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Generic graph iterator to enumerate the SCCs of a graph

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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
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Vikram S. Adve 2002-11-04 14:15:57 +00:00
parent 02606637e0
commit 5fe9171b38
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include/Support/SCCIterator.h Normal file
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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

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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