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This module contains an implementation of the A* pathfinding algorithm. The tests are likely the best place to see how it is used.

aStar :
(comparable -> List ( comparable, number ))
-> (comparable -> number)
-> List comparable
-> Set comparable
-> Maybe (List comparable)

```
aStar getNeighbors heuristic sources goals
```

Returns a shortest path from a source node to a goal node.
If a path does not exist `Nothing`

is returned.

Arguments:

- getNeighbors: A function which given a node returns a list of tuples with both that node's neighbors and their distance from that node.
- heuristic: A function which takes a point and returns a value used to prioritize exploration. Often this is either the manhattan or euclidean distance to a goal. This function must be admissable.
- sources: A list of inital points to start from
- goals: A set of goals

aStarArray :
(comparable -> List ( comparable, number ))
-> (comparable -> number)
-> List comparable
-> Set comparable
-> Maybe (Array comparable)

Works identically to `aStar`

except it return the underlying
`Array`

used rather than converting it into a `List`

.

```
module AStar exposing (aStar, aStarArray)
{-| This module contains an implementation of the
[A* pathfinding algorithm](https://en.wikipedia.org/wiki/A*_search_algorithm).
The tests are likely the best place to see how it is used.
# Convenience function
@docs aStar
# For more performance
@docs aStarArray
-}
import Array exposing (Array(..))
import Maybe exposing (Maybe(..))
import Set exposing (Set(..))
import PairingHeap as PH
import Debug exposing (log)
{-|
aStar getNeighbors heuristic sources goals
Returns a shortest path from a source node to a goal node.
If a path does not exist `Nothing` is returned.
Arguments:
* getNeighbors: A function which given a node returns a list of tuples with
both that node's neighbors and their distance from that node.
* heuristic: A function which takes a point and returns a value used to
prioritize exploration. Often this is either the manhattan or euclidean
distance to a goal. This function must be [admissable](https://en.wikipedia.org/wiki/Admissible_heuristic).
* sources: A list of inital points to start from
* goals: A set of goals
-}
aStar :
(comparable -> List ( comparable, number ))
-> (comparable -> number)
-> List comparable
-> Set comparable
-> Maybe (List comparable)
aStar getNeighbors heuristic sources goals =
Maybe.map Array.toList (aStarArray getNeighbors heuristic sources goals)
aStar' :
(comparable -> List ( comparable, number ))
-> (comparable -> number)
-> List comparable
-> Set comparable
-> PH.PairingHeap number ( number, comparable, Array comparable )
-> Set comparable
-> Maybe (Array comparable)
aStar' getNeighbors heuristic sources goals open closed =
case (PH.findMin open) of
Nothing ->
Nothing
Just ( cost, ( dist, nextNode, partPath ) ) ->
if Set.member nextNode closed then
-- Ignore if we already explored this node
aStar' getNeighbors heuristic sources goals (PH.deleteMin open) closed
else if Set.member nextNode goals then
Just partPath
else
let
closed' : Set comparable
closed' =
Set.insert nextNode closed
neighbors : List ( comparable, number )
neighbors =
List.filter (\( x, _ ) -> not (Set.member x closed')) (getNeighbors nextNode)
open' : PH.PairingHeap number ( number, comparable, Array comparable )
open' =
List.foldl
(\( x, d ) ->
PH.insert ( dist + d + heuristic x, ( dist + d, x, Array.push x partPath ) )
)
(PH.deleteMin open)
neighbors
in
aStar' getNeighbors heuristic sources goals open' closed'
{-| Works identically to [`aStar`](aStar) except it return the underlying
`Array` used rather than converting it into a `List`.
-}
aStarArray :
(comparable -> List ( comparable, number ))
-> (comparable -> number)
-> List comparable
-> Set comparable
-> Maybe (Array comparable)
aStarArray getNeighbors heuristic sources goals =
aStar' getNeighbors heuristic sources goals (PH.fromList (List.map (\x -> ( heuristic x, ( 0, x, Array.repeat 1 x ) )) sources)) Set.empty
```