Traced BeFS and recursive DFS, implemented BeFS, and discussed admissibility.

graph-search/notes.md

@@ -113,24 +113,34 @@ Four moves: `123` → `213` → `231` → `312` → `321`
     ------------      --------------
     (⊥, a, 0) → 2 ✓   a → (⊥, a, 0)
     (a, c, 7) → 9 ✓   c → (a, c, 7)
-    (c, e, 12) → 13
-    (c, b, 8) → 9
+    (c, e, 12) → 13 ✓ b → (c, b, 8)
+    (c, b, 8) → 9 ✓   e → (c, e, 12)
+    (b, e, 17) → 18   d → (e, d, 15)
+    (b, a, 12) → 14 ✓
+    (e, d, 15) → 15 ✓
+    (e, f, 14) → 16
 
     Reversed Path
     ----
-    …
+    d ← e ← c ← a
 
 ## A*
 
-*   Worklist: …
-*   Priority: …
+*   Worklist: Priority Queue
+*   Priority: Distance travelled from the source plus estimated distance to the destination (using an *admissible* heuristic)
 *   Guaranteed to find a path with least weight
 *   Can have good best- and average-case time efficiency
 
 ## Recursive Depth-First Search (DFS)
 
-*   Worklist: …
+*   Worklist: The program stack
 
              Activation Frames            Backpointers     Returned
     -----------------------------------   ------------ ----------------
-    edge = (⊥, a), incidence = …
+    edge = (⊥, a), incidence = (a, c)     a → (⊥, a)   [a, c, b, e, f, d]
+    edge = (a, c), incidence = (c, b)     c → (a, c)   [c, b, e, f, d]
+    edge = (c, b), incidence = (b, e)     b → (c, b)   [b, e, f, d]
+    edge = (b, a)                                      ⊥
+    edge = (b, e), incidence = (e, f)     e → (b, e)   [e, f, d]
+    edge = (e, f), incidence = (f, d)     f → (e, f)   [f, d]
+    edge = (f, d)                         d → (f, d)   [d]

graph-search/src/features/search/search.js

@@ -90,11 +90,43 @@ export function dijkstras(graph, source, destination) {
 }
 
 function heuristic(vertex, destination) {
-  return 0; // TODO: stub
+  if ('acf'.includes(vertex)) {
+    return 2;
+  }
+  if ('be'.includes(vertex)) {
+    return 1;
+  }
+  return 0;
 }
 
 export function bestFirst(graph, source, destination) {
-  return undefined; // TODO: stub
+  const backpointers = new Map();
+  const worklist = new PriorityQueue();
+  worklist.insert(new Edge(undefined, source, 0), heuristic(source, destination));
+  while (worklist.size > 0) {
+    const workitem = worklist.remove();
+    if (backpointers.has(workitem.to) &&
+      backpointers.get(workitem.to).distance <= workitem.distance) {
+      continue;
+    }
+    backpointers.set(workitem.to, workitem);
+    if (workitem.to === destination) {
+      const reversedPath = [];
+      for (let current = destination;
+        current !== undefined;
+        current = backpointers.get(current).from) {
+        reversedPath.push(current);
+      }
+      return reversedPath.reverse();
+    }
+    for (const incidence of graph.getIncidences(workitem.to)) {
+      worklist.insert(
+        new Edge(workitem.to, incidence.destination, workitem.distance + incidence.weight),
+        workitem.distance + incidence.weight + heuristic(incidence.destination, destination),
+      );
+    }
+  }
+  return undefined;
 }
 
 export function recursiveDFS(graph, source, destination) {

graph-search/src/features/search/solution.js

@@ -29,7 +29,7 @@ function formatSolution(solution) {
 }
 
 export function Solution(props) {
-  const search = dijkstras;
+  const search = bestFirst;
   const firstSolution = search(firstExample, 'a', 'd');
   const secondSolution = search(secondExample, '123', '321');
   return (