/// <summary>
/// init
/// </summary>
/// <param name="g"></param>
/// <param name="source"></param>
protected void Init(EdgeWeightedDigraph g, int source)
{
this.source = source;
edgeTo = new DirectedEdge[g.V];
distTo = new double[g.V];
for (int i = 0; i < g.V; i++)
{
distTo[i] = double.NegativeInfinity;
}
distTo[source] = 0;
}
/// <summary>
/// constructor
/// </summary>
/// <param name="g"></param>
/// <param name="source"></param>
public SingleSourceShortPath(EdgeWeightedDigraph g, int source)
{
this.source = source;
edgeTo = new DirectedEdge[g.V];
distTo = new double[g.V];
for (int i = 0; i < g.V; i++)
{
//for simplicity， we don't init to positiveInfinity, because of overflow.
distTo[i] = double.PositiveInfinity / 2;
}
distTo[source] = 0;
}
public DagShortestPaths(EdgeWeightedDigraph g, int source) : base(g, source)
{
TopologicalSort topological = new TopologicalSort(g);
List <int> list = topological.GetTopoSort();
foreach (var i in list)
{
foreach (DirectedEdge e in g.Adj(i))
{
base.Relax(e);
}
}
}
/// <summary>
/// reverse graph
/// </summary>
/// <returns></returns>
public EdgeWeightedDigraph Reverse()
{
EdgeWeightedDigraph g = new EdgeWeightedDigraph(v);
g.e = e;
for (int i = 0; i < adj.Length; i++)
{
foreach (DirectedEdge edge in adj[i])
{
g.adj[edge.To].Add(new DirectedEdge(edge.To, edge.From, edge.Weight));
}
}
return(g);
}
/// <summary>
/// constructor
///
/// it runs at O(V^2*E)
/// </summary>
/// <param name="g"></param>
public AllPairShortestPathsUsingBellmanFordAlgorithm(EdgeWeightedDigraph g) : base(g)
{
for (int start = 0; start < g.V; start++)
{
BellmanFordAlgorithm bellmanFord = new BellmanFordAlgorithm(g, start);
for (int to = 0; to < g.V; to++)
{
if (bellmanFord.IsHavePathTo(to))
{
hasPathTo[start, to] = true;
weights[start, to] = bellmanFord.DistTo(to);
pathTo[start, to] = bellmanFord.PathTo(to).ToList();
}
}
}
}
/// <summary>
/// constructor
/// </summary>
/// <param name="g"></param>
public AllPairShortestPaths(EdgeWeightedDigraph g)
{
int n = g.V;
weights = new double[n, n];
hasPathTo = new bool[n, n];
pathTo = new List <DirectedEdge> [n, n];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
//for simplicity，no deal with PositiveInfinity+something
weights[i, j] = i == j?0:double.PositiveInfinity / 2;
}
}
}
private void dfs(EdgeWeightedDigraph g, int s)
{
nodes[s].Color = VertexColor.Gray;
nodes[s].Discovered = ++time;
foreach (DirectedEdge e in g.Adj(s))
{
int w = e.To;
if (nodes[w].Color == VertexColor.White)
{
nodes[w].Parent = nodes[s];
dfs(g, w);
}
}
nodes[s].Color = VertexColor.Black;
nodes[s].Finished = ++time;
postOrder.Enqueue(s);
}
public TopologicalSort(EdgeWeightedDigraph g)
{
postOrder = new Queue <int>();
nodes = new VertexNode[g.V];
for (int i = 0; i < nodes.Length; i++)
{
nodes[i] = new VertexNode(i);
nodes[i].Color = VertexColor.White;
}
for (int i = 0; i < g.V; i++)
{
if (nodes[i].Color == VertexColor.White)
{
dfs(g, i);
}
}
}
public DijkstraAlgorithm(EdgeWeightedDigraph digraph, int source) : base(digraph, source)
{
//pq maintain a set of vertex need to deal with.
IndexMinPQ <double> pq = new IndexMinPQ <double>(digraph.V);
pq.Insert(source, distTo[source]);
while (!pq.IsEmpty())
{
//when v pops up, the distance and path to v have been confirmed
int v = pq.DelMin();
foreach (DirectedEdge e in digraph.Adj(v))
{
Relax(pq, e);
}
}
}
/// <summary>
/// check Digraph is valid
/// </summary>
/// <param name="g"></param>
/// <returns></returns>
public bool IsValid(EdgeWeightedDigraph g)
{
if (g == null || g.V <= 0)
{
return(false);
}
foreach (DirectedEdge e in g.Edges())
{
if (e.Weight < 0)
{
return(false);
}
}
//TODO: add other check here
return(true);
}
/// <summary>
/// constructor
/// for any vertex v reachable from s, the path must at most v-1 edges.
/// we can get (vi-1,vi) in sequence because if p = (v0,v1,...,vk) is shortest path from s =v0 to vk, we relax the edges of p in order (v0,v1) (v1,v2) (vk-1,vk), then we can get the distTo
/// <param name="g"></param>
/// <param name="source"></param>
public BellmanFordAlgorithm(EdgeWeightedDigraph g, int source) : base(g, source)
{
List <DirectedEdge> edges = g.Edges();
for (int i = 0; i < g.V - 1; i++)
{
foreach (DirectedEdge e in edges)
{
base.Relax(e);
}
}
//assume this is negative cycle (v0,v1,...vk) vk=v0. then there must be at least one distTo[e.To] > distTo[e.From] + e.Weight
if (edges.Any(e => distTo[e.To] > distTo[e.From] + e.Weight))
{
IsNegativeCycle = true;
throw new Exception("there is negative cycle");
}
}
/// <summary>
/// constructor
/// </summary>
/// <param name="g"></param>
public MaxFlowFordFulkersonMethod(EdgeWeightedDigraph g)
{
if (!IsValid(g))
{
throw new ArgumentException();
}
int n = g.V;
flow = new double[n, n];
/*
* while there exists a path from s to t in the residual neteork Gf
* C(p) = min{Cf(u,v): (u,v) is in p}
* for each edge (u,v) in p
* if(u,v)∈E
* （u,v).f = (u,v).f + C(p)
* else
* (v,u).f = (v,u).f - C(p)
*/
}
public static double Cp(List <Job> jobs)
{
//the job id start from 0 to n-1
int n = jobs.Count;
for (int i = 0; i < n; i++)
{
jobs[i].JobID = i;
}
//source and sink vertex
int source = 2 * n;
int sink = 2 * n + 1;
//build graph
EdgeWeightedDigraph g = new EdgeWeightedDigraph(2 * n + 2);
for (int i = 0; i < n; i++)
{
//add edge from source to the start of job
g.AddEdge(new DirectedEdge(source, i, 0));
//add edge from the end of job to sink
g.AddEdge(new DirectedEdge(i + n, sink, 0));
//add edge from the start of job to the end of job and weight duration
g.AddEdge(new DirectedEdge(i, i + n, jobs[i].Duration));
foreach (var job in jobs[i].Constaints)
{
g.AddEdge(new DirectedEdge(job.JobID + n, i, 0));
}
}
//compute longest paths from source to sink
DagLogestPaths paths = new DagLogestPaths(g, source);
return(paths.DistTo(sink));
}