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Created March 19, 2021 04:51
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A* pathfinding implementation.
using System;
using System.Linq;
using System.Collections.Generic;
public static class Pathfinding
/// <summary>
/// A* implementation. Finds a path from start to goal.
/// </summary>
/// <param name="start">Where to begin.</param>
/// <param name="goal">Where we want to end up.</param>
/// <param name="getCostEstimate">Heuristic function that estimates the cost to reach the goal from node n.</param>
/// <param name="getEdgeWeight">Gets the weight of the edge from current to neighbor.</param>
/// <param name="getNeighbors">Gets nodes adjacent to the given one.</param>
/// <returns>Shortest path between the two nodes, or null if no path exists.</returns>
public static List<T> FindShortestPath<T>(
T start,
T goal,
Func<T, int> getCostEstimate,
Func<T, T, int> getEdgeWeight,
Func<T, IEnumerable<T>> getNeighbors) where T : IEquatable<T>
// Adapted from*_search_algorithm#Pseudocode.
// I translated the pseudocode as directly as possible and kept variable names the same.
// Except for h and d, which are terrible names. I renamed them to getCostEstimate and getEdgeWeight respectively.
// The set of discovered nodes that may need to be (re-)expanded.
// Initially, only the start node is known.
// This is usually implemented as a min-heap or priority queue rather than a hash-set.
var openSet = new HashSet<T> {start};
// For node n, cameFrom[n] is the node immediately preceding it on the cheapest path from start to n currently known.
var cameFrom = new Dictionary<T, T>();
// For node n, gScore[n] is the cost of the cheapest path from start to n currently known.
var gScore = new Dictionary<T, int>();
gScore[start] = 0;
// For node n, fScore[n] = gScore[n] + getCostEstimate(n).
// fScore[n] represents our current best guess as to how short a path from start to finish can be if it goes through n.
var fScore = new Dictionary<T, int>();
fScore[start] = getCostEstimate(start);
while (openSet.Count > 0)
// Find the node in openSet with the lowest fScore value.
// This operation can occur in O(1) time if openSet is a min-heap or a priority queue.
var current = openSet
.OrderBy(position => fScore.TryGetValue(position, out var fValue) ? fValue : int.MaxValue)
if (current.Equals(goal))
return ReconstructPath(cameFrom, current);
var neighbors = getNeighbors(current);
foreach (var neighbor in neighbors)
// tentativeGScore is the distance from start to the neighbor through current.
var tentativeGScore = gScore[current]+ getEdgeWeight(current, neighbor);
var neighborGScore = gScore.TryGetValue(neighbor, out var gValue) ? gValue : int.MaxValue;
if (tentativeGScore < neighborGScore)
// This path to neighbor is better than any previous one. Record it!
cameFrom[neighbor] = current;
gScore[neighbor] = tentativeGScore;
fScore[neighbor] = gScore[neighbor] + getCostEstimate(neighbor);
if (!openSet.Contains(neighbor))
// Open set is empty but goal was never reached.
return null;
static List<T> ReconstructPath<T>(Dictionary<T, T> cameFrom, T current)
var totalPath = new List<T> {current};
while (cameFrom.ContainsKey(current))
current = cameFrom[current];
totalPath.Insert(0, current);
return totalPath;
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