static int BranchAndBoundValue(BnBVertex vertex)
{
if (vertex.Vertices.Count == graph.Size)
{
return(graph.CalculateRoute(vertex.Vertices));
}
else
{
return(int.MaxValue);
}
}
static int BranchAndBoundLowerBound(BnBVertex vertex)
{
if (vertex.LowerBound != int.MaxValue)
{
return(vertex.LowerBound);
}
else
{
int lowerBound = 0;
int i, j, iPow2, jPow2, logicAnd;
// obliczanie wartości aktualnie zapisanej trasy
for (int it = 0; it < vertex.Vertices.Count - 1; it++)
{
i = vertex.Vertices[it];
j = vertex.Vertices[it + 1];
lowerBound += graph.Matrix[i, j];
}
// wyznaczenie minimów wychodzących z wierzchołków, z których jeszcze można wyjść
for (i = 0; i < graph.Size; i++)
{
int min = int.MaxValue;
iPow2 = 1 << i;
logicAnd = iPow2 & vertex.BitMask;
if (logicAnd == 0 || i == vertex.Vertices.Last())
{
for (j = 0; j < graph.Size; j++)
{
jPow2 = 1 << j;
logicAnd = jPow2 & vertex.BitMask;
if (logicAnd == 0)
{
int newMin = graph.Matrix[i, j];
if (newMin < min)
{
min = newMin;
}
}
}
lowerBound += min;
}
}
vertex.LowerBound = lowerBound;
return(lowerBound);
}
}
public static IList <int> BranchAndBoundBestFirst(MatrixGraph givenGraph)
{
graph = givenGraph;
var queue = new PriorityQueue <BnBVertex>();
queue.Enqueue(new BnBVertex(0, 0));
int higherBound = int.MaxValue;
List <int> bestPermutation = null;
int iPow2, logicAnd;
while (queue.Count != 0)
{
var vertexLowestBound = queue.Dequeue();
if (BranchAndBoundLowerBound(vertexLowestBound) < higherBound)
{
for (int i = 1; i < graph.Size; i++)
{
iPow2 = 1 << i;
logicAnd = iPow2 & vertexLowestBound.BitMask;
if (logicAnd == 0)
{
var childVertex = new BnBVertex(i, vertexLowestBound.BitMask + iPow2, vertexLowestBound);
int value = BranchAndBoundValue(childVertex);
if (value < higherBound)
{
higherBound = value;
bestPermutation = childVertex.Vertices;
}
BranchAndBoundLowerBound(childVertex);
if (childVertex.LowerBound < higherBound)
{
queue.Enqueue(childVertex);
}
}
}
}
}
return(bestPermutation);
}
