Why you not have canvas?

Path hops:

Path cost:

Think about the todo-list collection

A common pattern amongst the search algorithms (with the semi-exception of recursive exploration) is that they all build a collection which stores paths (or in some implementations nodes) that should be explored. I call this the search "todo" list.

Here is search pseudocode. Dijkstra uses a PriorityQueue to store the todo list. Change the collection type to switch between Deapth First Search, Breadth First Search and A Star.

The fundamental difference between Depth First Search, Breadth First Search, Dijkstra and A Star is the collection used to represent the "todo" list of paths to process.

Algorithm Todo Collection Benefit
Depth First Search Stack Uses little memory
Breadth First Search Queue Finds shortest hops
Dijkstra's Algorithm Priority Queue Finds shortest path
A Star Priority Queue Finds shortest path fast

Worth Thinking About

In all cases Recursive Exploration is the same of Depth First Search.

Breadth first search always finds the shortest path for unweighted graphs, but not for weighted graphs.

For graphs with unweighted edges, Breadth First Search is the same as Dijkstra's.