public UndirectedGraph <T> Add(UndirectedEdge <T> edge)
{
_edges.Add(edge);
foreach (var vertex in edge.Vertexs())
{
_vertexs.Add(vertex);
}
return(this);
}
/// <summary>
/// 假设G=（V，E）为一无向连通网，其中，V为网中顶点的集合，E为网中边的集合。
/// 设置两个新的集合U和T，其中，U为G的最小生成树的顶点的集合，T为G的最小生成树的边的集合。
/// 普里姆算法的思想是：令集合U的初值为U={u1}（假设构造最小生成树时从顶点u1开始），集合T的初值为T={}。
/// 从所有的顶点u∈U和顶点v∈V-U的带权边中选出具有最小权值的边（u,v），
/// 将顶点v加入集合U中，将边（u,v）加入集合T中。如此不断地重复直到U=V时，最小生成树构造完毕。
/// 此时，集合U中存放着最小生成树的所有顶点，集合T中存放着最小生成树的所有边。
/// </summary>
/// <returns></returns>
public List <UndirectedEdge <T> > PrimMinCostSpanTree(T begin_vertex)
{
if (!_vertexs.Contains(begin_vertex))
{
throw new InvalidOperationException("begin_vertex is not in Graph");
}
var ret = new List <UndirectedEdge <T> >();
var selected_set = new HashSet <T>();
var unselected_set = new HashSet <T>();
selected_set.Add(begin_vertex);
foreach (var vertex in _vertexs)
{
if (!vertex.Equals(begin_vertex))
{
unselected_set.Add(vertex);
}
}
while (unselected_set.Count > 0)
{
T vertex_unsel = default(T);
UndirectedEdge <T> edge_sel = null;
var min_cost = int.MaxValue;
foreach (var sel_item in selected_set)
{
foreach (var unsel_item in unselected_set)
{
foreach (var edge in _edges)
{
if (edge.ComposedWith(sel_item, unsel_item) && edge.Weight < min_cost)
{
vertex_unsel = unsel_item;
min_cost = edge.Weight;
edge_sel = edge;
}
}
}
}
if (vertex_unsel != null && vertex_unsel.Equals(default(T)))
{
continue;
}
selected_set.Add(vertex_unsel);
unselected_set.Remove(vertex_unsel);
ret.Add(edge_sel);
}
return(ret);
}
/// <summary>
/// 图是否存在环
/// 1.求出图中所有顶点的度，
/// 2.删除图中所有度小于等于1的顶点以及与该顶点相关的边，把与这些边相关的顶点的度减一
/// 3.如果还有度小于等于1的顶点重复步骤2
/// 4.最后如果还存在未被删除的顶点，则表示有环；否则没有环
/// </summary>
/// <returns></returns>
public bool HasLoop()
{
var dic = _vertexs.ToDictionary(v => v, v => 0); // vertex-degree
var edges = new HashSet <UndirectedEdge <T> >(_edges);
foreach (var edge in edges) // init degree of vertexs
{
foreach (var v in edge.Vertexs())
{
dic[v]++;
}
}
// delete all vertexs satified degree==0
var filtered_dic = dic.Where(item => item.Value > 0).ToDictionary(item => item.Key, item => item.Value);
var to_do_item = GetOneDegreeItem(filtered_dic); // get one vertex which degree == 1
while (!to_do_item.Equals(default(KeyValuePair <T, int>)))
{
UndirectedEdge <T> to_del_edge = null;
foreach (var edge in edges)
{
if (edge.Contain(to_do_item.Key))
{
to_del_edge = edge;
filtered_dic[edge.GetAdjoinVertex(to_do_item.Key)]--;
break;
}
}
filtered_dic.Remove(to_do_item.Key);
edges.Remove(to_del_edge);
to_do_item = GetOneDegreeItem(filtered_dic);
}
return(!(filtered_dic.Count == 0 ||
filtered_dic.All(item => item.Value == 0)));
}