Graph alg explanations

Author: lee-naish

src/algorithms/pseudocode/AStar.js

@@ -11,9 +11,15 @@ export default parse(`
             // on a measure of the distance from each node to e).
      \\In{
           initialise, with fontier={s}, stored in Nodes \\Ref Init
-            while Nodes not empty \\B 2
-            \\Expl{Nodes is the data structure where we store the nodes that are 
-		in the frontier.  In the A* algorithm, Nodes is a Priority Queue.
+            while Nodes is not empty \\B 2
+            \\Expl{ Nodes is the data structure used to represent the frontier.
+		For A*, Nodes is a priority queue, ordered on Length (the minumum
+                found so far) plus the heuristic value. Here we highlight the Min
+                value. The priority queue also contains nodes that have not been
+                seen, which have infinite Length. The frontier nodes are those
+                shown with a finite Length so far. Nodes with no Length shown
+                have been finalised. The frontier and finalised nodes are also
+                highlighted in the graph display.
             \\Expl}
             \\In{
                 remove next node n from Nodes and finalise it \\Ref Next_node

src/algorithms/pseudocode/BFS.js

@@ -11,7 +11,14 @@ export default parse(`
             // node i (if one has been found; Parent[i] = 0 otherwise).
     \\In{
         initialise, with fontier={s}, stored in Nodes \\Ref Init
-        while Nodes not empty \\B 2
+        while Nodes is not empty \\B 2
+            \\Expl{ Nodes is the data structure used to represent the frontier.
+                For BFS, Nodes is a queue, shown below the arrays.  The frontier
+                nodes are simply those in the queue (they are also marked as
+                Seen). The Seen nodes that are no longer in the queue are
+                finalised.  The frontier and finalised nodes are also highlighted
+                in the graph display.
+            \\Expl}
         \\In{
             remove next node n from Nodes and finalise it \\Ref Next_node 
             // The Parent of n has now been determined

src/algorithms/pseudocode/DFS.js

@@ -11,7 +11,15 @@ export default parse(`
             // node i (if one has been found; Parent[i] = 0 otherwise).
     \\In{
         initialise, with fontier={s}, stored in Nodes \\Ref Init
-        while Nodes not empty \\B 2
+        while Nodes is not empty \\B 2
+            \\Expl{ Nodes is the data structure used to represent the frontier.
+                For DFS, Nodes is a stack, shown below the arrays.
+                The stack can have repeated elements and when we pop a node off
+                the stack it is ignored if it has already been finalised.
+                The frontier nodes are those in the stack that are not finalised.
+                The frontier and finalised nodes are also highlighted in the
+                graph display.
+            \\Expl}
         \\In{
             remove next node n from Nodes and finalise it \\Ref Next_node
             // The Parent of n has now been determined

src/algorithms/pseudocode/dijkstra.js

@@ -11,7 +11,16 @@ Shortest(G, s) //Given a graph G find a shortest path from start node s \\B 1
         // node i (if one has been found; Parent[i] = 0 otherwise). 
         \\In{
                 initialise, with fontier={s}, stored in Nodes \\Ref Init
-                while Nodes not empty \\B 2
+                while Nodes is not empty \\B 2
+            \\Expl{ Nodes is the data structure used to represent the frontier.
+                For Dijkstra's algorithm, Nodes is a priority queue, ordered on
+                Cost (the minumum path length found so far). Here we highlight the Min
+                value. The priority queue also contains nodes that have not been
+                seen, which have infinite Cost. The frontier nodes are those
+                shown with a finite Cost. Nodes with no Cost shown
+                have been finalised. The frontier and finalised nodes are also
+                highlighted in the graph display.
+            \\Expl}
                 \\In{
                     remove next node n from Nodes and finalise it \\Ref Next_node
                     // The Parent of n has now been determined

src/algorithms/pseudocode/prim.js

@@ -12,7 +12,16 @@ Prim(G, s) // Given a weighted graph G, return a minimum spanning tree \\B 1
         // the root s (which has 0 as the parent).
         \\In{
                 initialise, with fontier={s}, stored in Nodes \\Ref Init
-                while Nodes not empty \\B 2
+                while Nodes is not empty \\B 2
+           \\Expl{ Nodes is the data structure used to represent the frontier.
+                For Prim's algorithm, Nodes is a priority queue, ordered on
+                Cost (the minumum edge weight found so far). Here we highlight the Min
+                value. The priority queue also contains nodes that have not been
+                seen, which have infinite Cost. The frontier nodes are those
+                shown with a finite Cost. Nodes with no Cost shown
+                have been finalised. The frontier and finalised nodes are also
+                highlighted in the graph display.
+            \\Expl}
                 \\In{
                     remove next node n from Nodes and finalise it \\Ref Next_node
                     // The Parent of n has now been determined