1 //===-- Support/TarjanSCCIterator.h -Generic 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.)
12 //===----------------------------------------------------------------------===//
14 #ifndef LLVM_SUPPORT_TARJANSCC_ITERATOR_H
15 #define LLVM_SUPPORT_TARJANSCC_ITERATOR_H
17 #include "Support/GraphTraits.h"
18 #include <Support/Statistic.h>
19 #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 //--------------------------------------------------------------------------
59 const unsigned long MAXLONG = (1 << (8 * sizeof(unsigned long) - 1));
62 Statistic<> NumSCCs("NumSCCs", "Number of Strongly Connected Components");
63 Statistic<> MaxSCCSize("MaxSCCSize", "Size of largest Strongly Connected Component");
66 template<class GraphT, class GT = GraphTraits<GraphT> >
67 class TarjanSCC_iterator : public forward_iterator<SCC<GraphT, GT>, ptrdiff_t>
69 typedef SCC<GraphT, GT> SccTy;
70 typedef forward_iterator<SccTy, ptrdiff_t> super;
71 typedef typename super::reference reference;
72 typedef typename super::pointer pointer;
73 typedef typename GT::NodeType NodeType;
74 typedef typename GT::ChildIteratorType ChildItTy;
76 // The visit counters used to detect when a complete SCC is on the stack.
77 // visitNum is the global counter.
78 // nodeVisitNumbers are per-node visit numbers, also used as DFS flags.
79 unsigned long visitNum;
80 std::map<NodeType *, unsigned long> nodeVisitNumbers;
82 // SCCNodeStack - Stack holding nodes of the SCC.
83 std::stack<NodeType *> SCCNodeStack;
85 // CurrentSCC - The current SCC, retrieved using operator*().
88 // VisitStack - Used to maintain the ordering. Top = current block
89 // First element is basic block pointer, second is the 'next child' to visit
90 std::stack<std::pair<NodeType *, ChildItTy> > VisitStack;
92 // MinVistNumStack - Stack holding the "min" values for each node in the DFS.
93 // This is used to track the minimum uplink values for all children of
94 // the corresponding node on the VisitStack.
95 std::stack<unsigned long> MinVisitNumStack;
97 // A single "visit" within the non-recursive DFS traversal.
98 void DFSVisitOne(NodeType* N) {
99 ++visitNum; // Global counter for the visit order
100 nodeVisitNumbers[N] = visitNum;
101 SCCNodeStack.push(N);
102 MinVisitNumStack.push(visitNum);
103 VisitStack.push(make_pair(N, GT::child_begin(N)));
104 DEBUG(std::cerr << "TarjanSCC: Node " << N <<
105 " : visitNum = " << visitNum << "\n");
108 // The stack-based DFS traversal; defined below.
109 void DFSVisitChildren() {
110 assert(!VisitStack.empty());
111 while (VisitStack.top().second != GT::child_end(VisitStack.top().first))
112 { // TOS has at least one more child so continue DFS
113 NodeType *childN = *VisitStack.top().second++;
114 if (nodeVisitNumbers.find(childN) == nodeVisitNumbers.end())
115 { // this node has never been seen
120 unsigned long childNum = nodeVisitNumbers[childN];
121 if (MinVisitNumStack.top() > childNum)
122 MinVisitNumStack.top() = childNum;
127 // Compute the next SCC using the DFS traversal.
129 assert(VisitStack.size() == MinVisitNumStack.size());
130 CurrentSCC.clear(); // Prepare to compute the next SCC
131 while (! VisitStack.empty())
135 assert(VisitStack.top().second==GT::child_end(VisitStack.top().first));
136 NodeType* visitingN = VisitStack.top().first;
137 unsigned long minVisitNum = MinVisitNumStack.top();
139 MinVisitNumStack.pop();
140 if (! MinVisitNumStack.empty() && MinVisitNumStack.top() > minVisitNum)
141 MinVisitNumStack.top() = minVisitNum;
143 DEBUG(std::cerr << "TarjanSCC: Popped node " << visitingN <<
144 " : minVisitNum = " << minVisitNum << "; Node visit num = " <<
145 nodeVisitNumbers[visitingN] << "\n");
147 if (minVisitNum == nodeVisitNumbers[visitingN])
148 { // A full SCC is on the SCCNodeStack! It includes all nodes below
149 // visitingN on the stack. Copy those nodes to CurrentSCC,
150 // reset their minVisit values, and return (this suspends
151 // the DFS traversal till the next ++).
153 CurrentSCC.push_back(SCCNodeStack.top());
155 nodeVisitNumbers[CurrentSCC.back()] = MAXLONG;
156 } while (CurrentSCC.back() != visitingN);
159 if (CurrentSCC.size() > MaxSCCSize) MaxSCCSize = CurrentSCC.size();
166 inline TarjanSCC_iterator(NodeType *entryN) : visitNum(0) {
170 inline TarjanSCC_iterator() { /* End is when DFS stack is empty */ }
173 typedef TarjanSCC_iterator<GraphT, GT> _Self;
175 // Provide static "constructors"...
176 static inline _Self begin(GraphT& G) { return _Self(GT::getEntryNode(G)); }
177 static inline _Self end (GraphT& G) { return _Self(); }
179 // Direct loop termination test (I.fini() is more efficient than I == end())
180 inline bool fini() const {
181 return VisitStack.empty();
184 inline bool operator==(const _Self& x) const {
185 return VisitStack == x.VisitStack;
187 inline bool operator!=(const _Self& x) const { return !operator==(x); }
189 // Iterator traversal: forward iteration only
190 inline _Self& operator++() { // Preincrement
194 inline _Self operator++(int) { // Postincrement
195 _Self tmp = *this; ++*this; return tmp;
198 // Retrieve a pointer to the current SCC. Returns NULL when done.
199 inline const SccTy* operator*() const {
200 assert(!CurrentSCC.empty() || fini());
201 return CurrentSCC.empty()? NULL : &CurrentSCC;
203 inline SccTy* operator*() {
204 assert(!CurrentSCC.empty() || fini());
205 return CurrentSCC.empty()? NULL : &CurrentSCC;
210 // Global constructor for the Tarjan SCC iterator. Use *I == NULL or I.fini()
211 // to test termination efficiently, instead of I == the "end" iterator.
213 TarjanSCC_iterator<T> tarj_begin(T G)
215 return TarjanSCC_iterator<T>::begin(G);
219 TarjanSCC_iterator<T> tarj_end(T G)
221 return TarjanSCC_iterator<T>::end(G);
224 //===----------------------------------------------------------------------===//