advent-of-code/2021/15/Dijkstra.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Day15
{
    public class Dijkstra
    {
        public object PartOne(string input) => Solve(GetRiskLevelMap(input));
        public object PartTwo(string input) => Solve(ScaleUp(GetRiskLevelMap(input)));

        int Solve(Dictionary<Point, int> riskMap)
        {
            // Disjktra algorithm

            var topLeft = new Point(0, 0);
            var bottomRight = new Point(riskMap.Keys.MaxBy(p => p.x).x, riskMap.Keys.MaxBy(p => p.y).y);

            // Visit points in order of cumulted risk
            // ⭐ .Net 6 finally has a PriorityQueue collection :)
            var q = new PriorityQueue<Point, int>();
            var totalRiskMap = new Dictionary<Point, int>();

            totalRiskMap[topLeft] = 0;
            q.Enqueue(topLeft, 0);

            // It would be enough to go until we find the bottom right corner, but computing all 
            // risk levels is not much more work 
            while (q.Count > 0)
            {
                var p = q.Dequeue();

                foreach (var n in Neighbours(p))
                {
                    if (riskMap.ContainsKey(n) && !totalRiskMap.ContainsKey(n))
                    {
                        var totalRisk = totalRiskMap[p] + riskMap[n];
                        totalRiskMap[n] = totalRisk;
                        if (n == bottomRight)
                        {
                            break;
                        }
                        var h = 0; //bottomRight.y - n.y + bottomRight.x - n.x;
                        q.Enqueue(n, totalRisk + h);
                    }
                }
            }

            // return bottom right corner's total risk:
            return totalRiskMap[bottomRight];
        }

        // Create an 5x scaled up map, as described in part 2
        Dictionary<Point, int> ScaleUp(Dictionary<Point, int> map)
        {
            var (ccol, crow) = (map.Keys.MaxBy(p => p.x).x + 1, map.Keys.MaxBy(p => p.y).y + 1);

            var res = new Dictionary<Point, int>(
                from y in Enumerable.Range(0, crow * 5)
                from x in Enumerable.Range(0, ccol * 5)

                    // x, y and risk level in the original map:
            let tileY = y % crow
                let tileX = x % ccol
                let tileRiskLevel = map[new Point(tileX, tileY)]

            // risk level is increased by tile distance from origin:
            let tileDistance = (y / crow) + (x / ccol)

            // risk level wraps around from 9 to 1:
            let riskLevel = (tileRiskLevel + tileDistance - 1) % 9 + 1
                select new KeyValuePair<Point, int>(new Point(x, y), riskLevel)
            );

            return res;
        }

        // store the points in a dictionary so that we can iterate over them and 
        // to easily deal with points outside the area
        Dictionary<Point, int> GetRiskLevelMap(string input)
        {
            var map = input.Split("\n");
            return new Dictionary<Point, int>(
                from y in Enumerable.Range(0, map[0].Length)
                from x in Enumerable.Range(0, map.Length)
                select new KeyValuePair<Point, int>(new Point(x, y), map[y][x] - '0')
            );
        }

        IEnumerable<Point> Neighbours(Point point) =>
            new[] {
           point with {y = point.y + 1},
           point with {y = point.y - 1},
           point with {x = point.x + 1},
           point with {x = point.x - 1},
            };
    }
}
record Point(int x, int y);