pathfinding part 1

site/blog/2024-05-19-pathfiinding-part1/pathfindingpart1.md

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+---
+slug: Pathfinding Algorithms Part 1
+title: Pathfinding Part 1 with Dijkstra's Algorithm
+authors: [justin]
+tags: [dijkstra pathfinding graph]
+---
+
+One of the most common problems that need solved in game development is navigating from one tile to a separate tile somewhere else. Or
+sometimes, I need just to understand if that path is clear between one tile and another. Sometimes you can have a graph node tree, and
+need to understand the cheapest decision. These are the kinds of challenges where one could use a pathfinding algorithm to solve.
+
+![Image of pathfinding demo](./img/image-1.png)
+
+[Link to Pathfinding Demo](https://excaliburjs.com/sample-pathfinding/)
+
+## Pathfinding, what is it
+
+Quick research on pathfinding gives a plethora of resources discussing it. Pathfinding is calculating the shortest path through some
+'network'. That network can be tiles on a game level, it could be roads across the country, it could be aisles and desks in an office,
+etc etc.
+
+Pathfinding is also an algorithm tool to calculate the shortest path through a graph network. A graph network is a series of nodes and
+edges to form a chart. For more information on this: [click here](https://www.google.com/search?q=Graph%20Thoery)
+
+For the sake of clarity, there are two algorithms we specifically dig into with this demonstration: Dijkstra's Algorithm and A\*.
+
+COMING SOON
+We study A\* more in Part 2
+
+## Quick History
+
+### Dijkstra's Algorithm
+
+Dijkstra's Algorithm is a formula for finding the shortest path through a graph that presents weighting (distances) between
+different nodes. The algorithm essentially dictates a starting node, then it systematically calculates the distance to all other nodes
+in the graph, thus, giving one the ability to find the shortest path.
+
+![Graph Network](./img/image-2.png)
+
+Edsger Dijkstra, was sipping coffee at a cafe in Amtserdam in 1956, and was working through a mental exercise regarding
+how to get from Roggerdam to Groningen. Over the course of 20 minutes, he figured out the algorithm. In 1959, it was formally
+published.
+
+## Algorithm Walkthrough
+
+### Dijkstra's Algorithm
+
+![Graph Network](./img/image-2.png)
+
+Let's start with this example graph network. We will manage our walkthrough using a results table and two lists, one for unvisited
+nodes, and one for visited nodes.
+
+Let's declare A our starting node and update our results object with this current information. Since we are starting at node A, we then
+review A's connected neighbors, in this example its nodes B and C.
+
+![starting chart](./img/image-3.png)
+
+Knowing that B is distance 10 from A, and that C is distance 5 from A, we can update our results chart with the current information.
+
+With that update, we can move node A from unvisited to visited list, and we have this new state.
+
+![Visiting A](./img/image-4.png)
+
+Now the algorithm can start to be recursive. We identify the node with the smallest distance to A of our unvisited nodes. In this
+instance, that is node C.
+
+Now that we are evaluating C, we start with identifying its unvisited neighbors, which in this case is only node D. The algorithm would
+update all the unvisited neighbors with their distance, adding it to the cumulative amount traveled from A to this point. So with that,
+D has a distance of 15 from C, and we'll add that to the 5 from A to C.
+
+We continue to repeat this algorithm until we have visited all nodes.
+
+From here we will quickly loop through the rest of the table.
+
+This is when we visit node C:
+
+![Visitng C](./img/image-5.png)
+
+Node B is closer to Source than node D, so we visit it next.
+
+![Visiting B](./img/image-6.png)
+
+Unvisited neighbors of B are E and F. E is closes to A, so we visit it next.
+
+D is E's unvisited neighbor, but its distance via E is longer than what's already in the result index, so we do not add this data up.
+
+D is the only unvisited neighbor, and we hit a dead end on this branch, so D gets visited, but with no updates to the results table
+
+![Visiting D](./img/image-7.png)
+
+So since we are looping through all unvisited Nodes, F is the final unvisited node, and its a neighbor of B. We can now visit F through
+B, and we do not have any results table updates with this visit, as F has no unvisited neighbors.
+
+## What do we do with this data?
+
+My library module for using this algorithm includes a method that runs the analysis, then uses the results table to get the shortest
+path.
+
+It takes in the starting node, and ending (destination) node and returns the list of nodes needed to traverse the path.
+
+```ts
+  shortestPath(startnode: Node, endnode: Node): Node[] {
+    let dAnalysis = this.dijkstra(startnode);
+
+    //iterate through dAnalysis to plot shortest path to endnode
+    let path: Node[] = [];
+    let current: Node | null | undefined = endnode;
+    while (current != null) {
+      path.push(current);
+      current = dAnalysis.find(node => node.node == current)?.previous;
+      if (current == null) {
+        break;
+      }
+    }
+    path.reverse();
+    return path;
+  }
+```
+
+So for Example, if I said starting node is A, and endingnode is D, then the returned array would look like.
+
+```ts
+//[Node C, Node D]
+```
+
+If you need the starting node in the path, you can unshift it in.
+
+```ts
+path.unshift(startnode);
+//[Node A, Node C, Node D]
+```
+
+## The test
+
+![Demo Test](./img/image-8.png)
+
+[Link to Demo](https://excaliburjs.com/sample-pathfinding/)
+
+[Link to Github Project](https://github.com/excaliburjs/sample-pathfinding)
+
+The demo is a simple example of using a Excalibur Tilemap and the pathfinding plugin. When the player clicks a tile that does NOT have
+a tree on it, the pathfinding algorithm selected is used to calculate the path. Displayed in the demo is the amount of tiles to
+traverse, and the overall duration of the process required to make the calculation.
+
+Also included, are the ability to add diagonal traversals in the graph. Which simply modifies the graph created with extra edges added,
+please note, diagonal traversal is slightly more expensive than straight up/down, left/right traversal.
+
+## Conclusion
+
+In this article, we reviewed a brief history of Dijkstra's Algorithm, then we created and example graph network and stepped through it
+using the algorithm, and then was able to use it to determine the shortest path of nodes.
+
+This algorithm I have found is more expensive than A\*, but is a nice tool to use when you don't understand the shape and size of the
+graph network. As a programming exercise, I had a lot of fun interating on this problem till I got it working, and it felt like an
+intermediate coding problem to tackle.
+
+