// See www.openfst.org for extensive documentation on this weighted
|
// finite-state transducer library.
|
//
|
// Union-find algorithm for dense sets of non-negative integers, implemented
|
// using disjoint tree forests with rank heuristics and path compression.
|
|
#ifndef FST_UNION_FIND_H_
|
#define FST_UNION_FIND_H_
|
|
#include <stack>
|
#include <vector>
|
|
namespace fst {
|
|
// Union-Find algorithm for dense sets of non-negative integers.
|
template <class T>
|
class UnionFind {
|
public:
|
// Creates a disjoint set forest for the range [0; max); 'fail' is a value
|
// indicating that an element hasn't been initialized using MakeSet(...).
|
// The upper bound of the range can be reset (increased) using MakeSet(...).
|
UnionFind(T max, T fail) : parent_(max, fail), rank_(max), fail_(fail) {}
|
|
// Finds the representative of the set 'item' belongs to, performing path
|
// compression if necessary.
|
T FindSet(T item) {
|
if (item >= parent_.size() || item == fail_ || parent_[item] == fail_) {
|
return fail_;
|
}
|
auto *p = &parent_[item];
|
for (; *p != item; item = *p, p = &parent_[item]) exec_stack_.push(p);
|
for (; !exec_stack_.empty(); exec_stack_.pop()) *exec_stack_.top() = *p;
|
return *p;
|
}
|
|
// Creates the (destructive) union of the sets x and y belong to.
|
void Union(T x, T y) { Link(FindSet(x), FindSet(y)); }
|
|
// Initialization of an element: creates a singleton set containing 'item'.
|
// The range [0; max) is reset if item >= max.
|
T MakeSet(T item) {
|
if (item >= parent_.size()) {
|
// New value in parent_ should be initialized to fail_.
|
const auto nitem = item > 0 ? 2 * item : 2;
|
parent_.resize(nitem, fail_);
|
rank_.resize(nitem);
|
}
|
parent_[item] = item;
|
return item;
|
}
|
|
// Initialization of all elements starting from 0 to max - 1 to distinct sets.
|
void MakeAllSet(T max) {
|
parent_.resize(max);
|
for (T item = 0; item < max; ++item) parent_[item] = item;
|
}
|
|
private:
|
// Links trees rooted in 'x' and 'y'.
|
void Link(T x, T y) {
|
if (x == y) return;
|
if (rank_[x] > rank_[y]) {
|
parent_[y] = x;
|
} else {
|
parent_[x] = y;
|
if (rank_[x] == rank_[y]) {
|
++rank_[y];
|
}
|
}
|
}
|
|
UnionFind(const UnionFind &) = delete;
|
|
UnionFind &operator=(const UnionFind &) = delete;
|
|
std::vector<T> parent_; // Parent nodes.
|
std::vector<int> rank_; // Rank of an element = min. depth in tree.
|
T fail_; // Value indicating lookup failure.
|
std::stack<T *> exec_stack_; // Used for path compression.
|
};
|
|
} // namespace fst
|
|
#endif // FST_UNION_FIND_H_
|
