union-find.h revision f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2
1f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
2f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// Licensed under the Apache License, Version 2.0 (the "License");
3f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// you may not use this file except in compliance with the License.
4f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// You may obtain a copy of the License at
5f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson//
6f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson//     http://www.apache.org/licenses/LICENSE-2.0
7f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson//
8f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// Unless required by applicable law or agreed to in writing, software
9f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// distributed under the License is distributed on an "AS IS" BASIS,
10f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
11f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// See the License for the specific language governing permissions and
12f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// limitations under the License.
13f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson//
14f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// Copyright 2005-2010 Google, Inc.
15f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// Author: wojciech@google.com (Wojciech Skut)
16f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson//
17f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// \file Union-Find algorithm for dense sets of non-negative
18f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// integers. Implemented using disjoint tree forests with rank
19f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// heuristics and path compression.
20f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
21f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson#ifndef __fst_union_find_inl_h__
22f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson#define __fst_union_find_inl_h__
23f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
24f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson#include <stack>
25f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson#include <vector>
26f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodsonusing std::vector;
27f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson#include <fst/types.h>
28f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
29f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodsonnamespace fst {
30f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
31f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// Union-Find algorithm for dense sets of non-negative integers
32f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson// (exact type: T).
33f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodsontemplate <class T>
34f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodsonclass UnionFind {
35f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson public:
36f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // Ctor: creates a disjoint set forest for the range [0;max).
37f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // 'fail' is a value indicating that an element hasn't been
38f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // initialized using MakeSet(...). The upper bound of the range
39f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // can be reset (increased) using MakeSet(...).
40f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  UnionFind(T max, T fail)
41f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      : parent_(max, fail), rank_(max), fail_(fail) { }
42f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
43f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // Finds the representative of the set 'item' belongs to.
44f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // Performs path compression if needed.
45f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  T FindSet(T item) {
46f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    if (item >= parent_.size()
47f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson        || item == fail_
48f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson        || parent_[item] == fail_) return fail_;
49f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
50f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    T *p = &parent_[item];
51f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    for (; *p != item; item = *p, p = &parent_[item]) {
52f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      exec_stack_.push(p);
53f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    }
54f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    for (; ! exec_stack_.empty(); exec_stack_.pop()) {
55f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      *exec_stack_.top() = *p;
56f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    }
57f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    return *p;
58f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  }
59f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
60f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // Creates the (destructive) union of the sets x and y belong to.
61f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  void Union(T x, T y) {
62f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    Link(FindSet(x), FindSet(y));
63f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  }
64f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
65f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // Initialization of an element: creates a singleton set containing
66f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // 'item'. The range [0;max) is reset if item >= max.
67f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  T MakeSet(T item) {
68f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    if (item >= parent_.size()) {
69f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      // New value in parent_ should be initialized to fail_
70f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      size_t nitem = item > 0 ? 2 * item : 2;
71f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      parent_.resize(nitem, fail_);
72f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      rank_.resize(nitem);
73f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    }
74f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    parent_[item] = item;
75f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    return item;
76f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  }
77f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
78f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // Initialization of all elements starting from 0 to max - 1 to distinct sets
79f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  void MakeAllSet(T max) {
80f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    parent_.resize(max);
81f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    for (T item = 0; item < max; ++item) {
82f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      parent_[item] = item;
83f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    }
84f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  }
85f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
86f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson private:
87f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  vector<T> parent_;      // Parent nodes.
88f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  vector<int> rank_;      // Rank of an element = min. depth in tree.
89f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  T fail_;                // Value indicating lookup failure.
90f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  stack<T*> exec_stack_;  // Used for path compression.
91f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
92f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  // Links trees rooted in 'x' and 'y'.
93f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  void Link(T x, T y) {
94f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    if (x == y) return;
95f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
96f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    if (rank_[x] > rank_[y]) {
97f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      parent_[y] = x;
98f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    } else {
99f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      parent_[x] = y;
100f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      if (rank_[x] == rank_[y]) {
101f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson        ++rank_[y];
102f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson      }
103f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson    }
104f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  }
105f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson  DISALLOW_COPY_AND_ASSIGN(UnionFind);
106f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson};
107f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
108f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson}  // namespace fst
109f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson
110f4c12fce1ee58e670f9c3fce46c40296ba9ee8a2Ian Hodson#endif  // __fst_union_find_inl_h__
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