Generic graph iterator to enumerate the SCCs of a graph

in linear time using Tarjan's DFS algorithm.


git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@4531 91177308-0d34-0410-b5e6-96231b3b80d8

1 files changed, 221 insertions, 0 deletions

diff --git a/include/Support/SCCIterator.h b/include/Support/SCCIterator.h
new file mode 100644
index 0000000..e737f7c
--- /dev/null
+++ b/include/Support/SCCIterator.h
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+//===-- Support/TarjanSCCIterator.h -Generic Tarjan SCC iterator -*- C++ -*--=//
+//
+// This builds on the Support/GraphTraits.h file to find the strongly 
+// connected components (SCCs) of a graph in O(N+E) time using
+// Tarjan's DFS algorithm.
+//
+// The SCC iterator has the important property that if a node in SCC S1
+// has an edge to a node in SCC S2, then it visits S1 *after* S2.
+// 
+// To visit S1 *before* S2, use the TarjanSCCIterator on the Inverse graph.
+// (NOTE: This requires some simple wrappers and is not supported yet.)
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_SUPPORT_TARJANSCC_ITERATOR_H
+#define LLVM_SUPPORT_TARJANSCC_ITERATOR_H
+
+#include "Support/GraphTraits.h"
+#include <Support/Statistic.h>
+#include <Support/iterator>
+#include <vector>
+#include <stack>
+#include <map>
+
+
+//--------------------------------------------------------------------------
+// class SCC : A simple representation of an SCC in a generic Graph.
+//--------------------------------------------------------------------------
+
+template<class GraphT, class GT = GraphTraits<GraphT> >
+struct SCC: public std::vector<typename GT::NodeType*> {
+
+  typedef typename GT::NodeType NodeType;
+  typedef typename GT::ChildIteratorType ChildItTy;
+
+  typedef std::vector<typename GT::NodeType*> super;
+  typedef typename super::iterator               iterator;
+  typedef typename super::const_iterator         const_iterator;
+  typedef typename super::reverse_iterator       reverse_iterator;
+  typedef typename super::const_reverse_iterator const_reverse_iterator;
+
+  // HasLoop() -- Test if this SCC has a loop.  If it has more than one
+  // node, this is trivially true.  If not, it may still contain a loop
+  // if the node has an edge back to itself.
+  bool HasLoop() const {
+    if (size() > 1) return true;
+    NodeType* N = front();
+    for (ChildItTy CI=GT::child_begin(N), CE=GT::child_end(N); CI != CE; ++CI)
+      if (*CI == N)
+        return true;
+    return false;
+  }
+};
+
+//--------------------------------------------------------------------------
+// class TarjanSCC_iterator: Enumerate the SCCs of a directed graph, in
+// reverse topological order of the SCC DAG.
+//--------------------------------------------------------------------------
+
+const unsigned long MAXLONG = (1 << (8 * sizeof(unsigned long) - 1));
+
+namespace {
+  Statistic<> NumSCCs("NumSCCs", "Number of Strongly Connected Components");
+  Statistic<> MaxSCCSize("MaxSCCSize", "Size of largest Strongly Connected Component");
+}
+
+template<class GraphT, class GT = GraphTraits<GraphT> >
+class TarjanSCC_iterator : public forward_iterator<SCC<GraphT, GT>, ptrdiff_t>
+{
+  typedef SCC<GraphT, GT> SccTy;
+  typedef forward_iterator<SccTy, ptrdiff_t> super;
+  typedef typename super::reference reference;
+  typedef typename super::pointer pointer;
+  typedef typename GT::NodeType          NodeType;
+  typedef typename GT::ChildIteratorType ChildItTy;
+
+  // The visit counters used to detect when a complete SCC is on the stack.
+  // visitNum is the global counter.
+  // nodeVisitNumbers are per-node visit numbers, also used as DFS flags.
+  unsigned long visitNum;
+  std::map<NodeType *, unsigned long> nodeVisitNumbers;
+
+  // SCCNodeStack - Stack holding nodes of the SCC.
+  std::stack<NodeType *> SCCNodeStack;
+
+  // CurrentSCC - The current SCC, retrieved using operator*().
+  SccTy CurrentSCC;
+
+  // VisitStack - Used to maintain the ordering.  Top = current block
+  // First element is basic block pointer, second is the 'next child' to visit
+  std::stack<std::pair<NodeType *, ChildItTy> > VisitStack;
+
+  // MinVistNumStack - Stack holding the "min" values for each node in the DFS.
+  // This is used to track the minimum uplink values for all children of
+  // the corresponding node on the VisitStack.
+  std::stack<unsigned long> MinVisitNumStack;
+
+  // A single "visit" within the non-recursive DFS traversal.
+  void DFSVisitOne(NodeType* N) {
+    ++visitNum;                         // Global counter for the visit order
+    nodeVisitNumbers[N] = visitNum;
+    SCCNodeStack.push(N);
+    MinVisitNumStack.push(visitNum);
+    VisitStack.push(make_pair(N, GT::child_begin(N)));
+    DEBUG(std::cerr << "TarjanSCC: Node " << N <<
+          " : visitNum = " << visitNum << "\n");
+  }
+
+  // The stack-based DFS traversal; defined below.
+  void DFSVisitChildren() {
+    assert(!VisitStack.empty());
+    while (VisitStack.top().second != GT::child_end(VisitStack.top().first))
+      { // TOS has at least one more child so continue DFS
+        NodeType *childN = *VisitStack.top().second++;
+        if (nodeVisitNumbers.find(childN) == nodeVisitNumbers.end())
+          { // this node has never been seen
+            DFSVisitOne(childN);
+          }
+        else
+          {
+            unsigned long childNum = nodeVisitNumbers[childN];
+            if (MinVisitNumStack.top() > childNum)
+              MinVisitNumStack.top() = childNum;
+          }
+      }
+  }
+
+  // Compute the next SCC using the DFS traversal.
+  void GetNextSCC() {
+    assert(VisitStack.size() == MinVisitNumStack.size());
+    CurrentSCC.clear();                 // Prepare to compute the next SCC
+    while (! VisitStack.empty())
+      {
+        DFSVisitChildren();
+
+        assert(VisitStack.top().second==GT::child_end(VisitStack.top().first));
+        NodeType* visitingN = VisitStack.top().first;
+        unsigned long minVisitNum = MinVisitNumStack.top();
+        VisitStack.pop();
+        MinVisitNumStack.pop();
+        if (! MinVisitNumStack.empty() && MinVisitNumStack.top() > minVisitNum)
+          MinVisitNumStack.top() = minVisitNum;
+
+        DEBUG(std::cerr << "TarjanSCC: Popped node " << visitingN <<
+              " : minVisitNum = " << minVisitNum << "; Node visit num = " <<
+              nodeVisitNumbers[visitingN] << "\n");
+
+        if (minVisitNum == nodeVisitNumbers[visitingN])
+          { // A full SCC is on the SCCNodeStack!  It includes all nodes below
+            // visitingN on the stack.  Copy those nodes to CurrentSCC,
+            // reset their minVisit values, and return (this suspends
+            // the DFS traversal till the next ++).
+            do {
+              CurrentSCC.push_back(SCCNodeStack.top());
+              SCCNodeStack.pop();
+              nodeVisitNumbers[CurrentSCC.back()] = MAXLONG; 
+            } while (CurrentSCC.back() != visitingN);
+
+            ++NumSCCs;
+            if (CurrentSCC.size() > MaxSCCSize) MaxSCCSize = CurrentSCC.size();
+            
+            return;
+          }
+      }
+  }
+
+  inline TarjanSCC_iterator(NodeType *entryN) : visitNum(0) {
+    DFSVisitOne(entryN);
+    GetNextSCC();
+  }
+  inline TarjanSCC_iterator() { /* End is when DFS stack is empty */ }
+
+public:
+  typedef TarjanSCC_iterator<GraphT, GT> _Self;
+
+  // Provide static "constructors"...
+  static inline _Self begin(GraphT& G) { return _Self(GT::getEntryNode(G)); }
+  static inline _Self end  (GraphT& G) { return _Self(); }
+
+  // Direct loop termination test (I.fini() is more efficient than I == end())
+  inline bool fini() const {
+    return VisitStack.empty();
+  }
+
+  inline bool operator==(const _Self& x) const { 
+    return VisitStack == x.VisitStack;
+  }
+  inline bool operator!=(const _Self& x) const { return !operator==(x); }
+
+  // Iterator traversal: forward iteration only
+  inline _Self& operator++() {          // Preincrement
+    GetNextSCC();
+    return *this; 
+  }
+  inline _Self operator++(int) {        // Postincrement
+    _Self tmp = *this; ++*this; return tmp; 
+  }
+
+  // Retrieve a pointer to the current SCC.  Returns NULL when done.
+  inline const SccTy* operator*() const { 
+    assert(!CurrentSCC.empty() || fini());
+    return CurrentSCC.empty()? NULL : &CurrentSCC;
+  }
+  inline SccTy* operator*() { 
+    assert(!CurrentSCC.empty() || fini());
+    return CurrentSCC.empty()? NULL : &CurrentSCC;
+  }
+};
+
+
+// Global constructor for the Tarjan SCC iterator.  Use *I == NULL or I.fini()
+// to test termination efficiently, instead of I == the "end" iterator.
+template <class T>
+TarjanSCC_iterator<T> tarj_begin(T G)
+{
+  return TarjanSCC_iterator<T>::begin(G);
+}
+
+
+//===----------------------------------------------------------------------===//
+
+#endif