1 //===-- Support/TarjanSCCIterator.h - Tarjan SCC iterator -------*- C++ -*-===//
3 // This builds on the Support/GraphTraits.h file to find the strongly
4 // connected components (SCCs) of a graph in O(N+E) time using
5 // Tarjan's DFS algorithm.
7 // The SCC iterator has the important property that if a node in SCC S1
8 // has an edge to a node in SCC S2, then it visits S1 *after* S2.
10 // To visit S1 *before* S2, use the TarjanSCCIterator on the Inverse graph.
11 // (NOTE: This requires some simple wrappers and is not supported yet.)
13 //===----------------------------------------------------------------------===//
15 #ifndef SUPPORT_TARJANSCCITERATOR_H
16 #define SUPPORT_TARJANSCCITERATOR_H
18 #include "Support/GraphTraits.h"
19 #include "Support/Statistic.h"
20 #include "Support/iterator"
25 //--------------------------------------------------------------------------
26 // class SCC : A simple representation of an SCC in a generic Graph.
27 //--------------------------------------------------------------------------
29 template<class GraphT, class GT = GraphTraits<GraphT> >
30 struct SCC: public std::vector<typename GT::NodeType*> {
32 typedef typename GT::NodeType NodeType;
33 typedef typename GT::ChildIteratorType ChildItTy;
35 typedef std::vector<typename GT::NodeType*> super;
36 typedef typename super::iterator iterator;
37 typedef typename super::const_iterator const_iterator;
38 typedef typename super::reverse_iterator reverse_iterator;
39 typedef typename super::const_reverse_iterator const_reverse_iterator;
41 // HasLoop() -- Test if this SCC has a loop. If it has more than one
42 // node, this is trivially true. If not, it may still contain a loop
43 // if the node has an edge back to itself.
44 bool HasLoop() const {
45 if (size() > 1) return true;
46 NodeType* N = front();
47 for (ChildItTy CI=GT::child_begin(N), CE=GT::child_end(N); CI != CE; ++CI)
54 //--------------------------------------------------------------------------
55 // class TarjanSCC_iterator: Enumerate the SCCs of a directed graph, in
56 // reverse topological order of the SCC DAG.
57 //--------------------------------------------------------------------------
60 Statistic<> NumSCCs("NumSCCs", "Number of Strongly Connected Components");
61 Statistic<> MaxSCCSize("MaxSCCSize", "Size of largest Strongly Connected Component");
64 template<class GraphT, class GT = GraphTraits<GraphT> >
65 class TarjanSCC_iterator : public forward_iterator<SCC<GraphT, GT>, ptrdiff_t>
67 typedef SCC<GraphT, GT> SccTy;
68 typedef forward_iterator<SccTy, ptrdiff_t> super;
69 typedef typename super::reference reference;
70 typedef typename super::pointer pointer;
71 typedef typename GT::NodeType NodeType;
72 typedef typename GT::ChildIteratorType ChildItTy;
74 // The visit counters used to detect when a complete SCC is on the stack.
75 // visitNum is the global counter.
76 // nodeVisitNumbers are per-node visit numbers, also used as DFS flags.
77 unsigned long visitNum;
78 std::map<NodeType *, unsigned long> nodeVisitNumbers;
80 // SCCNodeStack - Stack holding nodes of the SCC.
81 std::stack<NodeType *> SCCNodeStack;
83 // CurrentSCC - The current SCC, retrieved using operator*().
86 // VisitStack - Used to maintain the ordering. Top = current block
87 // First element is basic block pointer, second is the 'next child' to visit
88 std::stack<std::pair<NodeType *, ChildItTy> > VisitStack;
90 // MinVistNumStack - Stack holding the "min" values for each node in the DFS.
91 // This is used to track the minimum uplink values for all children of
92 // the corresponding node on the VisitStack.
93 std::stack<unsigned long> MinVisitNumStack;
95 // A single "visit" within the non-recursive DFS traversal.
96 void DFSVisitOne(NodeType* N) {
97 ++visitNum; // Global counter for the visit order
98 nodeVisitNumbers[N] = visitNum;
100 MinVisitNumStack.push(visitNum);
101 VisitStack.push(make_pair(N, GT::child_begin(N)));
102 DEBUG(std::cerr << "TarjanSCC: Node " << N <<
103 " : visitNum = " << visitNum << "\n");
106 // The stack-based DFS traversal; defined below.
107 void DFSVisitChildren() {
108 assert(!VisitStack.empty());
109 while (VisitStack.top().second != GT::child_end(VisitStack.top().first))
110 { // TOS has at least one more child so continue DFS
111 NodeType *childN = *VisitStack.top().second++;
112 if (nodeVisitNumbers.find(childN) == nodeVisitNumbers.end())
113 { // this node has never been seen
118 unsigned long childNum = nodeVisitNumbers[childN];
119 if (MinVisitNumStack.top() > childNum)
120 MinVisitNumStack.top() = childNum;
125 // Compute the next SCC using the DFS traversal.
127 assert(VisitStack.size() == MinVisitNumStack.size());
128 CurrentSCC.clear(); // Prepare to compute the next SCC
129 while (! VisitStack.empty())
133 assert(VisitStack.top().second==GT::child_end(VisitStack.top().first));
134 NodeType* visitingN = VisitStack.top().first;
135 unsigned long minVisitNum = MinVisitNumStack.top();
137 MinVisitNumStack.pop();
138 if (! MinVisitNumStack.empty() && MinVisitNumStack.top() > minVisitNum)
139 MinVisitNumStack.top() = minVisitNum;
141 DEBUG(std::cerr << "TarjanSCC: Popped node " << visitingN <<
142 " : minVisitNum = " << minVisitNum << "; Node visit num = " <<
143 nodeVisitNumbers[visitingN] << "\n");
145 if (minVisitNum == nodeVisitNumbers[visitingN])
146 { // A full SCC is on the SCCNodeStack! It includes all nodes below
147 // visitingN on the stack. Copy those nodes to CurrentSCC,
148 // reset their minVisit values, and return (this suspends
149 // the DFS traversal till the next ++).
151 CurrentSCC.push_back(SCCNodeStack.top());
153 nodeVisitNumbers[CurrentSCC.back()] = ~0UL;
154 } while (CurrentSCC.back() != visitingN);
157 if (CurrentSCC.size() > MaxSCCSize) MaxSCCSize = CurrentSCC.size();
164 inline TarjanSCC_iterator(NodeType *entryN) : visitNum(0) {
168 inline TarjanSCC_iterator() { /* End is when DFS stack is empty */ }
171 typedef TarjanSCC_iterator<GraphT, GT> _Self;
173 // Provide static "constructors"...
174 static inline _Self begin(GraphT& G) { return _Self(GT::getEntryNode(G)); }
175 static inline _Self end (GraphT& G) { return _Self(); }
177 // Direct loop termination test (I.fini() is more efficient than I == end())
178 inline bool fini() const {
179 assert(!CurrentSCC.empty() || VisitStack.empty());
180 return CurrentSCC.empty();
183 inline bool operator==(const _Self& x) const {
184 return VisitStack == x.VisitStack && CurrentSCC == x.CurrentSCC;
186 inline bool operator!=(const _Self& x) const { return !operator==(x); }
188 // Iterator traversal: forward iteration only
189 inline _Self& operator++() { // Preincrement
193 inline _Self operator++(int) { // Postincrement
194 _Self tmp = *this; ++*this; return tmp;
197 // Retrieve a pointer to the current SCC. Returns NULL when done.
198 inline const SccTy* operator*() const {
199 assert(!CurrentSCC.empty() || VisitStack.empty());
200 return CurrentSCC.empty()? NULL : &CurrentSCC;
202 inline SccTy* operator*() {
203 assert(!CurrentSCC.empty() || VisitStack.empty());
204 return CurrentSCC.empty()? NULL : &CurrentSCC;
209 // Global constructor for the Tarjan SCC iterator. Use *I == NULL or I.fini()
210 // to test termination efficiently, instead of I == the "end" iterator.
212 TarjanSCC_iterator<T> tarj_begin(T G)
214 return TarjanSCC_iterator<T>::begin(G);
218 TarjanSCC_iterator<T> tarj_end(T G)
220 return TarjanSCC_iterator<T>::end(G);
223 //===----------------------------------------------------------------------===//