C#

using System.Diagnostics;
using Common;

namespace Day10;

static class Program
{
    static void Main()
    {
        var start = Stopwatch.GetTimestamp();

        var sampleInput = Input.ParseInput("sample.txt");
        var programInput = Input.ParseInput("input.txt");

        Console.WriteLine($"Part 1 sample: {Part1(sampleInput)}");
        Console.WriteLine($"Part 1 input: {Part1(programInput)}");

        Console.WriteLine($"Part 2 sample: {Part2(sampleInput)}");
        Console.WriteLine($"Part 2 input: {Part2(programInput)}");

        Console.WriteLine($"That took about {Stopwatch.GetElapsedTime(start)}");
    }

    static object Part1(Input i) => GetTrailheads(i)
        .Sum(th => CountTheNines(th, i, new HashSet<Point>(), false));

    static object Part2(Input i) => GetTrailheads(i)
        .Sum(th => CountTheNines(th, i, new HashSet<Point>(), true));

    static int CountTheNines(Point loc, Input i, ISet<Point> visited, bool allPaths)
    {
        if (!visited.Add(loc)) return 0;
        
        var result =
            (ElevationAt(loc, i) == 9) ? 1 :
            loc.GetCardinalMoves()
                .Where(move => move.IsInBounds(i.Bounds.Row, i.Bounds.Col))
                .Where(move => (ElevationAt(move, i) - ElevationAt(loc, i)) == 1)
                .Where(move => !visited.Contains(move))
                .Sum(move => CountTheNines(move, i, visited, allPaths));
        
        if(allPaths) visited.Remove(loc);
        
        return result;
    }

    static IEnumerable<Point> GetTrailheads(Input i) => Grid.EnumerateAllPoints(i.Bounds)
        .Where(loc => ElevationAt(loc, i) == 0);

    static int ElevationAt(Point p, Input i) => i.Map[p.Row][p.Col];
}

public class Input
{
    public required Point Bounds { get; init; }
    public required int[][] Map { get; init; }
    
    public static Input ParseInput(string file)
    {
        using var reader = new StreamReader(file);
        var map = reader.EnumerateLines()
            .Select(l => l.Select(c => (int)(c - '0')).ToArray())
            .ToArray();
        var bounds = new Point(map.Length, map.Max(l => l.Length));
        return new Input()
        {
            Map = map,
            Bounds = bounds,
        };
    }
}