The AStar library implements the classic A* path-finding algorithm. It uses a min priority queue for managing potential paths, ordered by each path's known and estimated cost. The AStar class delegates map-related functionality to a GraphOracle protocol to determine valid locations as well as the cost of adding a location to a path candidate. An example of a GraphOracle can be found in the AStarTests.swift file.

API Documentation: AStar

The AStar API is quite basic: there is just the static find method which provides the oracle to use, and the start and end locations for the path.

let oracle = Oracle(data: [
    [.🌊, .🌲, .🌲, .🌲, .🚩, .🌲, .🌲, .🌲],
    [.🌊, .🌲, .🌲, .🌲, .🌲, .🌲, .🌲, .🌲],
    [.🌲, .🌲, .🌲, .🌲, .🗻, .🌲, .🌲, .🌲],
    [.🌲, .🌲, .🗻, .🗻, .🗻, .🗻, .🗻, .🌲],
    [.🌲, .🌲, .🗻, .🌲, .🏁, .🗻, .🌊, .🌊],
    [.🌲, .🌲, .🗻, .🌲, .🗻, .🌲, .🌲, .🌊],
    [.🌊, .🌲, .🗻, .🌲, .🌲, .🌲, .🗻, .🗻],
    [.🌊, .🌲, .🌲, .🌲, .🌲, .🌲, .🗻, .🌲]
])

let start = Coord2D(x: 4, y: 0) // location of 🚩 above
let end = Coord2D(x: 4, y: 4)   // location of 🏁 above
let path = AStar.find(
  oracle: oracle, 
  start: start, 
  end: end
)

You supply an oracle entity that implements the GraphOracle protocol like the Oracle above. The oracle provides information used by the A* algorithm to learn about the routes available from a location and the costs involved in picking one. The start and end points indicate where to start the path and the goal to reach with the lowest possible cost.

You get back an optional array of Position values. If this is nil then no path was found. Otherwise, the array will have the map coordinates and their associated costs for the path that was found, starting at start and ending with end.

Here is the visual representation of the map with the found path. The starting position appears as a red flag (🚩) and the end position is a checkered flag (🏁). The path in between these two points contains an adventurer (🏃).

let image = mapData.asString(path: path!)
print(image)
🌊🌲🌲🌲🚩🌲🌲🌲
🌊🌲🌲🌲🌲🏃🌲🌲
🌲🌲🌲🌲🗻🌲🏃🌲
🌲🌲🗻🗻🗻🗻🗻🏃
🌲🌲🗻🌲🏁🗻🏃🌊
🌲🌲🗻🌲🗻🏃🌲🌊
🌊🌲🗻🌲🌲🌲🗻🗻
🌊🌲🌲🌲🌲🌲🗻🌲

For this example, the map contains three different terrain elements, each with their own cost for travelling into their square:

• 🌲 tree (1)
• 🌊 water (2)
• 🗻 boulder (99)

The algorithm minimizes the cost of traveling over terrain elements while at the same time trying to keep to the shortest path. For comparison, here is what the algorithm finds when constrained to not use diagonal moves:

🌊🌲🌲🌲🚩🌲🌲🌲
🌊🌲🌲🏃🏃🌲🌲🌲
🌲🏃🏃🏃🗻🌲🌲🌲
🌲🏃🗻🗻🗻🗻🗻🌲
🌲🏃🗻🏃🏁🗻🌊🌊
🌲🏃🗻🏃🗻🌲🌲🌊
🌊🏃🗻🏃🌲🌲🗻🗻
🌊🏃🏃🏃🌲🌲🗻🌲

Note that this is not the only path to the flag in 16 moves -- there is another path to goes to the right but it goes over two 🌊 positions which increases the total cost of the route by 2. Thus the algorithm chose the one shown above due to the overal lower cost of the journey.

This package relies on the PriorityQueue package for Swift that provides a min/max ordering of items using a binary heap.