/// <summary>
/// Do DFS to find all unique edges.
/// </summary>
private void dfs(WeightedGraphVertex <T, TW> currentVertex, System.Collections.Generic.HashSet <T> visitedVertices, Dictionary <T, System.Collections.Generic.HashSet <T> > visitedEdges,
List <MSTEdge <T, TW> > result)
{
if (!visitedVertices.Contains(currentVertex.Value))
{
visitedVertices.Add(currentVertex.Value);
foreach (var edge in currentVertex.Edges)
{
if (!visitedEdges.ContainsKey(currentVertex.Value) ||
!visitedEdges[currentVertex.Value].Contains(edge.Key.Value))
{
result.Add(new MSTEdge <T, TW>(currentVertex.Value, edge.Key.Value, edge.Value));
//update visited edge
if (!visitedEdges.ContainsKey(currentVertex.Value))
{
visitedEdges.Add(currentVertex.Value, new HashSet <T>());
}
visitedEdges[currentVertex.Value].Add(edge.Key.Value);
//update visited back edge
if (!visitedEdges.ContainsKey(edge.Key.Value))
{
visitedEdges.Add(edge.Key.Value, new HashSet <T>());
}
visitedEdges[edge.Key.Value].Add(currentVertex.Value);
}
dfs(edge.Key, visitedVertices, visitedEdges, result);
}
}
}
/// <summary>
/// Do DFS to pick smallest weight neighbour edges
/// of current spanning tree one by one
/// </summary>
/// <param name="graph"></param>
/// <param name="currentVertex"></param>
/// <param name="spanTreeVertices"></param>
/// <param name="spanTreeNeighbours"> Use Fibornacci Min Heap to pick smallest edge neighbour </param>
/// <param name="spanTreeEdges">result MST edges</param>
private void DFS(WeightedGraph <T, W> graph,
WeightedGraphVertex <T, W> currentVertex,
BMinHeap <MSTEdge <T, W> > spanTreeNeighbours,
HashSet <T> spanTreeVertices,
List <MSTEdge <T, W> > spanTreeEdges)
{
//add all edges to Fibornacci Heap
//So that we can pick the min edge in next step
foreach (var edge in currentVertex.Edges)
{
spanTreeNeighbours.Insert(new MSTEdge <T, W>(
currentVertex.Value,
edge.Key.Value, edge.Value));
}
//pick min edge
var minNeighbourEdge = spanTreeNeighbours.ExtractMin();
//skip edges already in MST
while (spanTreeVertices.Contains(minNeighbourEdge.Source) &&
spanTreeVertices.Contains(minNeighbourEdge.Destination))
{
minNeighbourEdge = spanTreeNeighbours.ExtractMin();
//if no more neighbours to explore
//time to end exploring
if (spanTreeNeighbours.Count == 0)
{
return;
}
}
//keep track of visited vertices
//do not duplicate vertex
if (!spanTreeVertices.Contains(minNeighbourEdge.Source))
{
spanTreeVertices.Add(minNeighbourEdge.Source);
}
//Destination vertex will never be a duplicate
//since this is an unexplored Vertex
spanTreeVertices.Add(minNeighbourEdge.Destination);
//add edge to result
spanTreeEdges.Add(minNeighbourEdge);
//now explore the destination vertex
DFS(graph, graph.Vertices[minNeighbourEdge.Destination],
spanTreeNeighbours, spanTreeVertices, spanTreeEdges);
}
public void Base()
{
var sut = new CriticalPath();
var vertex1 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 1,
Weight = 5
},
new WeightedGraphNodeEdge
{
To = 3,
Weight = 9
},
new WeightedGraphNodeEdge
{
To = 4,
Weight = 14
}
}
};
var vertex2 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 2,
Weight = 7
}
}
};
var vertex3 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 4,
Weight = 4
}
}
};
var vertex4 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 4,
Weight = 11
}
}
};
var vertex5 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>()
};
var graph = new [] { vertex1, vertex2, vertex3, vertex4, vertex5 };
Assert.Equal(20, sut.GetCriticalPath(graph));
}
public void BiggerGraph()
{
var sut = new CriticalPath();
var vertex1 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 1,
Weight = 17
}
}
};
var vertex2 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 2,
Weight = 13
}
}
};
var vertex3 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 3,
Weight = 9
}
}
};
var vertex4 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 4,
Weight = 11
},
new WeightedGraphNodeEdge
{
To = 8,
Weight = 10
}
}
};
var vertex5 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
}
};
var vertex6 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 6,
Weight = 11
},
new WeightedGraphNodeEdge
{
To = 9,
Weight = 15
}
}
};
var vertex7 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 7,
Weight = 18
}
}
};
var vertex8 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 3,
Weight = 16
},
new WeightedGraphNodeEdge
{
To = 8,
Weight = 13
},
new WeightedGraphNodeEdge
{
To = 11,
Weight = 19
}
}
};
var vertex9 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
}
};
var vertex10 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 10,
Weight = 14
},
}
};
var vertex11 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge
{
To = 11,
Weight = 17
},
}
};
var vertex12 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
}
};
var graph = new []
{
vertex1, vertex2, vertex3, vertex4, vertex5,
vertex6, vertex7, vertex8, vertex9,
vertex10, vertex11, vertex12
};
Assert.Equal(56, sut.GetCriticalPath(graph));
}
public void CanCalculateMinDistancesForGraphWithCycles()
{
var sut = new FloydWarshall();
var graph = new WeightedGraphVertex[4];
var node1 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge {
To = 2, Weight = 3
},
new WeightedGraphNodeEdge {
To = 3, Weight = 0
},
}
};
var node2 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge {
To = 0, Weight = -2
},
new WeightedGraphNodeEdge {
To = 3, Weight = 1
},
}
};
var node3 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge {
To = 3, Weight = 5
},
}
};
var node4 = new WeightedGraphVertex
{
Edges = new System.Collections.Generic.List <WeightedGraphNodeEdge>
{
new WeightedGraphNodeEdge {
To = 1, Weight = 4
},
}
};
graph[0] = node1;
graph[1] = node2;
graph[2] = node3;
graph[3] = node4;
var(distances, path) = sut.MinDistances(graph);
Assert.Collection(distances[0],
arg => Assert.Equal(0, arg),
arg => Assert.Equal(4, arg),
arg => Assert.Equal(3, arg),
arg => Assert.Equal(0, arg));
Assert.Collection(distances[1],
arg => Assert.Equal(-2, arg),
arg => Assert.Equal(0, arg),
arg => Assert.Equal(1, arg),
arg => Assert.Equal(-2, arg));
Assert.Collection(distances[2],
arg => Assert.Equal(7, arg),
arg => Assert.Equal(9, arg),
arg => Assert.Equal(0, arg),
arg => Assert.Equal(5, arg));
Assert.Collection(distances[3],
arg => Assert.Equal(2, arg),
arg => Assert.Equal(4, arg),
arg => Assert.Equal(5, arg),
arg => Assert.Equal(0, arg));
}
