/// <summary>
/// <para><paramref name="from"/> からの最短経路長をベルマン・フォード法で求める。負の長さにも使える</para>
/// <para>計算量: O(|V|・|E|)</para>
/// </summary>
public static T[] BellmanFord <T, TOp, TNode, TEdge>(this IWGraph <T, TOp, TNode, TEdge> graph, int from)
where T : struct
where TOp : struct, INumOperator <T>
where TNode : IGraphNode <TEdge>
where TEdge : IWGraphEdge <T>
{
TOp op = default;
var graphArr = graph.AsArray();
var INF = op.Divide(op.MaxValue, op.Increment(op.MultiplyIdentity));
var res = new T[graphArr.Length];
Array.Fill(res, INF);
res[from] = default;
for (int i = 1; i <= graphArr.Length; i++)
{
foreach (var node in graphArr)
{
foreach (var e in node.Children)
{
var to = e.To;
var x = op.Add(res[node.Index], e.Value);
if (op.GreaterThan(res[to], x))
{
res[to] = x;
if (i == graphArr.Length)
{
throw new InvalidOperationException("負の閉路");
}
}
}
}
}
return(res);
}
/// <summary>
/// <para><paramref name="from"/> からの最短経路長を01-BSFで求める。</para>
/// <para>計算量: O(|E| + |V|)</para>
/// </summary>
public static T[] ShortestPath01BFS <T, TOp, TNode, TEdge>(this IWGraph <T, TOp, TNode, TEdge> graph, int from)
where T : struct
where TOp : struct, INumOperator <T>
where TNode : IGraphNode <TEdge>
where TEdge : IWGraphEdge <T>
{
TOp op = default;
var graphArr = graph.AsArray();
var INF = op.MaxValue;
var res = new T[graphArr.Length];
System.Array.Fill(res, INF);
res[from] = default;
var used = new bool[graphArr.Length];
int count = 0;
var remains = new Deque <int>(graphArr.Length)
{
from
};
while (remains.Count > 0)
{
var ix = remains.PopFirst();
if (used[ix])
{
continue;
}
used[ix] = true;
if (++count >= graphArr.Length)
{
break;
}
var len = res[ix];
foreach (var e in graphArr[ix].Children)
{
var to = e.To;
var nextLength = len;
if (EqualityComparer <T> .Default.Equals(e.Value, default))
{
if (op.GreaterThan(res[to], nextLength))
{
res[to] = nextLength;
remains.AddFirst(to);
}
}
else
{
nextLength = op.Increment(nextLength);
if (op.GreaterThan(res[to], nextLength))
{
res[to] = nextLength;
remains.AddLast(to);
}
}
}
}
return(res);
}
/// <summary>
/// <para><paramref name="from"/> からの最短経路長をダイクストラ法で求める。</para>
/// <para>計算量: O( (|E| + |V|) log |V| )</para>
/// </summary>
public static T[] Dijkstra <T, TOp, TNode, TEdge>(this IWGraph <T, TOp, TNode, TEdge> graph, int from)
where T : struct
where TOp : struct, INumOperator <T>
where TNode : IGraphNode <TEdge>
where TEdge : IWGraphEdge <T>
{
TOp op = default;
var graphArr = graph.AsArray();
var INF = op.MaxValue;
var res = new T[graphArr.Length];
System.Array.Fill(res, INF);
res[from] = default;
var used = new bool[graphArr.Length];
int count = 0;
var remains = new PriorityQueueDijkstra <T, TOp>(graphArr.Length);
remains.Enqueue(default, from);
/// <summary>
/// <para>各頂点間の最短経路長をワーシャルフロイド法で求める</para>
/// <para>計算量: O(|V|^3)</para>
/// </summary>
public static T[][] WarshallFloyd <T, TOp, TNode, TEdge>(this IWGraph <T, TOp, TNode, TEdge> graph)
where T : struct
where TOp : struct, INumOperator <T>
where TNode : IGraphNode <TEdge>
where TEdge : IWGraphEdge <T>
{
TOp op = default;
var graphArr = graph.AsArray();
var INF = op.Divide(op.MaxValue, op.Increment(op.MultiplyIdentity));
var res = new T[graphArr.Length][];
for (var i = 0; i < graphArr.Length; i++)
{
res[i] = new T[graphArr.Length];
System.Array.Fill(res[i], INF);
res[i][i] = default;
foreach (var e in graphArr[i].Children)
{
res[i][e.To] = e.Value;
}
}
for (var k = 0; k < graphArr.Length; k++)
{
for (var i = 0; i < graphArr.Length; i++)
{
for (var j = 0; j < graphArr.Length; j++)
{
var x = op.Add(res[i][k], res[k][j]);
if (op.GreaterThan(res[i][j], x))
{
res[i][j] = x;
}
}
}
}
return(res);
}