I'm learning F# and I've decided to solve Project Euler's Problem #81 with Dijkstra's algorithm.
In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by only moving to the right and down, is indicated in bold red and is equal to 2427.
131 673 234 103 18 201 96 342 965 150 630 803 746 422 111 537 699 497 121 956 805 732 524 37 331Find the minimal path sum, in matrix.txt (right click and 'Save Link/Target As...'), a 31K text file containing a 80 by 80 matrix, from the top left to the bottom right by only moving right and down.
Are there any obvious mistakes, inefficiency, any obvious possible improvements, any non-idiomatic use of the F# language?
open System
open System.IO
open Microsoft.FSharp.Collections
// Solving Project Euler #81 with Dijkstra's algorithm
// http://projecteuler.net/problem=81
// Explanation of the algorithm can be found here (Dijkstra is A* with H = 0)
// http://www.policyalmanac.org/games/aStarTutorial.htm
// The costs are provided in a text file and are comma-separated
// We read them into a jagged array of ints
let costs = File.ReadAllLines("matrix.txt")
|> Array.map(fun line -> line.Split(',') |> Array.map int32)
let height = costs.Length;
let width = costs.[0].Length;
// A node has fixed coords, but both its parent and cost can be changed
type Node = {
Coords: int*int
mutable Parent: Node
mutable Cost: int
}
// The total cost of moving to a node is the cost of moving to its parent
// plus the inherent cost of the node as given by the file
let cost srcNode (x, y) =
srcNode.Cost + costs.[y].[x]
// This function returns the next nodes to explore
// In this particular problem, we can only move down or right (no diagonals either)
let neighbours node =
let coords = function
| x, y when (x < width - 1 && y < height - 1) -> [(x + 1, y); (x, y + 1)]
| x, y when (x < width - 1) -> [(x + 1, y)]
| x, y when (y < height - 1) -> [(x, y + 1)]
| _ -> []
coords(node.Coords) |> List.map (fun coord -> { node with Coords = coord;
Parent = node;
Cost = cost node coord })
// Start is top-left; end is bottom-right
let rec startNode = { Coords = 0, 0; Parent = startNode; Cost = costs.[0].[0] }
let rec endNode = { Coords = width - 1, height - 1; Parent = endNode; Cost = Int32.MaxValue }
let currentNode = startNode
let openSet = new ResizeArray<Node>()
let closedSet = new ResizeArray<Node>()
// returns whether node exists in set
let existsIn set node =
set |> Seq.exists(fun n -> n.Coords = node.Coords)
// This is the main function. It returns the path as a list of nodes.
let findPath() =
// 1) Add the starting square (or node) to the open list.
openSet.Add(startNode)
// 2) Repeat the following:
while not(endNode |> existsIn closedSet) do
// a) Look for the lowest cost node on the open list.
// We refer to this as the current node.
let currentNode = openSet |> Seq.minBy (fun node -> node.Cost)
// b) Switch it to the closed list.
// Note that using "Remove" would cause Stackoverflow with the starting node
// since it is defined recursively
openSet.RemoveAll(fun node -> node.Coords = currentNode.Coords) |> ignore
closedSet.Add(currentNode)
// c) For each of the nodes adjacent to this current node …
// If it is not walkable or if it is on the closed list, ignore it.
let neighbourNodes = neighbours currentNode |> List.filter ((existsIn closedSet) >> not)
for node in neighbourNodes do
// If it isn’t on the open list, add it to the open list.
// Make the current node the parent of this node.
// Record the cost of the node.
match openSet |> Seq.tryFind (fun n -> n.Coords = node.Coords) with
| None -> (openSet.Add(node)
node.Parent <- currentNode
node.Cost <- cost currentNode node.Coords)
// If it is on the open list already, check to see if this path to that node is better.
// A lower G cost means that this is a better path.
// If so, change the parent of the square to the current square,
// and recalculate the G and F scores of the square.
| Some(n) -> (let newCost = cost currentNode n.Coords
if newCost < n.Cost then
n.Parent <- currentNode
n.Cost <- newCost)
// 3) Save the path. Working backwards from the target square,
// go from each square to its parent square until you reach the starting square.
// That is your path.
let rec walkBack node =
seq {
if node.Coords <> startNode.Coords then
yield! walkBack node.Parent
yield node
}
walkBack (closedSet.Find(fun n -> n.Coords = endNode.Coords))
// Execute and print!
do
let path = findPath()
for n in path do
let x, y = n.Coords
printfn "%A %A" n.Coords costs.[y].[x]
printfn "Total cost : %A" (Seq.last path).Cost
