ShortestPath does not acually return the shortest path on a big graph

foxwhite25 commented 1 year ago

This question is from advent of code Day 12 part 1. https://adventofcode.com/2022/day/12

Problem

The heightMap is a 2d array with shape [41 143], when I create a graph and input all the data, ShortestPath returns a path that looks to be semi random, ranging from 500 to 600.

After this failed I implimented my own Dijkstra's Algorithm and got the accepted answer 468. Maybe you can look into Dijkstra's Algorithm?

This method works fine with the small example on the question page, but no the much bigger input data.

Code

func findShortestPathToHighest(heightMap [][]int, start Coordinate, end Coordinate) int {
    coordinateHash := func(c Coordinate) string {
        return strconv.Itoa(c.X) + "," + strconv.Itoa(c.Y)
    }
    g := graph.New(coordinateHash, graph.Directed())
    for y, line := range heightMap {
        for x, _ := range line {
            err := g.AddVertex(Coordinate{X: x, Y: y})
            if err != nil {
                panic(err)
            }
        }
    }

    for y, line := range heightMap {
        for x, height := range line {
            neighbors := getNeighbors(heightMap, x, y)
            for _, neighbor := range neighbors {
                if heightMap[neighbor.Y][neighbor.X] <= height+1 {
                    err := g.AddEdge(coordinateHash(Coordinate{X: x, Y: y}), coordinateHash(neighbor))
                    if err != nil {
                        panic(err)
                    }
                }
            }
        }
    }
    shortest := 999999999
    for i := 0; i < 1000; i++ {
        path, err := graph.ShortestPath(g, coordinateHash(start), coordinateHash(end))
        if err != nil {
            panic(err)
        }
        if len(path)-1 < shortest {
            println("new shortest:", len(path)-1)
            shortest = len(path) - 1
        }
    }
    return shortest
}

My input data

https://gist.github.com/foxwhite25/06ee39218c9f3340056d2a14b81b3f50

dominikbraun commented 1 year ago

Interesting, thanks for figuring this out. I'm going to take a look at it.

asphaltbuffet commented 1 year ago

Oh my, I'd been debugging my code for quite a while on the same issue! 😆

asphaltbuffet commented 1 year ago

Possibly helpful information is that this only seems to be an issue for unweighted graphs. Setting all edge weights to 1 works just fine.

dominikbraun commented 1 year ago

Possibly helpful information is that this only seems to be an issue for unweighted graphs. Setting all edge weights to 1 works just fine.

That's a valuable remark, thanks.

geoah commented 1 year ago

Hey @foxwhite25, I was looking into this mostly for fun and I can't find where in the code you posted you're adding the weight of the edge.

Do you still have a full example of this example that I could play around with by any chance?

I've attempted to recreate this and I'm also getting some random results between 500 and 600, but once I add a weight to the edge it seems to consistently return the expected result (468).

(I'm not really paying attention to the actual problem so not sure if the weight of the edge needs to be the the diff of the two points or whatever, so I'm just adding a random number to make sure they're not negative.)

Assuming I'm not messing something up this seems to be inline with @asphaltbuffet's finding that the issue seems to be only with unweighted graphs.

Thank you very much in advance. ps. I'll see if I can find what the unweighted graphs don't work as expected.

Adding the following should result in 468.

err := g.AddEdge(
    coordinateHash(Coordinate{X: x, Y: y}),
    coordinateHash(neighbor),
+   EdgeWeight(
+       999+
+           heightMap[y][x]-
+           heightMap[neighbor.Y][neighbor.X],
+   ),
)

The test I'm using to replicate this.

func TestDirectedShortestPath_Issue70(t *testing.T) {
    heightmap := `abccccccccaaaaccccaaacaccccaaaaaacccccccccccaaaccccccccccaaaaaaacccccccccccccccccccccccccccccacaaaccccccccccccccccccccccccccccccccccccccccaaaaa
abccccccccaaaaccaaaaaaaacccaaaaaacccccccccccaaaacccccccccaaaaaaaaaacccccccccccccccaaccccccccaaaaaccaaaccaacccccccccccccccccccccccccccccccaaaaaa
abcccccccccaacccaaaaaaaaccccaaaaacccccccccccaaaacccccccaaaaaaaaaaaaaccccccccccaaaaaaccccccccaaaaaaaaaaaaaaccccccccccccccccaaaccccccccccccaaaaaa
abcccccccccccccccaaaaaccccccaacaaccccaacccccaaacccccccaaaaaaaaaaaaaaccccccccccaaaaaaacccccccccaaaaacaaaaaaccccccccccccccccaaccccccccccccccccaaa
abccccccccccccccccaaaaaccccccccccaaccaacccccccccccccccaaaaacaaaacacacccccaacccaaaaaaaacccccccaaaaacaaaaaaaccccccccccccccccaaacccccccccccccccaaa
abcccccccccccccccaaaaaaccccccccccaaaaaaccccccccccccccccaaaaaaaacaaaaacaaaaaccccaaaaaaacccccccaacaacaaaaaaaaccccccccaaaaccaakcccccccccccccccccaa
abcccccccccccccccaaaccacccccccccccaaaaaaacccccccaaaccccccaaaaaacaaaaaccaaaaaccaaaaaaccccccccccccaacaaaaaaaacccccccccaaaakkkklllcccccccccccccccc
abcccccaaaccccccccccccccccccccccccaaaaaaacccccccaaacacccaaaaaaaaaaaaacaaaaaaccaaaaaacccccccccccccccccaaaccccccccccccaaakkkkkllllcccccccaacccccc
abccccaaaacccccccccccccccccccccccaaaaaacccccccaccaaaaaccaaaaaaaaaaaaacaaaaccccccccaaccccccccccccccccccaaccccccccccccckkkkkkpllllccccaaaaaaccccc
abccccaaaacccccccccccccccccaaacccaaaaaacccccccaaaaaaaacccaaaaacaaaaaacccaaaccccccccccccccccccccccccccccccccccccccccckkkkpppppplllcccaaaaacccccc
abcccccaaaccccccccccccccccaaaacccccccaaccccccccaaaaacccccaaaccccaaacccccccccccccccccccccccccaaccccccccccccccccccjjjkkkkpppppppplllcccaaaaaacccc
abccccccccccccccccccccccccaaaaccccccccccccccccccaaaaacccccccccccccccccccccccccccccccccccccccaaaaaccccccccccccjjjjjjkkkrppppuppplllccccaaaaacccc
abccccccccccccccaaaccccccccaaaccccccccccccccccccaacaaccccccccccccccccccccccaaaccccccccaacccaaaaaccccccccccccjjjjjjjjrrrpuuuuuppplllcccccaaacccc
abcccccaaccaacccaaacacccccccccccccccccccccccccacaaaaccccccccccccccccccccccaaaaaaccccaaaacccaaaaaaccaccccccccjjjrrrrrrrrruuuuuppplllmcccddcccccc
abcccccaaaaaacaaaaaaaaccccccccccccccccccccccccaacaaaccccccccccccccccccccccaaaaaaccccaaaaaacccaaaaccaaacaaacjjjrrrrrrrrruuuxuuupqqlmmmmddddccccc
abcccccaaaaaccaaaaaaaaccccccccccccccccccccccccaaaaaccccaacccccccccccccccccaaaaaacccccaaaacccaacccccaaaaaaacjjjrrrrtuuuuuuxxyuvqqqqmmmmmddddcccc
abaacccaaaaaaccaaaaaccccccccccccccccccaaaaccccaaaaaaccaaaccccccccccccccccccaaaaaccccaaaaaccccccccccaaaaaaccjjjrrrtttuuuuuxxyvvvqqqqqmmmmdddcccc
abaaccaaaaaaaaccaaaaaccccccccccccccccaaaaaaaaaaaaaaaacaaacaaaccccccccccccccaacaacaacaacaaccccccccaaaaaaaaccijjqqrtttxxxxxxyyvvvvvqqqqmmmmdddccc
abaaccaaaaaaaacaaaaaaccccccccccccccccaaaaaaaaaaaaaaaaaaaaaaaacccccccccccccccaaacaaaccccccccccaaccaaaaaaaaaciiiqqqttxxxxxxxyyvvvvvvvqqqmmmdddccc
abaaaccccaaccccaaaccacccccccccccccccccaaaaaaccccaacaaaaaaaaaaccaaaccccccccccaaaaaaaccccccccccaaaaaaaaaaaaaaiiiqqqtttxxxxxxyyyyyyvvvqqqmmmdddccc
SbaaaccccaacccccccccccccccccccccccccaaaaaaaaccccaacccaaaaaaccaaaaaaccccccccccaaaaaacccccccccccaaaaacaaacaaaaiiiqqqttxxxxEzzyyyyyvvvqqqmmmdddccc
abaaaccccccccccccccccccccccccccccccaaaaaaaaaaccccccccaaaaaaccaaaaaaccccccccccaaaaaaaaccccccccaaaaaacaaaccaaaiiiqqqtttxxxyyyyyyvvvvqqqmmmdddcccc
abaccccccaacccccccccccccccccccccccccaaaaaaaaaaaacccccaaaaaaacaaaaaacccccccccaaaaaaaaacccccccaaaaaaaacaaaaaaaiiiqqqtttxxyyyyyyvvvvqqqqnnmeddcccc
abccccccaaaaccccccccccccaaaccccccccccccaaaaaaaaaaacccaaacaaacaaaaacccccccccaaaaaaaaaacccccccaaaaaaaaccaaaaaaaiiiqqtttxxyyyyyywvrrrrnnnneeeccccc
abccccccaaaacccccaacccccaaaacccccccccccaaaccaaaaaacccacccccccaaaaacccccccccaaacaaacccccccccccccaacccccccaaaaaiiqqqttxxwywwyyywwrrrnnnneeeeccccc
abccccccaaaaccaacaaaccccaaaaccccccaacccaacccaaaaaccccccccccccccccccccccccccccccaaacccccccccccccaaccccccaaaaaaiiqqqttwwwwwwwwywwrrrnnneeeecccccc
abccccccccccccaaaaacccccaaaccccacaaacccccccccaaaaacccccccccccccccccccccccccccccaaacccccccccccccccccccccaaaaaaiiqqpsswwwwsswwwwwrrnnneeeeccccccc
abcccccccccccccaaaaaacccccccccaaaaacaacccccccaacaacccccaaccccccccccccccccccccccccccccccccccccccccccccccaccaahhhpppssssssssswwwwrrnnneeeaccccccc
abcccccccccccaaaaaaaacccccccccaaaaaaaacccccaaccccccaaacaaccccccccccccccccccccccccccccccccccccaaaccaccccccccchhhpppsssssssssswwrrrnnneeeaaaacccc
abcccccccccccaaaaacaacccccccccccaaaaaccaaaaaaccccccaaaaaaccccccccccccccccccccccccccccaaccaaccaaaaaacccccccccchhpppppsspppossrrrrrnnneeeaaaacccc
abccccccccccccacaaaccccccccccccaaaaacccaaaaaaaacccccaaaaaaaccaaaccccccccaaaacccccccccaaaaaacccaaaaacccccccccchhhpppppppppoosrrrroonffeaaaaacccc
abccccccccccccccaaaccccccccccccaacaaaccaaaaaaaaccccaaaaaaaaacaaaccccccccaaaacccccccccaaaaaccaaaaaaacccccccccchhhhpppppppoooooooooonfffaaaaccccc
abcccccccccccccccccccccccaaaccccccaaccccaaaaaaaccccaaaaaaaaaaaaaaaccccccaaaacccccccccaaaaaacaaaaaaaacccccaacchhhhhhhhgggggoooooooofffaaaaaacccc
abcccccccccccccccccccccccaaaaacccaacccccaaaaaccccccaaaaaacaaaaaaaaccccccaaacccccccccaaaaaaaaaaaaaaaaccccaaacccchhhhhgggggggooooooffffaaaaaacccc
abccaaacccccccccccccccccaaaaaaccaaaccccaaaaaacccccccccaaacccaaaaacccccccccccccccccccaaaaaaaaccaaacacccccaaacaaachhhggggggggggfffffffcaacccccccc
abcaaaaccccccccccaacccccaaaaaaccaaacaaaccccaaccccccccccccccaaaaacccccccccccccccccccccccaacccccaaaccccaaaaaaaaaacccccccccaagggffffffcccccccccccc
abcaaaaccccccccccaaccccccaaaaaaaaaaaaaaccccccccccccccccccccaaaaaaccccccccccccccccccccccaaccccccccccccaaaaaaaaaccccccccccaaacgfffffcccccccccccaa
abccaaacccccccaaaaaaaacccaaaaaaaaaaaaaaccccccccaaaaaccaaaaaaaaaaaaaacaacccccccccaaaccacccccccccccccccccaaaaacccccccccccaaaaccccccccccccccccccaa
abccccccccccccaaaaaaaacccccccccaaaaaaccccccccccaaaaaccaaaaaaaaaaaaaacaaaaaacccccaaaaaacccccccccccccccccaaaaaacccccccccccaacccccccccccccccacacaa
abccccccccccccccaaaacccccccccccaaaaaacccccccccaaaaaacccaaaaaaaaaaaaacaaaaaacccccaaaaaacccccccccccccccccaaaaaaaccccccccccaacccccccccccccccaaaaaa
abcccccccccccccaaaaaaccccccccccaaaaaaaccccccccaaaaaaccccccaaaaaacccaaaaaaaaccccaaaaaaaaccccccccccccccccaaacaaacccccccccccccccccccccccccccaaaaaa`

    type Coordinate struct {
        X int
        Y int
    }

    start := Coordinate{X: 0, Y: 0}
    end := Coordinate{X: 0, Y: 0}

    convertToIntArray := func(heightmap string) [][]int {
        lines := strings.Split(heightmap, "\n")
        rows := len(lines)
        cols := len(lines[0])
        result := make([][]int, rows)
        for i := range result {
            result[i] = make([]int, cols)
        }
        for i := 0; i < rows; i++ {
            for j := 0; j < cols; j++ {
                char := lines[i][j]
                if char == 'S' {
                    fmt.Println("found start", i, j)
                    start = Coordinate{X: j, Y: i}
                    char = 'a'
                }
                if char == 'E' {
                    fmt.Println("found end", i, j)
                    end = Coordinate{X: j, Y: i}
                    char = 'z'
                }
                result[i][j] = int(char) - int('a')
            }
        }
        return result
    }

    getNeighbors := func(heightMap [][]int, x int, y int) []Coordinate {
        neighbors := []Coordinate{}
        if x > 0 {
            neighbors = append(neighbors, Coordinate{X: x - 1, Y: y})
        }
        if x < len(heightMap[0])-1 {
            neighbors = append(neighbors, Coordinate{X: x + 1, Y: y})
        }
        if y > 0 {
            neighbors = append(neighbors, Coordinate{X: x, Y: y - 1})
        }
        if y < len(heightMap)-1 {
            neighbors = append(neighbors, Coordinate{X: x, Y: y + 1})
        }
        return neighbors
    }

    findShortestPathToHighest := func(heightMap [][]int, start Coordinate, end Coordinate) int {
        coordinateHash := func(c Coordinate) string {
            return strconv.Itoa(c.X) + "," + strconv.Itoa(c.Y)
        }
        g := New(coordinateHash, Directed())
        for y, line := range heightMap {
            for x := range line {
                err := g.AddVertex(Coordinate{X: x, Y: y})
                if err != nil {
                    panic(err)
                }
            }
        }

        for y, line := range heightMap {
            for x, height := range line {
                neighbors := getNeighbors(heightMap, x, y)
                for _, neighbor := range neighbors {
                    if heightMap[neighbor.Y][neighbor.X] <= height+1 {
                        err := g.AddEdge(
                            coordinateHash(Coordinate{X: x, Y: y}),
                            coordinateHash(neighbor),
                            // This is the added weight, removing this will break this whole thing
                            EdgeWeight(
                                999+
                                    heightMap[y][x]-
                                    heightMap[neighbor.Y][neighbor.X],
                            ),
                        )
                        if err != nil {
                            panic(err)
                        }
                    }
                }
            }
        }
        shortest := 999999999
        for i := 0; i < 1000; i++ {
            path, err := ShortestPath(g, coordinateHash(start), coordinateHash(end))
            if err != nil {
                panic(err)
            }
            if len(path)-1 < shortest {
                println("new shortest:", len(path)-1)
                shortest = len(path) - 1
            }
        }
        return shortest
    }

    findShortestPathToHighest(convertToIntArray(heightmap), start, end)
}

dominikbraun commented 1 year ago

Adding the following should result in 468.

err := g.AddEdge(
  coordinateHash(Coordinate{X: x, Y: y}),
  coordinateHash(neighbor),
+ EdgeWeight(
+     999+
+         heightMap[y][x]-
+         heightMap[neighbor.Y][neighbor.X],
+ ),
)

@geoah Removing or adding EdgeWeight doesn't change the result for me, which always is:

=== RUN   TestDirectedShortestPath_Issue70
new shortest: 0
--- PASS: TestDirectedShortestPath_Issue70 (0.00s)
PASS

geoah commented 1 year ago

@dominikbraun sigh; sorry for that, the test had a stupid formatting issue because I added a leading linebreak to the heightmap string for better visibility.

Please try this, only difference should be that in this one there is no leading linebreak.

Without the EdgeWeight I get random results such as

=== RUN   TestDirectedShortestPath_Issue70
found start 20 0
found end 20 120
new shortest: 604
new shortest: 578
new shortest: 558
new shortest: 544
new shortest: 538
new shortest: 522
new shortest: 516

With the EdgeWeight I get

=== RUN   TestDirectedShortestPath_Issue70
found start 20 0
found end 20 120
new shortest: 468

package graph

import (
    "fmt"
    "strconv"
    "strings"
    "testing"
)

func TestDirectedShortestPath_Issue70(t *testing.T) {
    heightmap := `abccccccccaaaaccccaaacaccccaaaaaacccccccccccaaaccccccccccaaaaaaacccccccccccccccccccccccccccccacaaaccccccccccccccccccccccccccccccccccccccccaaaaa
abccccccccaaaaccaaaaaaaacccaaaaaacccccccccccaaaacccccccccaaaaaaaaaacccccccccccccccaaccccccccaaaaaccaaaccaacccccccccccccccccccccccccccccccaaaaaa
abcccccccccaacccaaaaaaaaccccaaaaacccccccccccaaaacccccccaaaaaaaaaaaaaccccccccccaaaaaaccccccccaaaaaaaaaaaaaaccccccccccccccccaaaccccccccccccaaaaaa
abcccccccccccccccaaaaaccccccaacaaccccaacccccaaacccccccaaaaaaaaaaaaaaccccccccccaaaaaaacccccccccaaaaacaaaaaaccccccccccccccccaaccccccccccccccccaaa
abccccccccccccccccaaaaaccccccccccaaccaacccccccccccccccaaaaacaaaacacacccccaacccaaaaaaaacccccccaaaaacaaaaaaaccccccccccccccccaaacccccccccccccccaaa
abcccccccccccccccaaaaaaccccccccccaaaaaaccccccccccccccccaaaaaaaacaaaaacaaaaaccccaaaaaaacccccccaacaacaaaaaaaaccccccccaaaaccaakcccccccccccccccccaa
abcccccccccccccccaaaccacccccccccccaaaaaaacccccccaaaccccccaaaaaacaaaaaccaaaaaccaaaaaaccccccccccccaacaaaaaaaacccccccccaaaakkkklllcccccccccccccccc
abcccccaaaccccccccccccccccccccccccaaaaaaacccccccaaacacccaaaaaaaaaaaaacaaaaaaccaaaaaacccccccccccccccccaaaccccccccccccaaakkkkkllllcccccccaacccccc
abccccaaaacccccccccccccccccccccccaaaaaacccccccaccaaaaaccaaaaaaaaaaaaacaaaaccccccccaaccccccccccccccccccaaccccccccccccckkkkkkpllllccccaaaaaaccccc
abccccaaaacccccccccccccccccaaacccaaaaaacccccccaaaaaaaacccaaaaacaaaaaacccaaaccccccccccccccccccccccccccccccccccccccccckkkkpppppplllcccaaaaacccccc
abcccccaaaccccccccccccccccaaaacccccccaaccccccccaaaaacccccaaaccccaaacccccccccccccccccccccccccaaccccccccccccccccccjjjkkkkpppppppplllcccaaaaaacccc
abccccccccccccccccccccccccaaaaccccccccccccccccccaaaaacccccccccccccccccccccccccccccccccccccccaaaaaccccccccccccjjjjjjkkkrppppuppplllccccaaaaacccc
abccccccccccccccaaaccccccccaaaccccccccccccccccccaacaaccccccccccccccccccccccaaaccccccccaacccaaaaaccccccccccccjjjjjjjjrrrpuuuuuppplllcccccaaacccc
abcccccaaccaacccaaacacccccccccccccccccccccccccacaaaaccccccccccccccccccccccaaaaaaccccaaaacccaaaaaaccaccccccccjjjrrrrrrrrruuuuuppplllmcccddcccccc
abcccccaaaaaacaaaaaaaaccccccccccccccccccccccccaacaaaccccccccccccccccccccccaaaaaaccccaaaaaacccaaaaccaaacaaacjjjrrrrrrrrruuuxuuupqqlmmmmddddccccc
abcccccaaaaaccaaaaaaaaccccccccccccccccccccccccaaaaaccccaacccccccccccccccccaaaaaacccccaaaacccaacccccaaaaaaacjjjrrrrtuuuuuuxxyuvqqqqmmmmmddddcccc
abaacccaaaaaaccaaaaaccccccccccccccccccaaaaccccaaaaaaccaaaccccccccccccccccccaaaaaccccaaaaaccccccccccaaaaaaccjjjrrrtttuuuuuxxyvvvqqqqqmmmmdddcccc
abaaccaaaaaaaaccaaaaaccccccccccccccccaaaaaaaaaaaaaaaacaaacaaaccccccccccccccaacaacaacaacaaccccccccaaaaaaaaccijjqqrtttxxxxxxyyvvvvvqqqqmmmmdddccc
abaaccaaaaaaaacaaaaaaccccccccccccccccaaaaaaaaaaaaaaaaaaaaaaaacccccccccccccccaaacaaaccccccccccaaccaaaaaaaaaciiiqqqttxxxxxxxyyvvvvvvvqqqmmmdddccc
abaaaccccaaccccaaaccacccccccccccccccccaaaaaaccccaacaaaaaaaaaaccaaaccccccccccaaaaaaaccccccccccaaaaaaaaaaaaaaiiiqqqtttxxxxxxyyyyyyvvvqqqmmmdddccc
SbaaaccccaacccccccccccccccccccccccccaaaaaaaaccccaacccaaaaaaccaaaaaaccccccccccaaaaaacccccccccccaaaaacaaacaaaaiiiqqqttxxxxEzzyyyyyvvvqqqmmmdddccc
abaaaccccccccccccccccccccccccccccccaaaaaaaaaaccccccccaaaaaaccaaaaaaccccccccccaaaaaaaaccccccccaaaaaacaaaccaaaiiiqqqtttxxxyyyyyyvvvvqqqmmmdddcccc
abaccccccaacccccccccccccccccccccccccaaaaaaaaaaaacccccaaaaaaacaaaaaacccccccccaaaaaaaaacccccccaaaaaaaacaaaaaaaiiiqqqtttxxyyyyyyvvvvqqqqnnmeddcccc
abccccccaaaaccccccccccccaaaccccccccccccaaaaaaaaaaacccaaacaaacaaaaacccccccccaaaaaaaaaacccccccaaaaaaaaccaaaaaaaiiiqqtttxxyyyyyywvrrrrnnnneeeccccc
abccccccaaaacccccaacccccaaaacccccccccccaaaccaaaaaacccacccccccaaaaacccccccccaaacaaacccccccccccccaacccccccaaaaaiiqqqttxxwywwyyywwrrrnnnneeeeccccc
abccccccaaaaccaacaaaccccaaaaccccccaacccaacccaaaaaccccccccccccccccccccccccccccccaaacccccccccccccaaccccccaaaaaaiiqqqttwwwwwwwwywwrrrnnneeeecccccc
abccccccccccccaaaaacccccaaaccccacaaacccccccccaaaaacccccccccccccccccccccccccccccaaacccccccccccccccccccccaaaaaaiiqqpsswwwwsswwwwwrrnnneeeeccccccc
abcccccccccccccaaaaaacccccccccaaaaacaacccccccaacaacccccaaccccccccccccccccccccccccccccccccccccccccccccccaccaahhhpppssssssssswwwwrrnnneeeaccccccc
abcccccccccccaaaaaaaacccccccccaaaaaaaacccccaaccccccaaacaaccccccccccccccccccccccccccccccccccccaaaccaccccccccchhhpppsssssssssswwrrrnnneeeaaaacccc
abcccccccccccaaaaacaacccccccccccaaaaaccaaaaaaccccccaaaaaaccccccccccccccccccccccccccccaaccaaccaaaaaacccccccccchhpppppsspppossrrrrrnnneeeaaaacccc
abccccccccccccacaaaccccccccccccaaaaacccaaaaaaaacccccaaaaaaaccaaaccccccccaaaacccccccccaaaaaacccaaaaacccccccccchhhpppppppppoosrrrroonffeaaaaacccc
abccccccccccccccaaaccccccccccccaacaaaccaaaaaaaaccccaaaaaaaaacaaaccccccccaaaacccccccccaaaaaccaaaaaaacccccccccchhhhpppppppoooooooooonfffaaaaccccc
abcccccccccccccccccccccccaaaccccccaaccccaaaaaaaccccaaaaaaaaaaaaaaaccccccaaaacccccccccaaaaaacaaaaaaaacccccaacchhhhhhhhgggggoooooooofffaaaaaacccc
abcccccccccccccccccccccccaaaaacccaacccccaaaaaccccccaaaaaacaaaaaaaaccccccaaacccccccccaaaaaaaaaaaaaaaaccccaaacccchhhhhgggggggooooooffffaaaaaacccc
abccaaacccccccccccccccccaaaaaaccaaaccccaaaaaacccccccccaaacccaaaaacccccccccccccccccccaaaaaaaaccaaacacccccaaacaaachhhggggggggggfffffffcaacccccccc
abcaaaaccccccccccaacccccaaaaaaccaaacaaaccccaaccccccccccccccaaaaacccccccccccccccccccccccaacccccaaaccccaaaaaaaaaacccccccccaagggffffffcccccccccccc
abcaaaaccccccccccaaccccccaaaaaaaaaaaaaaccccccccccccccccccccaaaaaaccccccccccccccccccccccaaccccccccccccaaaaaaaaaccccccccccaaacgfffffcccccccccccaa
abccaaacccccccaaaaaaaacccaaaaaaaaaaaaaaccccccccaaaaaccaaaaaaaaaaaaaacaacccccccccaaaccacccccccccccccccccaaaaacccccccccccaaaaccccccccccccccccccaa
abccccccccccccaaaaaaaacccccccccaaaaaaccccccccccaaaaaccaaaaaaaaaaaaaacaaaaaacccccaaaaaacccccccccccccccccaaaaaacccccccccccaacccccccccccccccacacaa
abccccccccccccccaaaacccccccccccaaaaaacccccccccaaaaaacccaaaaaaaaaaaaacaaaaaacccccaaaaaacccccccccccccccccaaaaaaaccccccccccaacccccccccccccccaaaaaa
abcccccccccccccaaaaaaccccccccccaaaaaaaccccccccaaaaaaccccccaaaaaacccaaaaaaaaccccaaaaaaaaccccccccccccccccaaacaaacccccccccccccccccccccccccccaaaaaa`

    type Coordinate struct {
        X int
        Y int
    }

    start := Coordinate{X: 0, Y: 0}
    end := Coordinate{X: 0, Y: 0}

    convertToIntArray := func(heightmap string) [][]int {
        lines := strings.Split(heightmap, "\n")
        rows := len(lines)
        cols := len(lines[0])
        result := make([][]int, rows)
        for i := range result {
            result[i] = make([]int, cols)
        }
        for i := 0; i < rows; i++ {
            for j := 0; j < cols; j++ {
                char := lines[i][j]
                if char == 'S' {
                    fmt.Println("found start", i, j)
                    start = Coordinate{X: j, Y: i}
                    char = 'a'
                }
                if char == 'E' {
                    fmt.Println("found end", i, j)
                    end = Coordinate{X: j, Y: i}
                    char = 'z'
                }
                result[i][j] = int(char) - int('a')
            }
        }
        return result
    }

    getNeighbors := func(heightMap [][]int, x int, y int) []Coordinate {
        neighbors := []Coordinate{}
        if x > 0 {
            neighbors = append(neighbors, Coordinate{X: x - 1, Y: y})
        }
        if x < len(heightMap[0])-1 {
            neighbors = append(neighbors, Coordinate{X: x + 1, Y: y})
        }
        if y > 0 {
            neighbors = append(neighbors, Coordinate{X: x, Y: y - 1})
        }
        if y < len(heightMap)-1 {
            neighbors = append(neighbors, Coordinate{X: x, Y: y + 1})
        }
        return neighbors
    }

    findShortestPathToHighest := func(heightMap [][]int, start Coordinate, end Coordinate) int {
        coordinateHash := func(c Coordinate) string {
            return strconv.Itoa(c.X) + "," + strconv.Itoa(c.Y)
        }
        g := New(coordinateHash, Directed())
        for y, line := range heightMap {
            for x := range line {
                err := g.AddVertex(Coordinate{X: x, Y: y})
                if err != nil {
                    panic(err)
                }
            }
        }

        for y, line := range heightMap {
            for x, height := range line {
                neighbors := getNeighbors(heightMap, x, y)
                for _, neighbor := range neighbors {
                    if heightMap[neighbor.Y][neighbor.X] <= height+1 {
                        err := g.AddEdge(
                            coordinateHash(Coordinate{X: x, Y: y}),
                            coordinateHash(neighbor),
                            EdgeWeight(
                                999+
                                    heightMap[y][x]-
                                    heightMap[neighbor.Y][neighbor.X],
                            ),
                        )
                        if err != nil {
                            panic(err)
                        }
                    }
                }
            }
        }
        shortest := 999999999
        for i := 0; i < 1000; i++ {
            path, err := ShortestPath(g, coordinateHash(start), coordinateHash(end))
            if err != nil {
                panic(err)
            }
            if len(path)-1 < shortest {
                println("new shortest:", len(path)-1)
                shortest = len(path) - 1
            }
        }
        return shortest
    }

    findShortestPathToHighest(convertToIntArray(heightmap), start, end)
}

geoah commented 1 year ago

package graph

import (
    "fmt"
    "testing"

    "github.com/stretchr/testify/require"
)

func TestDirectedShortedPath_Issue70(t *testing.T) {
    weightMap := [][]int{
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 10, 10, 10, 10, 11, 11, 11, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 10, 10, 10, 10, 10, 11, 11, 11, 11, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 10, 10, 15, 11, 11, 11, 11, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 15, 15, 15, 15, 15, 15, 11, 11, 11, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 10, 10, 10, 10, 15, 15, 15, 15, 15, 15, 15, 15, 11, 11, 11, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 10, 10, 10, 17, 15, 15, 15, 15, 20, 15, 15, 15, 11, 11, 11, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 9, 9, 9, 9, 9, 17, 17, 17, 15, 20, 20, 20, 20, 20, 15, 15, 15, 11, 11, 11, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 9, 9, 9, 17, 17, 17, 17, 17, 17, 17, 17, 17, 20, 20, 20, 20, 20, 15, 15, 15, 11, 11, 11, 12, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 9, 9, 9, 17, 17, 17, 17, 17, 17, 17, 17, 17, 20, 20, 20, 23, 20, 20, 20, 15, 16, 16, 11, 12, 12, 12, 12, 3, 3, 3, 3, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 9, 9, 9, 17, 17, 17, 17, 19, 20, 20, 20, 20, 20, 20, 23, 23, 24, 20, 21, 16, 16, 16, 16, 12, 12, 12, 12, 12, 3, 3, 3, 3, 2, 2, 2, 2},
        {0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 9, 9, 9, 17, 17, 17, 19, 19, 19, 20, 20, 20, 20, 20, 23, 23, 24, 21, 21, 21, 16, 16, 16, 16, 16, 12, 12, 12, 12, 3, 3, 3, 2, 2, 2, 2},
        {0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 8, 9, 9, 16, 16, 17, 19, 19, 19, 23, 23, 23, 23, 23, 23, 24, 24, 21, 21, 21, 21, 21, 16, 16, 16, 16, 12, 12, 12, 12, 3, 3, 3, 2, 2, 2},
        {0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 8, 8, 16, 16, 16, 19, 19, 23, 23, 23, 23, 23, 23, 23, 24, 24, 21, 21, 21, 21, 21, 21, 21, 16, 16, 16, 12, 12, 12, 3, 3, 3, 2, 2, 2},
        {0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 16, 16, 16, 19, 19, 19, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 21, 21, 21, 16, 16, 16, 12, 12, 12, 3, 3, 3, 2, 2, 2},
        {0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 8, 8, 8, 16, 16, 16, 19, 19, 23, 23, 23, 23, 25, 25, 25, 24, 24, 24, 24, 24, 21, 21, 21, 16, 16, 16, 12, 12, 12, 3, 3, 3, 2, 2, 2},
        {0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 8, 8, 8, 16, 16, 16, 19, 19, 19, 23, 23, 23, 24, 24, 24, 24, 24, 24, 21, 21, 21, 21, 16, 16, 16, 12, 12, 12, 3, 3, 3, 2, 2, 2, 2},
        {0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 16, 16, 16, 19, 19, 19, 23, 23, 24, 24, 24, 24, 24, 24, 21, 21, 21, 21, 16, 16, 16, 16, 13, 13, 12, 4, 3, 3, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 16, 16, 19, 19, 19, 23, 23, 24, 24, 24, 24, 24, 24, 22, 21, 17, 17, 17, 17, 13, 13, 13, 13, 4, 4, 4, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 8, 8, 16, 16, 16, 19, 19, 23, 23, 22, 24, 22, 22, 24, 24, 24, 22, 22, 17, 17, 17, 13, 13, 13, 13, 4, 4, 4, 4, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 8, 8, 16, 16, 16, 19, 19, 22, 22, 22, 22, 22, 22, 22, 22, 24, 22, 22, 17, 17, 17, 13, 13, 13, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 8, 8, 16, 16, 15, 18, 18, 22, 22, 22, 22, 18, 18, 22, 22, 22, 22, 22, 17, 17, 13, 13, 13, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 7, 7, 7, 15, 15, 15, 18, 18, 18, 18, 18, 18, 18, 18, 18, 22, 22, 22, 22, 17, 17, 13, 13, 13, 4, 4, 4, 0, 2, 2, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 15, 15, 15, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 22, 22, 17, 17, 17, 13, 13, 13, 4, 4, 4, 0, 0, 0, 0, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 15, 15, 15, 15, 15, 18, 18, 15, 15, 15, 14, 18, 18, 17, 17, 17, 17, 17, 13, 13, 13, 4, 4, 4, 0, 0, 0, 0, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 15, 15, 15, 15, 15, 15, 15, 15, 15, 14, 14, 18, 17, 17, 17, 17, 14, 14, 13, 5, 5, 4, 0, 0, 0, 0, 0, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7, 15, 15, 15, 15, 15, 15, 15, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 13, 5, 5, 5, 0, 0, 0, 0, 2, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 14, 14, 14, 14, 14, 14, 14, 14, 5, 5, 5, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 14, 14, 14, 14, 14, 14, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2},
        {0, 1, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2},
        {0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 6, 6, 6, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2},
        {0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 6, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0},
        {0, 1, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0},
        {0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0},
    }

    g := New(StringHash, Directed())

    addToGraph := func(sourceX, sourceY, targetX, targetY int) {
        // Check if the source and target are within the bounds of the map
        if sourceX < 0 || sourceX >= len(weightMap) || sourceY < 0 || sourceY >= len(weightMap[0]) {
            return
        }
        if targetX < 0 || targetX >= len(weightMap) || targetY < 0 || targetY >= len(weightMap[0]) {
            return
        }

        // Create the source and target ids
        source := fmt.Sprintf("%d,%d", sourceX, sourceY)
        target := fmt.Sprintf("%d,%d", targetX, targetY)

        // Get the weights of the source and target
        sourceWeight := weightMap[sourceX][sourceY]
        targetWeight := weightMap[targetX][targetY]

        // Check the difference between the two points
        if targetWeight > sourceWeight+1 {
            return
        }

        // Add the vertices to the graph
        g.AddVertex(source)
        g.AddVertex(target)

        // Add edge between the two points
        g.AddEdge(
            source,
            target,
            // Note(geoah): Commenting out the following line should result in
            // random results on every test execution
            EdgeWeight(1000+targetWeight-sourceWeight),
        )
    }

    // Add all the edges and vertices to the graph
    for x := range weightMap {
        for y := range weightMap[x] {
            addToGraph(x, y, x-1, y)
            addToGraph(x, y, x, y+1)
            addToGraph(x, y, x+1, y)
            addToGraph(x, y, x, y-1)
        }
    }

    // Find the shortest path from the start to the end
    path, err := ShortestPath(g, "20,0", "20,120")
    require.NoError(t, err)
    require.Len(t, path, 469) // 468 + source
}

@dominikbraun a cleaner version of the previous test with the same results.

dominikbraun commented 1 year ago

@geoah Thanks! I've updated #72 accordingly. I'm also currently trying to visualize that test graph and the dot command is running for half an hour now and still going ...

foxwhite25 commented 1 year ago

Hey @foxwhite25, I was looking into this mostly for fun and I can't find where in the code you posted you're adding the weight of the edge.

@geoah

I didn't add weights because I don't need the weights for this particular AOC day, as you can't go up two levels and there are no specific preference for any action.

As asphaltbuffet pointed out, you can also set the weight to 1 to workaround this issues, which only happens with unweighted graphs.

dominikbraun commented 1 year ago

Good news: The error doesn't exclusively happen in these super large graphs, but also in simpler ones. For instance, ShortestPath randomly fails for the example graph when the weights are removed:

This can be proved with the respective test case to TestDirectedShortestPath:

"graph as on img/dijkstra.svg without weights": {
    vertices: []string{"A", "B", "C", "D", "E", "F", "G"},
    edges: []Edge[string]{
        {Source: "A", Target: "C", Properties: EdgeProperties{}},
        {Source: "A", Target: "F", Properties: EdgeProperties{}},
        {Source: "C", Target: "D", Properties: EdgeProperties{}},
        {Source: "C", Target: "E", Properties: EdgeProperties{}},
        {Source: "C", Target: "F", Properties: EdgeProperties{}},
        {Source: "D", Target: "B", Properties: EdgeProperties{}},
        {Source: "E", Target: "B", Properties: EdgeProperties{}},
        {Source: "E", Target: "F", Properties: EdgeProperties{}},
        {Source: "F", Target: "G", Properties: EdgeProperties{}},
        {Source: "G", Target: "B", Properties: EdgeProperties{}},
    },
    sourceHash:           "A",
    targetHash:           "B",
    expectedShortestPath: []string{"A", "C", "E", "B"},
},

I've opened #73 to fix this.

dominikbraun commented 1 year ago

I've figured that the computation of the weight of an edge is flaky for unweighted graphs:

https://github.com/dominikbraun/graph/blob/994d3e899b1f8dbc6b8b9f45288222c2f8133626/paths.go#L120

If all weights are 0, a path A-B-D has a total weight of 0, and so does a path like A-B-C-D - so a random path is returned. Adding 1 to that weight seems to solve this problem, because then A-B-D has a total weight of 3 and A-B-C-D has a weight of 4.

I've provided a test as part of #73 to prove this, but it somehow still works without adding 1. For the example provided by @geoah however, it seems to work. Maybe this is due to the graph size? I'm not sure, but the off-by-one error sounds like a reasonable explanation to me.

dominikbraun commented 1 year ago

This issue should be fixed with graph v0.15.1, but we're lacking reliable test cases still. If you encounter incorrect shortest paths in large graphs again, feel free to re-open this issue or file a new one.

dominikbraun / graph