public ArrayList RunTSP(City[] Cities)
{
Route = new ArrayList();
Stopwatch timer = new Stopwatch();
bAndBTime = new TimeSpan();
timer.Start();
Greedy greedyAlgorithm = new Greedy(Cities);
ArrayList greedyRoute = greedyAlgorithm.RunGreedyTSP();
double[,] matrix = new double[Cities.Length, Cities.Length];
//Populate each array item with each respective edge cost
for (int i = 0; i < Cities.Length; i++)
{//O(n^2)
for (int j = 0; j < Cities.Length; j++)
{
if (i == j)
{
matrix[i, j] = double.PositiveInfinity;
}
else
{
matrix[i, j] = Cities[i].costToGetTo(Cities[j]);
}
}
}
IntervalHeap <State> queue = new IntervalHeap <State>();
double bestSolutionSoFar = greedyAlgorithm.BestSolutionSoFar();
bssfUpdatesAmt = 0;
prunedAmt = 0;
State bssfState = null;
totalStatesCreated = 0;
//Start with some problem
State curState = new State(matrix, 0, new Edge(-1, -1));
totalStatesCreated++;
//Reduce Matrix
//O(4n^2)
curState.Reduce();
//Let the queue be the set of active subproblems
//O(log(n))
queue.Add(curState);
maxQueueCount = 0;
bool timesUp = false;
while (queue.Count > 0)
{//O(2^n) or O(2^(8n^2 + 9n + 2log(n)))
if (timer.Elapsed.Seconds >= 30)
{
timesUp = true;
break;
}
//Choose a subproblem and remove it from the queue
if (queue.Count > maxQueueCount)
{
maxQueueCount = queue.Count;
}
//O(log(n))
curState = queue.DeleteMin();
if (curState.Cost() < bestSolutionSoFar)
{//O(8n^2 + 9n + 2log(n))
//For each lowest cost (each 0)
double highestScore = double.NegativeInfinity;
State[] includeExcludeStates = new State[2];
foreach (Edge edge in curState.LowestNums())
{ //O(8n^2 + 9n)
//Include Matrix
State includeState = new State(curState, edge); //O(n)
totalStatesCreated++;
includeState.IncludeMatrix(edge.Row(), edge.Col()); //O(4n^2 + 7n)
//Exclude Matrix
State excludeState = new State(curState, edge); //O(n)
totalStatesCreated++;
excludeState.ExcludeMatrix(edge.Row(), edge.Col()); //O(4n^2)
//Find the score for that edge (Exclude cost - Include cost)
double score = excludeState.Cost() - includeState.Cost();
if (score > highestScore)
{
includeExcludeStates[0] = includeState;
includeExcludeStates[1] = excludeState;
highestScore = score;
}
}
foreach (State subproblemState in includeExcludeStates)
{//O(2log(n))
//if each P (subproblem) chosen is a complete solution, update the bssf
if (subproblemState.CompleteSolution() && subproblemState.Cost() < bestSolutionSoFar)
{
bestSolutionSoFar = subproblemState.Cost();
bssfState = subproblemState;
bssfUpdatesAmt++;
}
//else if lowerBound < bestSolutionSoFar
else if (!subproblemState.CompleteSolution() && subproblemState.Cost() < bestSolutionSoFar)
{
//O(log(n))
queue.Add(subproblemState);
}
else
{
prunedAmt++;
}
}
}
}
if (!timesUp)
{
prunedAmt += queue.Count;
}
//Call this the best solution so far. bssf is the route that will be drawn by the Draw method.
if (bssfState != null)
{
int index = bssfState.Exited(0);
Route.Add(Cities[index]);
index = bssfState.Exited(bssfState.Exited(0));
while (index != bssfState.Exited(0))
{//O(n)
Route.Add(Cities[index]);
index = bssfState.Exited(index);
}
}
else
{
Route = greedyRoute;
}
timer.Stop();
bAndBTime = timer.Elapsed;
this.count = bssfState.Cost();
// update the cost of the tour.
timer.Reset();
return(Route);
}