_cost_node = $node
+        }
+    }
+    return $lowest_cost_node
+}
+
+# Find the lowest-cost node that you haven't processed yet.
+$node = Find-GRKLowestCostNode $costs
+$i = 0
+# If you've processed all the nodes, this while loop is done.
+while ($node -ne $null)
+{
+    $i++
+    $cost = $costs[$node.Key]
+    $neighbors = $graph[$node.Key]
+    foreach ($n in $neighbors.Keys)
+    {
+        $new_cost = $cost + $neighbors[$n]
+        # If it's cheaper to get to this neighbor by going through this node...
+        if ($costs[$n] -gt $new_cost)
+        {
+            # ... update the cost for this node.
+            $costs[$n] = $new_cost
+            # This node becomes the new parent for this neighbor.
+            $parents[$n] = $node.Key
+        }
+    }
+    # Mark the node as processed.
+    $processed.Add($node.Key) >$null
+    # Find the next node to process, and loop.
+    $node = Find-GRKLowestCostNode $costs
+}
+
+Write-Host "Cost from the start to each node:"
+Write-Host ($costs | Out-String)