// Follows a route
// Returns a new matrix with the same values, changed so that
// the route from node i to node j has been followed. Makes it
// so that nothing from i or to j will be followed again. Also
// makes it so that the route from j to the beginning node can't
// be followed. Returns a reduced matrix.
public Matrix FollowRoute(int i, int j)
{
double[,] costs = Costs.Clone() as double[, ];
for (int k = 0; k < Costs.GetLength(0); k++)
{
costs[i, k] = Double.PositiveInfinity;
costs[k, j] = Double.PositiveInfinity;
}
// Make it so that it can't go to the start city (unless this is the last city
if (CitiesVisited < Cities.Length - 2)
{
costs[j, 0] = Double.PositiveInfinity;
}
return(new Matrix(Cities, costs, LowerBound, CitiesVisited + 1).Reduce());
}
// Reduces a matrix.
// Creates a new matrix, with the same values as the current
// instance, with the change that each row and each column
// is reduced so that there is at least 1 zero in each.
// LowerBound is increased by the amount subtracted from
// each row and column.
public Matrix Reduce()
{
double lowerBound = LowerBound;
double[,] costs = Costs.Clone() as double[, ];
for (int i = 0; i < costs.GetLength(0); i++)
{
int lowestJInd = 0;
double lowestJ = costs[i, 0];
// Find the lowest
for (int j = 1; j < costs.GetLength(0); j++)
{
if (costs[i, j] < lowestJ)
{
lowestJInd = j;
lowestJ = costs[i, j];
}
}
if (!Double.IsInfinity(lowestJ))
{
// Increase lower bound and decrease each element in row
lowerBound += lowestJ;
for (int j = 0; j < costs.GetLength(0); j++)
{
costs[i, j] -= lowestJ;
}
}
}
for (int j = 0; j < costs.GetLength(0); j++)
{
int lowestIInd = 0;
double lowestI = costs[0, j];
// Find lowest
for (int i = 1; i < costs.GetLength(0); i++)
{
if (costs[i, j] < lowestI)
{
lowestIInd = i;
lowestI = costs[i, j];
}
}
if (!Double.IsInfinity(lowestI))
{
// Increase lower bound and decrease each element in row
lowerBound += lowestI;
for (int i = 0; i < costs.GetLength(0); i++)
{
costs[i, j] -= lowestI;
}
}
}
// Return a new instance (don't change current in any way)
return(new Matrix(Cities, costs, lowerBound, CitiesVisited));
}
