/// <summary>
/// Implements <a href="http://en.wikipedia.org/wiki/Tarjan's_strongly_connected_components_algorithm">Tarjan's algorithm</a>
/// for finding the strongly connected components of the automaton graph.
/// </summary>
/// <param name="currentState">The state currently being traversed.</param>
/// <param name="traversalIndex">The traversal index (as defined by the Tarjan's algorithm).</param>
/// <param name="stateIdToStateInfo">A dictionary mapping state indices to info records maintained by the Tarjan's algorithm.</param>
/// <param name="stateIdStack">The traversal stack (as defined by the Tarjan's algorithm).</param>
private void FindStronglyConnectedComponents(
State currentState,
ref int traversalIndex,
Dictionary <int, TarjanStateInfo> stateIdToStateInfo,
Stack <State> stateIdStack)
{
Debug.Assert(!stateIdToStateInfo.ContainsKey(currentState.Index), "Visited states must not be revisited.");
var stateInfo = new TarjanStateInfo(traversalIndex);
stateIdToStateInfo.Add(currentState.Index, stateInfo);
++traversalIndex;
stateIdStack.Push(currentState);
stateInfo.InStack = true;
for (int transitionIndex = 0; transitionIndex < currentState.TransitionCount; ++transitionIndex)
{
Transition transition = currentState.GetTransition(transitionIndex);
if (!this.transitionFilter(transition))
{
continue;
}
TarjanStateInfo destinationStateInfo;
if (!stateIdToStateInfo.TryGetValue(transition.DestinationStateIndex, out destinationStateInfo))
{
this.FindStronglyConnectedComponents(
this.Root.Owner.states[transition.DestinationStateIndex], ref traversalIndex, stateIdToStateInfo, stateIdStack);
stateInfo.Lowlink = Math.Min(stateInfo.Lowlink, stateIdToStateInfo[transition.DestinationStateIndex].Lowlink);
}
else if (destinationStateInfo.InStack)
{
stateInfo.Lowlink = Math.Min(stateInfo.Lowlink, destinationStateInfo.TraversalIndex);
}
}
if (stateInfo.Lowlink == stateInfo.TraversalIndex)
{
var statesInComponent = new List <State>();
State state;
do
{
state = stateIdStack.Pop();
stateIdToStateInfo[state.Index].InStack = false;
statesInComponent.Add(state);
}while (state.Index != currentState.Index);
this.components.Add(new StronglyConnectedComponent(this.transitionFilter, statesInComponent, this.useApproximateClosure));
}
}
/// <summary>
/// Implements <a href="http://en.wikipedia.org/wiki/Tarjan's_strongly_connected_components_algorithm">Tarjan's algorithm</a>
/// for finding the strongly connected components of the automaton graph.
/// </summary>
private List <StronglyConnectedComponent> FindStronglyConnectedComponents()
{
var components = new List <StronglyConnectedComponent>();
var states = this.automaton.States;
var stateIdStack = new Stack <int>();
var stateIdToStateInfo = new Dictionary <int, TarjanStateInfo>();
int traversalIndex = 0;
var traversalStack = new Stack <(TarjanStateInfo, int stateIndex, int currentTransitionIndex)>();
traversalStack.Push((null, this.Root.Index, 0));
while (traversalStack.Count > 0)
{
var(stateInfo, currentStateIndex, currentTransitionIndex) = traversalStack.Pop();
var currentState = states[currentStateIndex];
var transitions = currentState.Transitions;
if (stateInfo == null)
{
// Entered into processing of this state for the first time: create Tarjan info for it
// and push the state onto Tarjan stack.
stateInfo = new TarjanStateInfo(traversalIndex);
stateIdToStateInfo.Add(currentStateIndex, stateInfo);
++traversalIndex;
stateIdStack.Push(currentStateIndex);
stateInfo.InStack = true;
}
else
{
// Just returned from recursion into 'currentTransitionIndex': update Lowlink
// and advance to next transition.
var lastDestination = transitions[currentTransitionIndex].DestinationStateIndex;
stateInfo.Lowlink = Math.Min(stateInfo.Lowlink, stateIdToStateInfo[lastDestination].Lowlink);
++currentTransitionIndex;
}
for (; currentTransitionIndex < transitions.Count; ++currentTransitionIndex)
{
var transition = transitions[currentTransitionIndex];
if (!this.transitionFilter(transition))
{
continue;
}
var destinationStateIndex = transition.DestinationStateIndex;
if (!stateIdToStateInfo.TryGetValue(destinationStateIndex, out var destinationStateInfo))
{
// Return to this (state/transition) after destinationState is processed.
// Processing will resume from currentTransitionIndex.
traversalStack.Push((stateInfo, currentStateIndex, currentTransitionIndex));
// Process destination state.
traversalStack.Push((null, destinationStateIndex, 0));
// Do not process other transitions until destination state is processed.
break;
}
if (destinationStateInfo.InStack)
{
stateInfo.Lowlink = Math.Min(stateInfo.Lowlink, destinationStateInfo.TraversalIndex);
}
}
if (currentTransitionIndex < transitions.Count)
{
// Not all states processed: continue processing according to stack. Current state
// is already pushed onto it -> will be processed again.
continue;
}
if (stateInfo.Lowlink == stateInfo.TraversalIndex)
{
var statesInComponent = new List <State>();
int stateIndex;
do
{
stateIndex = stateIdStack.Pop();
stateIdToStateInfo[stateIndex].InStack = false;
statesInComponent.Add(states[stateIndex]);
} while (stateIndex != currentStateIndex);
components.Add(new StronglyConnectedComponent(
this.automaton, this.transitionFilter, statesInComponent, this.useApproximateClosure));
this.TotalStatesCount += statesInComponent.Count;
}
}
return(components);
}
