private string backtrackTSP(int key, PointsList pointsList, Dictionary <PointsList, double[]> C)
{
if (pointsList.Count == 0)
{
return("0");
}
else
{
var mins = new List <double>();
Point l = new Point(Double.MinValue, Double.MinValue, Int32.MinValue);
foreach (var k in pointsList.Points)
{
mins.Add(C[pointsList][k.Id] + DistanceMatrix[k.Id, key]);
}
var min_cost = mins.Min();
string res = "";
foreach (var k in pointsList.Points)
{
if (min_cost == C[pointsList][k.Id] + DistanceMatrix[k.Id, key])
{
l = k;
var cropPoints = PointsList.Copy(pointsList);
cropPoints.Points.Remove(k);
res = backtrackTSP(k.Id, cropPoints, C);
break;
}
}
return(l.Id + "-" + res);
}
}
private string optimalPathTSP(double optimalCost, PointsList pointsListWOFirst, Dictionary <PointsList, double[]> C)
{
string optimalPath = "0-";
string res = "";
Point l = new Point(Double.MinValue, Double.MinValue, Int32.MinValue);
foreach (var k in pointsListWOFirst.Points)
{
if (optimalCost == (C[pointsListWOFirst][k.Id] + DistanceMatrix[k.Id, 0]))
{
l = k;
var cropPoints = PointsList.Copy(pointsListWOFirst);
cropPoints.Points.Remove(k);
res = backtrackTSP(k.Id, cropPoints, C);
break;
}
}
optimalPath += l.Id + "-" + res;
return(optimalPath);
}
//https://en.wikipedia.org/wiki/Held%E2%80%93Karp_algorithm
public double TSP(bool withPrint)
{
//tworze wszystkie mozliwe kombinacje punktow
var combosTmp = Helper.Combinations(Points);
//... i pakuje do klasy PointsList
List <PointsList> combos = new List <PointsList>();
foreach (var combo in combosTmp)
{
combos.Add(new PointsList(combo));
}
//sortuje po dlugosci kombinacji i indexach
combos = combos.OrderBy(p => p).ToList();
//tworze dictionary z pointLista i tablica odleglosci (double, +inf)
var C = new Dictionary <PointsList, double[]>();
foreach (var c in combos)
{
C[c] = Helper.CreateDoubleMaxValueArray(Points.Count);
}
//Zczytanie dystansow z macierzy dystansow do dictionary
for (int i = 0; i < Points.Count; i++)
{
C[combos[i]][i] = DistanceMatrix[0, i];
}
for (int i = 2; i < Points.Count; i++)
{
var currentCombos = combos.FindAll(p => p.Count == i).ToList();
foreach (var s in currentCombos)
{
var currentMinList = new List <double>();
foreach (var k in s.Points)
{
foreach (var l in s.Points)
{
if (k.Id != l.Id)
{
var key = PointsList.Copy(s);
key.Points.Remove(k);
currentMinList.Add(C[key][l.Id] + DistanceMatrix[k.Id, l.Id]);
}
}
C[s][k.Id] = currentMinList.Min();
}
}
}
var minList = new List <double>();
var pointsListWOFirst = new PointsList(new List <Point>(Points.GetRange(1, Points.Count - 1)));
for (int i = 1; i < Points.Count; i++)
{
minList.Add(C[pointsListWOFirst][i] + DistanceMatrix[i, 0]);
}
var optimalCost = minList.Min();
if (withPrint)
{
Console.WriteLine(optimalPathTSP(optimalCost, pointsListWOFirst, C));
}
return(optimalCost);
}