// 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_