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//===- llvm/Analysis/MaximumSpanningTree.h - Interface ----------*- 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
// This module provides means for calculating a maximum spanning tree for a
// given set of weighted edges. The type parameter T is the type of a node.
#include "llvm/ADT/EquivalenceClasses.h"
#include "llvm/IR/BasicBlock.h"
#include <algorithm>
#include <vector>
namespace llvm {
/// MaximumSpanningTree - A MST implementation.
/// The type parameter T determines the type of the nodes of the graph.
template <typename T>
class MaximumSpanningTree {
typedef std::pair<const T*, const T*> Edge;
typedef std::pair<Edge, double> EdgeWeight;
typedef std::vector<EdgeWeight> EdgeWeights;
typedef std::vector<Edge> MaxSpanTree;
MaxSpanTree MST;
// A comparing class for comparing weighted edges.
struct EdgeWeightCompare {
static bool getBlockSize(const T *X) {
const BasicBlock *BB = dyn_cast_or_null<BasicBlock>(X);
return BB ? BB->size() : 0;
bool operator()(EdgeWeight X, EdgeWeight Y) const {
if (X.second > Y.second) return true;
if (X.second < Y.second) return false;
// Equal edge weights: break ties by comparing block sizes.
size_t XSizeA = getBlockSize(X.first.first);
size_t YSizeA = getBlockSize(Y.first.first);
if (XSizeA > YSizeA) return true;
if (XSizeA < YSizeA) return false;
size_t XSizeB = getBlockSize(X.first.second);
size_t YSizeB = getBlockSize(Y.first.second);
if (XSizeB > YSizeB) return true;
if (XSizeB < YSizeB) return false;
return false;
static char ID; // Class identification, replacement for typeinfo
/// MaximumSpanningTree() - Takes a vector of weighted edges and returns a
/// spanning tree.
MaximumSpanningTree(EdgeWeights &EdgeVector) {
llvm::stable_sort(EdgeVector, EdgeWeightCompare());
// Create spanning tree, Forest contains a special data structure
// that makes checking if two nodes are already in a common (sub-)tree
// fast and cheap.
EquivalenceClasses<const T*> Forest;
for (typename EdgeWeights::iterator EWi = EdgeVector.begin(),
EWe = EdgeVector.end(); EWi != EWe; ++EWi) {
Edge e = (*EWi).first;
// Iterate over the sorted edges, biggest first.
for (typename EdgeWeights::iterator EWi = EdgeVector.begin(),
EWe = EdgeVector.end(); EWi != EWe; ++EWi) {
Edge e = (*EWi).first;
if (Forest.findLeader(e.first) != Forest.findLeader(e.second)) {
Forest.unionSets(e.first, e.second);
// So we know now that the edge is not already in a subtree, so we push
// the edge to the MST.
typename MaxSpanTree::iterator begin() {
return MST.begin();
typename MaxSpanTree::iterator end() {
return MST.end();
} // End llvm namespace