union-find.h revision f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2 
1
2// Licensed under the Apache License, Version 2.0 (the "License");
3// you may not use this file except in compliance with the License.
4// You may obtain a copy of the License at
5//
6//     http://www.apache.org/licenses/LICENSE-2.0
7//
8// Unless required by applicable law or agreed to in writing, software
9// distributed under the License is distributed on an "AS IS" BASIS,
10// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
11// See the License for the specific language governing permissions and
12// limitations under the License.
13//
14// Copyright 2005-2010 Google, Inc.
15// Author: wojciech@google.com (Wojciech Skut)
16//
17// \file Union-Find algorithm for dense sets of non-negative
18// integers. Implemented using disjoint tree forests with rank
19// heuristics and path compression.
20
21#ifndef __fst_union_find_inl_h__
22#define __fst_union_find_inl_h__
23
24#include <stack>
25#include <vector>
26using std::vector;
27#include <fst/types.h>
28
29namespace fst {
30
31// Union-Find algorithm for dense sets of non-negative integers
32// (exact type: T).
33template <class T>
34class UnionFind {
35 public:
36  // Ctor: creates a disjoint set forest for the range [0;max).
37  // 'fail' is a value indicating that an element hasn't been
38  // initialized using MakeSet(...). The upper bound of the range
39  // can be reset (increased) using MakeSet(...).
40  UnionFind(T max, T fail)
41      : parent_(max, fail), rank_(max), fail_(fail) { }
42
43  // Finds the representative of the set 'item' belongs to.
44  // Performs path compression if needed.
45  T FindSet(T item) {
46    if (item >= parent_.size()
47        || item == fail_
48        || parent_[item] == fail_) return fail_;
49
50    T *p = &parent_[item];
51    for (; *p != item; item = *p, p = &parent_[item]) {
52      exec_stack_.push(p);
53    }
54    for (; ! exec_stack_.empty(); exec_stack_.pop()) {
55      *exec_stack_.top() = *p;
56    }
57    return *p;
58  }
59
60  // Creates the (destructive) union of the sets x and y belong to.
61  void Union(T x, T y) {
62    Link(FindSet(x), FindSet(y));
63  }
64
65  // Initialization of an element: creates a singleton set containing
66  // 'item'. The range [0;max) is reset if item >= max.
67  T MakeSet(T item) {
68    if (item >= parent_.size()) {
69      // New value in parent_ should be initialized to fail_
70      size_t nitem = item > 0 ? 2 * item : 2;
71      parent_.resize(nitem, fail_);
72      rank_.resize(nitem);
73    }
74    parent_[item] = item;
75    return item;
76  }
77
78  // Initialization of all elements starting from 0 to max - 1 to distinct sets
79  void MakeAllSet(T max) {
80    parent_.resize(max);
81    for (T item = 0; item < max; ++item) {
82      parent_[item] = item;
83    }
84  }
85
86 private:
87  vector<T> parent_;      // Parent nodes.
88  vector<int> rank_;      // Rank of an element = min. depth in tree.
89  T fail_;                // Value indicating lookup failure.
90  stack<T*> exec_stack_;  // Used for path compression.
91
92  // Links trees rooted in 'x' and 'y'.
93  void Link(T x, T y) {
94    if (x == y) return;
95
96    if (rank_[x] > rank_[y]) {
97      parent_[y] = x;
98    } else {
99      parent_[x] = y;
100      if (rank_[x] == rank_[y]) {
101        ++rank_[y];
102      }
103    }
104  }
105  DISALLOW_COPY_AND_ASSIGN(UnionFind);
106};
107
108}  // namespace fst
109
110#endif  // __fst_union_find_inl_h__
111