From 8bd2a1ec79b651d89ae3e7bc064d452b3491d1dc Mon Sep 17 00:00:00 2001
From: "Brady J. Garvin" <bgarvin@cse.unl.edu>
Date: Mon, 26 Sep 2022 13:36:01 -0500
Subject: [PATCH] Traced BeFS and recursive DFS, implemented BeFS, and
discussed admissibility.
---
graph-search/notes.md | 24 +++++++++----
graph-search/src/features/search/search.js | 36 ++++++++++++++++++--
graph-search/src/features/search/solution.js | 2 +-
3 files changed, 52 insertions(+), 10 deletions(-)
diff --git a/graph-search/notes.md b/graph-search/notes.md
index 98181fb..9890b80 100644
--- a/graph-search/notes.md
+++ b/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]
diff --git a/graph-search/src/features/search/search.js b/graph-search/src/features/search/search.js
index ec425c8..5918ee4 100644
--- a/graph-search/src/features/search/search.js
+++ b/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) {
diff --git a/graph-search/src/features/search/solution.js b/graph-search/src/features/search/solution.js
index a64ab47..da0ee23 100644
--- a/graph-search/src/features/search/solution.js
+++ b/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 (
--
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