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
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
|
import random
from rpython.tool.algo.graphlib import *
def copy_edges(edges):
result = {}
for key, value in edges.items():
result[key] = value[:]
return result
# ____________________________________________________________
class TestSimple:
edges = {
'A': [Edge('A','B'), Edge('A','C')],
'B': [Edge('B','D'), Edge('B','E')],
'C': [Edge('C','F')],
'D': [Edge('D','D')],
'E': [Edge('E','A'), Edge('E','C')],
'F': [],
'G': [],
}
def test_depth_first_search(self):
# 'D' missing from the list of vertices
lst = depth_first_search('A', list('ABCEFG'), self.edges)
assert lst == [
('start', 'A'),
('start', 'B'),
('start', 'E'),
('start', 'C'),
('start', 'F'),
('stop', 'F'),
('stop', 'C'),
('stop', 'E'),
('stop', 'B'),
('stop', 'A'),
]
def test_strong_components(self):
edges = self.edges
saved = copy_edges(edges)
result = list(strong_components(edges, edges))
assert edges == saved
for comp in result:
comp = list(comp)
comp.sort()
result = [''.join(comp) for comp in result]
result.sort()
assert result == ['ABE', 'C', 'D', 'F', 'G']
def test_all_cycles(self):
edges = self.edges
saved = copy_edges(edges)
cycles = list(all_cycles('A', edges, edges))
assert edges == saved
cycles.sort()
expected = [
[edges['A'][0], edges['B'][1], edges['E'][0]],
[edges['D'][0]],
]
expected.sort()
assert cycles == expected
def test_break_cycles(self):
edges = self.edges
saved = copy_edges(edges)
result = list(break_cycles(edges, edges))
assert edges == saved
assert len(result) == 2
assert edges['D'][0] in result
assert (edges['A'][0] in result or
edges['B'][1] in result or
edges['E'][0] in result)
def test_break_cycles_v(self):
edges = copy_edges(self.edges)
edges['R'] = [Edge('R', 'B')]
saved = copy_edges(edges)
result = list(break_cycles_v(edges, edges))
assert edges == saved
assert len(result) == 2
result.sort()
assert ''.join(result) == 'AD'
# the answers 'BD' and 'DE' are correct too, but 'AD' should
# be picked because 'A' is the cycle's node that is the further
# from the root 'R'.
def test_find_roots(self):
roots = list(find_roots(self.edges, self.edges))
roots.sort()
assert ''.join(roots) in ('AG', 'BG', 'EG')
edges = copy_edges(self.edges)
edges['R'] = [Edge('R', 'B')]
roots = list(find_roots(edges, edges))
roots.sort()
assert ''.join(roots) == 'GR'
class TestLoops:
# a graph with 20 loops of length 10 each, plus an edge from each loop to
# the next, non-cylically
edges = {}
for i in range(200):
j = i+1
if j % 10 == 0:
j -= 10
edges[i] = [Edge(i, j)]
for i in range(19):
edges[i*10].append(Edge(i*10, i*10+15))
vertices = dict([(i, True) for i in range(200)])
def test_strong_components(self):
edges = self.edges
result = list(strong_components(self.vertices, edges))
assert len(result) == 20
result2 = []
for comp in result:
comp = list(comp)
comp.sort()
result2.append(comp)
result2.sort()
for i in range(20):
comp = result2[i]
assert comp == range(i*10, (i+1)*10)
def test_break_cycles(self, edges=None):
edges = edges or self.edges
result = list(break_cycles(self.vertices, edges))
assert len(result) == 20
result = [(edge.source, edge.target) for edge in result]
result.sort()
for i in range(20):
assert i*10 <= result[i][0] <= (i+1)*10
assert i*10 <= result[i][1] <= (i+1)*10
def test_break_cycles_2(self):
edges = copy_edges(self.edges)
edges[190].append(Edge(190, 5))
self.test_break_cycles(edges)
def test_find_roots(self):
roots = find_roots(self.vertices, self.edges)
assert len(roots) == 1
v = list(roots)[0]
assert v in range(10)
def test_find_roots_2(self):
edges = copy_edges(self.edges)
edges[190].append(Edge(190, 5))
roots = find_roots(self.vertices, edges)
assert len(roots) == 1
class TestTree:
edges = make_edge_dict([Edge(i//2, i) for i in range(1, 52)])
def test_strong_components(self):
result = list(strong_components(self.edges, self.edges))
assert len(result) == 52
vertices = []
for comp in result:
assert len(comp) == 1
vertices += comp
vertices.sort()
assert vertices == range(52)
def test_all_cycles(self):
result = list(all_cycles(0, self.edges, self.edges))
assert not result
def test_break_cycles(self):
result = list(break_cycles(self.edges, self.edges))
assert not result
def test_find_roots(self):
roots = find_roots(self.edges, self.edges)
assert len(roots) == 1
v = list(roots)[0]
assert v == 0
class TestChainAndLoop:
edges = make_edge_dict([Edge(i,i+1) for i in range(100)] + [Edge(100,99)])
def test_strong_components(self):
result = list(strong_components(self.edges, self.edges))
assert len(result) == 100
vertices = []
for comp in result:
assert (len(comp) == 1 or
(len(comp) == 2 and 99 in comp and 100 in comp))
vertices += comp
vertices.sort()
assert vertices == range(101)
class TestBugCase:
edges = make_edge_dict([Edge(0,0), Edge(1,0), Edge(1,2), Edge(2,1)])
def test_strong_components(self):
result = list(strong_components(self.edges, self.edges))
assert len(result) == 2
result.sort()
assert list(result[0]) == [0]
assert list(result[1]) in ([1,2], [2,1])
class TestBadCase:
# a complete graph
NUM = 50
edges = make_edge_dict([Edge(i, j) for i in range(NUM)
for j in range(NUM)])
vertices = dict.fromkeys(range(NUM))
def test_break_cycles(self):
result = list(break_cycles(self.edges, self.edges))
print len(result)
assert result
def test_find_roots(self):
roots = find_roots(self.edges, self.edges)
assert len(roots) == 1
assert list(roots)[0] in self.edges
class TestRandom:
edges = make_edge_dict([Edge(random.randrange(0,100),
random.randrange(0,100)) for i in range(150)])
def test_strong_components(self):
result = list(strong_components(self.edges, self.edges))
vertices = []
for comp in result:
vertices += comp
vertices.sort()
expected = self.edges.keys()
expected.sort()
assert vertices == expected
def test_break_cycles(self):
list(break_cycles(self.edges, self.edges))
# assert is_acyclic(): included in break_cycles() itself
def test_break_cycles_v(self):
result = list(break_cycles_v(self.edges, self.edges))
# assert is_acyclic(): included in break_cycles_v() itself
print len(result), 'vertices removed'
def test_find_roots(self):
roots = find_roots(self.edges, self.edges)
reachable = set()
for root in roots:
reachable |= set(vertices_reachable_from(root, self.edges,
self.edges))
assert reachable == set(self.edges)
|
