1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
|
// topsort.h
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
//
// \file
// Topological sort of FSTs
#ifndef FST_LIB_TOPSORT_H__
#define FST_LIB_TOPSORT_H__
#include <algorithm>
#include <vector>
#include "fst/lib/dfs-visit.h"
#include "fst/lib/fst.h"
#include "fst/lib/statesort.h"
namespace fst {
// DFS visitor class to return topological ordering.
template <class A>
class TopOrderVisitor {
public:
typedef A Arc;
typedef typename A::StateId StateId;
// If acyclic, ORDER[i] gives the topological position of state Id i;
// otherwise unchanged. ACYCLIC will be true iff the FST has
// no cycles.
TopOrderVisitor(vector<StateId> *order, bool *acyclic)
: order_(order), acyclic_(acyclic) {}
void InitVisit(const Fst<A> &fst) {
finish_ = new vector<StateId>;
*acyclic_ = true;
}
bool InitState(StateId s, StateId r) { return true; }
bool TreeArc(StateId s, const A &arc) { return true; }
bool BackArc(StateId s, const A &arc) { return (*acyclic_ = false); }
bool ForwardOrCrossArc(StateId s, const A &arc) { return true; }
void FinishState(StateId s, StateId p, const A *) { finish_->push_back(s); }
void FinishVisit() {
if (*acyclic_) {
order_->clear();
for (StateId s = 0; s < (StateId)finish_->size(); ++s)
order_->push_back(kNoStateId);
for (StateId s = 0; s < (StateId)finish_->size(); ++s)
(*order_)[(*finish_)[finish_->size() - s - 1]] = s;
}
delete finish_;
}
private:
vector<StateId> *order_;
bool *acyclic_;
vector<StateId> *finish_; // states in finishing-time order
};
// Topologically sorts its input if acyclic, modifying it. Otherwise,
// the input is unchanged. When sorted, all transitions are from
// lower to higher state IDs.
//
// Complexity:
// - Time: O(V + E)
// - Space: O(V + E)
// where V = # of states and E = # of arcs.
template <class Arc>
bool TopSort(MutableFst<Arc> *fst) {
typedef typename Arc::StateId StateId;
vector<StateId> order;
bool acyclic;
TopOrderVisitor<Arc> top_order_visitor(&order, &acyclic);
DfsVisit(*fst, &top_order_visitor);
if (acyclic) {
StateSort(fst, order);
fst->SetProperties(kAcyclic | kInitialAcyclic | kTopSorted,
kAcyclic | kInitialAcyclic | kTopSorted);
} else {
fst->SetProperties(kCyclic | kNotTopSorted, kCyclic | kNotTopSorted);
}
return acyclic;
}
} // namespace fst
#endif // FST_LIB_TOPSORT_H__
|
