/// <summary>
/// ベルマン-フォード法
/// 最短経路を解くアルゴリズム
/// 負の辺が存在しても、正しい解を導出できる。
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="self"></param>
/// <param name="start"></param>
/// <param name="end"></param>
/// <returns></returns>
public static SelfStack <T> BellmanFordSearch <T>(this SelfGraph <T, int> self, T start, T end)
{
if (self.IsDirected)
{
throw new Exception("無方向グラフでしか対応してまてん");
}
var evalDic = InitializeEvalDictionary(self, start, end);
bool isUpdated = true;
while (isUpdated)
{
var queue = new Queue <T>();
queue.Enqueue(start);
while (queue.Count > 0)
{
var pos = queue.Dequeue();
evalDic[pos].Checked = true;
foreach (var(toVertex, eValue) in self.Data[pos])
{
if (evalDic[toVertex].Checked)
{
continue;
}
queue.Enqueue(toVertex);
isUpdated = UpdateEval(evalDic, pos, toVertex, eValue) || UpdateEval(evalDic, toVertex, pos, eValue);
}
}
}
return(CreateRoot(self, evalDic, start, end));
}
private static Dictionary <T, EvalVertex> InitializeEvalDictionary <T>(SelfGraph <T, int> graph, T start, T end)
{
var evalDic = new Dictionary <T, EvalVertex>();
foreach (var vertex in graph.Data.Keys)
{
if (vertex.Equals(start))
{
evalDic.Add(vertex, new EvalVertex(0));
continue;
}
evalDic.Add(vertex, new EvalVertex(int.MaxValue));
}
return(evalDic);
}
private static SelfStack <T> CreateRoot <T>(SelfGraph <T, int> graph, Dictionary <T, EvalVertex> evalDic, T start, T end)
{
var data = graph.Data;
var stack = new SelfStack <T>();
stack.Push(end);
var cur = end;
while (!cur.Equals(start))
{
foreach (var(vertex, edge) in data[cur])
{
if ((evalDic[cur].EvalValue - edge) == evalDic[vertex].EvalValue)
{
cur = vertex;
stack.Push(vertex);
break;
}
}
}
return(stack);
}
/// <summary>
/// ダイクストラ法
/// 最短経路を解くアルゴリズム
/// ベルマンフォード法より早いが、負の辺が存在する場合は正しい解を導出できない。
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="self"></param>
/// <param name="start"></param>
/// <returns></returns>
public static SelfStack <T> DijkstraSearch <T>(this SelfGraph <T, int> self, T start, T end)
{
if (self.IsDirected)
{
throw new Exception("無方向グラフでしかできまてん");
}
var evalDic = InitializeEvalDictionary(self, start, end);
var queue = new Queue <T>();
queue.Enqueue(start);
while (queue.Count > 0)
{
var pos = queue.Dequeue();
evalDic[pos].Checked = true;
foreach (var(vertex, value) in self.Data[pos])
{
if (evalDic[vertex].Checked)
{
continue;
}
UpdateEval(evalDic, pos, vertex, value);
}
var minEval = evalDic.Where(e => !e.Value.Checked).OrderBy(e => e.Value.EvalValue).FirstOrDefault();
if (minEval.Value != null)
{
if (minEval.Key.Equals(end))
{
break;
}
queue.Enqueue(minEval.Key);
}
}
return(CreateRoot(self, evalDic, start, end));
}