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//===- ADT/SCCIterator.h - Strongly Connected Comp. Iter. -------*- C++ -*-===//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
/// \file
/// This builds on the llvm/ADT/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 scc_iterator on the Inverse graph. (NOTE:
/// This requires some simple wrappers and is not supported yet.)
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/GraphTraits.h"
#include "llvm/ADT/iterator.h"
#include <cassert>
#include <cstddef>
#include <iterator>
#include <queue>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <vector>
namespace llvm {
/// Enumerate the SCCs of a directed graph in reverse topological order
/// of the SCC DAG.
/// This is implemented using Tarjan's DFS algorithm using an internal stack to
/// build up a vector of nodes in a particular SCC. Note that it is a forward
/// iterator and thus you cannot backtrack or re-visit nodes.
template <class GraphT, class GT = GraphTraits<GraphT>>
class scc_iterator : public iterator_facade_base<
scc_iterator<GraphT, GT>, std::forward_iterator_tag,
const std::vector<typename GT::NodeRef>, ptrdiff_t> {
using NodeRef = typename GT::NodeRef;
using ChildItTy = typename GT::ChildIteratorType;
using SccTy = std::vector<NodeRef>;
using reference = typename scc_iterator::reference;
/// Element of VisitStack during DFS.
struct StackElement {
NodeRef Node; ///< The current node pointer.
ChildItTy NextChild; ///< The next child, modified inplace during DFS.
unsigned MinVisited; ///< Minimum uplink value of all children of Node.
StackElement(NodeRef Node, const ChildItTy &Child, unsigned Min)
: Node(Node), NextChild(Child), MinVisited(Min) {}
bool operator==(const StackElement &Other) const {
return Node == Other.Node &&
NextChild == Other.NextChild &&
MinVisited == Other.MinVisited;
/// 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 visitNum;
DenseMap<NodeRef, unsigned> nodeVisitNumbers;
/// Stack holding nodes of the SCC.
std::vector<NodeRef> SCCNodeStack;
/// The current SCC, retrieved using operator*().
SccTy CurrentSCC;
/// DFS stack, Used to maintain the ordering. The top contains the current
/// node, the next child to visit, and the minimum uplink value of all child
std::vector<StackElement> VisitStack;
/// A single "visit" within the non-recursive DFS traversal.
void DFSVisitOne(NodeRef N);
/// The stack-based DFS traversal; defined below.
void DFSVisitChildren();
/// Compute the next SCC using the DFS traversal.
void GetNextSCC();
scc_iterator(NodeRef entryN) : visitNum(0) {
/// End is when the DFS stack is empty.
scc_iterator() = default;
static scc_iterator begin(const GraphT &G) {
return scc_iterator(GT::getEntryNode(G));
static scc_iterator end(const GraphT &) { return scc_iterator(); }
/// Direct loop termination test which is more efficient than
/// comparison with \c end().
bool isAtEnd() const {
assert(!CurrentSCC.empty() || VisitStack.empty());
return CurrentSCC.empty();
bool operator==(const scc_iterator &x) const {
return VisitStack == x.VisitStack && CurrentSCC == x.CurrentSCC;
scc_iterator &operator++() {
return *this;
reference operator*() const {
assert(!CurrentSCC.empty() && "Dereferencing END SCC iterator!");
return CurrentSCC;
/// Test if the current SCC has a cycle.
/// If the SCC has more than one node, this is trivially true. If not, it may
/// still contain a cycle if the node has an edge back to itself.
bool hasCycle() const;
/// This informs the \c scc_iterator that the specified \c Old node
/// has been deleted, and \c New is to be used in its place.
void ReplaceNode(NodeRef Old, NodeRef New) {
assert(nodeVisitNumbers.count(Old) && "Old not in scc_iterator?");
// Do the assignment in two steps, in case 'New' is not yet in the map, and
// inserting it causes the map to grow.
auto tempVal = nodeVisitNumbers[Old];
nodeVisitNumbers[New] = tempVal;
template <class GraphT, class GT>
void scc_iterator<GraphT, GT>::DFSVisitOne(NodeRef N) {
nodeVisitNumbers[N] = visitNum;
VisitStack.push_back(StackElement(N, GT::child_begin(N), visitNum));
#if 0 // Enable if needed when debugging.
dbgs() << "TarjanSCC: Node " << N <<
" : visitNum = " << visitNum << "\n";
template <class GraphT, class GT>
void scc_iterator<GraphT, GT>::DFSVisitChildren() {
while (VisitStack.back().NextChild != GT::child_end(VisitStack.back().Node)) {
// TOS has at least one more child so continue DFS
NodeRef childN = *VisitStack.back().NextChild++;
typename DenseMap<NodeRef, unsigned>::iterator Visited =
if (Visited == nodeVisitNumbers.end()) {
// this node has never been seen.
unsigned childNum = Visited->second;
if (VisitStack.back().MinVisited > childNum)
VisitStack.back().MinVisited = childNum;
template <class GraphT, class GT> void scc_iterator<GraphT, GT>::GetNextSCC() {
CurrentSCC.clear(); // Prepare to compute the next SCC
while (!VisitStack.empty()) {
// Pop the leaf on top of the VisitStack.
NodeRef visitingN = VisitStack.back().Node;
unsigned minVisitNum = VisitStack.back().MinVisited;
assert(VisitStack.back().NextChild == GT::child_end(visitingN));
// Propagate MinVisitNum to parent so we can detect the SCC starting node.
if (!VisitStack.empty() && VisitStack.back().MinVisited > minVisitNum)
VisitStack.back().MinVisited = minVisitNum;
#if 0 // Enable if needed when debugging.
dbgs() << "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 {
nodeVisitNumbers[CurrentSCC.back()] = ~0U;
} while (CurrentSCC.back() != visitingN);
template <class GraphT, class GT>
bool scc_iterator<GraphT, GT>::hasCycle() const {
assert(!CurrentSCC.empty() && "Dereferencing END SCC iterator!");
if (CurrentSCC.size() > 1)
return true;
NodeRef N = CurrentSCC.front();
for (ChildItTy CI = GT::child_begin(N), CE = GT::child_end(N); CI != CE;
if (*CI == N)
return true;
return false;
/// Construct the begin iterator for a deduced graph type T.
template <class T> scc_iterator<T> scc_begin(const T &G) {
return scc_iterator<T>::begin(G);
/// Construct the end iterator for a deduced graph type T.
template <class T> scc_iterator<T> scc_end(const T &G) {
return scc_iterator<T>::end(G);
/// Sort the nodes of a directed SCC in the decreasing order of the edge
/// weights. The instantiating GraphT type should have weighted edge type
/// declared in its graph traits in order to use this iterator.
/// This is implemented using Kruskal's minimal spanning tree algorithm followed
/// by a BFS walk. First a maximum spanning tree (forest) is built based on all
/// edges within the SCC collection. Then a BFS walk is initiated on tree nodes
/// that do not have a predecessor. Finally, the BFS order computed is the
/// traversal order of the nodes of the SCC. Such order ensures that
/// high-weighted edges are visited first during the tranversal.
template <class GraphT, class GT = GraphTraits<GraphT>>
class scc_member_iterator {
using NodeType = typename GT::NodeType;
using EdgeType = typename GT::EdgeType;
using NodesType = std::vector<NodeType *>;
// Auxilary node information used during the MST calculation.
struct NodeInfo {
NodeInfo *Group = this;
uint32_t Rank = 0;
bool Visited = true;
// Find the root group of the node and compress the path from node to the
// root.
NodeInfo *find(NodeInfo *Node) {
if (Node->Group != Node)
Node->Group = find(Node->Group);
return Node->Group;
// Union the source and target node into the same group and return true.
// Returns false if they are already in the same group.
bool unionGroups(const EdgeType *Edge) {
NodeInfo *G1 = find(&NodeInfoMap[Edge->Source]);
NodeInfo *G2 = find(&NodeInfoMap[Edge->Target]);
// If the edge forms a cycle, do not add it to MST
if (G1 == G2)
return false;
// Make the smaller rank tree a direct child or the root of high rank tree.
if (G1->Rank < G1->Rank)
G1->Group = G2;
else {
G2->Group = G1;
// If the ranks are the same, increment root of one tree by one.
if (G1->Rank == G2->Rank)
return true;
std::unordered_map<NodeType *, NodeInfo> NodeInfoMap;
NodesType Nodes;
scc_member_iterator(const NodesType &InputNodes);
NodesType &operator*() { return Nodes; }
template <class GraphT, class GT>
scc_member_iterator<GraphT, GT>::scc_member_iterator(
const NodesType &InputNodes) {
if (InputNodes.size() <= 1) {
Nodes = InputNodes;
// Initialize auxilary node information.
for (auto *Node : InputNodes) {
// This is specifically used to construct a `NodeInfo` object in place. An
// insert operation will involve a copy construction which invalidate the
// initial value of the `Group` field which should be `this`.
// Sort edges by weights.
struct EdgeComparer {
bool operator()(const EdgeType *L, const EdgeType *R) const {
return L->Weight > R->Weight;
std::multiset<const EdgeType *, EdgeComparer> SortedEdges;
for (auto *Node : InputNodes) {
for (auto &Edge : Node->Edges) {
if (NodeInfoMap.count(Edge.Target))
// Traverse all the edges and compute the Maximum Weight Spanning Tree
// using Kruskal's algorithm.
std::unordered_set<const EdgeType *> MSTEdges;
for (auto *Edge : SortedEdges) {
if (unionGroups(Edge))
// Do BFS on MST, starting from nodes that have no incoming edge. These nodes
// are "roots" of the MST forest. This ensures that nodes are visited before
// their decsendents are, thus ensures hot edges are processed before cold
// edges, based on how MST is computed.
for (const auto *Edge : MSTEdges)
NodeInfoMap[Edge->Target].Visited = false;
std::queue<NodeType *> Queue;
for (auto &Node : NodeInfoMap)
if (Node.second.Visited)
while (!Queue.empty()) {
auto *Node = Queue.front();
for (auto &Edge : Node->Edges) {
if (MSTEdges.count(&Edge) && !NodeInfoMap[Edge.Target].Visited) {
NodeInfoMap[Edge.Target].Visited = true;
assert(InputNodes.size() == Nodes.size() && "missing nodes in MST");
std::reverse(Nodes.begin(), Nodes.end());
} // end namespace llvm