SCCIterator.h revision 7a73b80b9052136c8cd2234eb3433a07df7cf38e 
1//===-- Support/TarjanSCCIterator.h - Tarjan SCC iterator -------*- C++ -*-===//
2//
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.
6//
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.
9//
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//
13//===----------------------------------------------------------------------===//
14
15#ifndef SUPPORT_TARJANSCCITERATOR_H
16#define SUPPORT_TARJANSCCITERATOR_H
17
18#include "Support/GraphTraits.h"
19#include "Support/Statistic.h"
20#include "Support/iterator"
21#include <vector>
22#include <stack>
23#include <map>
24
25//--------------------------------------------------------------------------
26// class SCC : A simple representation of an SCC in a generic Graph.
27//--------------------------------------------------------------------------
28
29template<class GraphT, class GT = GraphTraits<GraphT> >
30struct SCC: public std::vector<typename GT::NodeType*> {
31
32  typedef typename GT::NodeType NodeType;
33  typedef typename GT::ChildIteratorType ChildItTy;
34
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;
40
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)
48      if (*CI == N)
49        return true;
50    return false;
51  }
52};
53
54//--------------------------------------------------------------------------
55// class TarjanSCC_iterator: Enumerate the SCCs of a directed graph, in
56// reverse topological order of the SCC DAG.
57//--------------------------------------------------------------------------
58
59namespace {
60  Statistic<> NumSCCs("NumSCCs", "Number of Strongly Connected Components");
61  Statistic<> MaxSCCSize("MaxSCCSize", "Size of largest Strongly Connected Component");
62}
63
64template<class GraphT, class GT = GraphTraits<GraphT> >
65class TarjanSCC_iterator : public forward_iterator<SCC<GraphT, GT>, ptrdiff_t>
66{
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;
73
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;
79
80  // SCCNodeStack - Stack holding nodes of the SCC.
81  std::stack<NodeType *> SCCNodeStack;
82
83  // CurrentSCC - The current SCC, retrieved using operator*().
84  SccTy CurrentSCC;
85
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;
89
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;
94
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;
99    SCCNodeStack.push(N);
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");
104  }
105
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
114            DFSVisitOne(childN);
115          }
116        else
117          {
118            unsigned long childNum = nodeVisitNumbers[childN];
119            if (MinVisitNumStack.top() > childNum)
120              MinVisitNumStack.top() = childNum;
121          }
122      }
123  }
124
125  // Compute the next SCC using the DFS traversal.
126  void GetNextSCC() {
127    assert(VisitStack.size() == MinVisitNumStack.size());
128    CurrentSCC.clear();                 // Prepare to compute the next SCC
129    while (! VisitStack.empty())
130      {
131        DFSVisitChildren();
132
133        assert(VisitStack.top().second==GT::child_end(VisitStack.top().first));
134        NodeType* visitingN = VisitStack.top().first;
135        unsigned long minVisitNum = MinVisitNumStack.top();
136        VisitStack.pop();
137        MinVisitNumStack.pop();
138        if (! MinVisitNumStack.empty() && MinVisitNumStack.top() > minVisitNum)
139          MinVisitNumStack.top() = minVisitNum;
140
141        DEBUG(std::cerr << "TarjanSCC: Popped node " << visitingN <<
142              " : minVisitNum = " << minVisitNum << "; Node visit num = " <<
143              nodeVisitNumbers[visitingN] << "\n");
144
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 ++).
150            do {
151              CurrentSCC.push_back(SCCNodeStack.top());
152              SCCNodeStack.pop();
153              nodeVisitNumbers[CurrentSCC.back()] = ~0UL;
154            } while (CurrentSCC.back() != visitingN);
155
156            ++NumSCCs;
157            if (CurrentSCC.size() > MaxSCCSize) MaxSCCSize = CurrentSCC.size();
158
159            return;
160          }
161      }
162  }
163
164  inline TarjanSCC_iterator(NodeType *entryN) : visitNum(0) {
165    DFSVisitOne(entryN);
166    GetNextSCC();
167  }
168  inline TarjanSCC_iterator() { /* End is when DFS stack is empty */ }
169
170public:
171  typedef TarjanSCC_iterator<GraphT, GT> _Self;
172
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(); }
176
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();
181  }
182
183  inline bool operator==(const _Self& x) const {
184    return VisitStack == x.VisitStack && CurrentSCC == x.CurrentSCC;
185  }
186  inline bool operator!=(const _Self& x) const { return !operator==(x); }
187
188  // Iterator traversal: forward iteration only
189  inline _Self& operator++() {          // Preincrement
190    GetNextSCC();
191    return *this;
192  }
193  inline _Self operator++(int) {        // Postincrement
194    _Self tmp = *this; ++*this; return tmp;
195  }
196
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;
201  }
202  inline SccTy* operator*() {
203    assert(!CurrentSCC.empty() || VisitStack.empty());
204    return CurrentSCC.empty()? NULL : &CurrentSCC;
205  }
206};
207
208
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.
211template <class T>
212TarjanSCC_iterator<T> tarj_begin(T G)
213{
214  return TarjanSCC_iterator<T>::begin(G);
215}
216
217template <class T>
218TarjanSCC_iterator<T> tarj_end(T G)
219{
220  return TarjanSCC_iterator<T>::end(G);
221}
222
223//===----------------------------------------------------------------------===//
224
225#endif
226