-
Notifications
You must be signed in to change notification settings - Fork 31
/
UnionFind.py
290 lines (232 loc) · 8.98 KB
/
UnionFind.py
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
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
from collections import defaultdict
from typing import Callable, DefaultDict, Generic, Hashable, Iterable, List, Optional, TypeVar
T = TypeVar("T", bound=Hashable)
class UnionFindMap(Generic[T]):
"""当元素不是数组index时(例如字符串),更加通用的并查集写法,支持动态添加"""
__slots__ = ("part", "_parent", "_rank")
def __init__(self, iterable: Optional[Iterable[T]] = None):
self.part = 0
self._parent = dict()
self._rank = dict()
for item in iterable or []:
self.add(item)
def union(self, key1: T, key2: T) -> bool:
"""按秩合并."""
root1 = self.find(key1)
root2 = self.find(key2)
if root1 == root2:
return False
if self._rank[root1] > self._rank[root2]:
root1, root2 = root2, root1
self._parent[root1] = root2
self._rank[root2] += self._rank[root1]
self.part -= 1
return True
def unionTo(self, child: T, parent: T) -> bool:
"""定向合并."""
root1 = self.find(child)
root2 = self.find(parent)
if root1 == root2:
return False
self._parent[root1] = root2
self._rank[root2] += self._rank[root1]
self.part -= 1
return True
def find(self, key: T) -> T:
if key not in self._parent:
self.add(key)
return key
while self._parent.get(key, key) != key:
self._parent[key] = self._parent[self._parent[key]]
key = self._parent[key]
return key
def isConnected(self, key1: T, key2: T) -> bool:
return self.find(key1) == self.find(key2)
def getRoots(self) -> List[T]:
return list(set(self.find(key) for key in self._parent))
def getGroups(self) -> DefaultDict[T, List[T]]:
groups = defaultdict(list)
for key in self._parent:
root = self.find(key)
groups[root].append(key)
return groups
def getSize(self, key: T) -> int:
return self._rank[self.find(key)]
def add(self, key: T) -> bool:
if key in self._parent:
return False
self._parent[key] = key
self._rank[key] = 1
self.part += 1
return True
def __repr__(self) -> str:
return "\n".join(f"{root}: {member}" for root, member in self.getGroups().items())
def __len__(self) -> int:
return self.part
def __contains__(self, key: T) -> bool:
return key in self._parent
class UnionFindArray:
"""元素是0-n-1的并查集写法,不支持动态添加
初始化的连通分量个数 为 n
"""
__slots__ = ("n", "part", "_parent", "_rank")
def __init__(self, n: int):
self.n = n
self.part = n
self._parent = list(range(n))
self._rank = [1] * n
def find(self, x: int) -> int:
while self._parent[x] != x:
self._parent[x] = self._parent[self._parent[x]]
x = self._parent[x]
return x
def union(self, x: int, y: int) -> bool:
"""按秩合并."""
rootX = self.find(x)
rootY = self.find(y)
if rootX == rootY:
return False
if self._rank[rootX] > self._rank[rootY]:
rootX, rootY = rootY, rootX
self._parent[rootX] = rootY
self._rank[rootY] += self._rank[rootX]
self.part -= 1
return True
def unionTo(self, child: int, parent: int) -> bool:
"""定向合并.将child的父节点设置为parent."""
rootX = self.find(child)
rootY = self.find(parent)
if rootX == rootY:
return False
self._parent[rootX] = rootY
self._rank[rootY] += self._rank[rootX]
self.part -= 1
return True
def unionWithCallback(self, x: int, y: int, f: Callable[[int, int], None]) -> bool:
"""
f: 合并后的回调函数, 入参为 (big, small)
"""
rootX = self.find(x)
rootY = self.find(y)
if rootX == rootY:
return False
if self._rank[rootX] > self._rank[rootY]:
rootX, rootY = rootY, rootX
self._parent[rootX] = rootY
self._rank[rootY] += self._rank[rootX]
self.part -= 1
f(rootY, rootX)
return True
def isConnected(self, x: int, y: int) -> bool:
return self.find(x) == self.find(y)
def getGroups(self) -> DefaultDict[int, List[int]]:
groups = defaultdict(list)
for key in range(self.n):
root = self.find(key)
groups[root].append(key)
return groups
def getRoots(self) -> List[int]:
return list(set(self.find(key) for key in self._parent))
def getSize(self, x: int) -> int:
return self._rank[self.find(x)]
def __repr__(self) -> str:
return "\n".join(f"{root}: {member}" for root, member in self.getGroups().items())
def __len__(self) -> int:
return self.part
class UnionFindMap2(Generic[T]):
"""不自动合并 需要手动add添加元素"""
__slots__ = ("part", "_parent", "_rank")
def __init__(self, iterable: Optional[Iterable[T]] = None):
self.part = 0
self._parent = dict()
self._rank = defaultdict(lambda: 1)
for item in iterable or []:
self.add(item)
def add(self, key: T) -> "UnionFindMap2[T]":
if key in self._parent:
return self
self._parent[key] = key
self._rank[key] = 1
self.part += 1
return self
def union(self, key1: T, key2: T) -> bool:
"""rank一样时 默认key2作为key1的父节点"""
root1 = self.find(key1)
root2 = self.find(key2)
if root1 == root2 or root1 not in self._parent or root2 not in self._parent:
return False
if self._rank[root1] > self._rank[root2]:
root1, root2 = root2, root1
self._parent[root1] = root2
self._rank[root2] += self._rank[root1]
self.part -= 1
return True
def find(self, key: T) -> T:
"""此处不自动add"""
if key not in self._parent:
return key
if key != self._parent[key]:
root = self.find(self._parent[key])
self._parent[key] = root
return self._parent[key]
def isConnected(self, key1: T, key2: T) -> bool:
if key1 not in self._parent or key2 not in self._parent:
return False
return self.find(key1) == self.find(key2)
def getRoots(self) -> List[T]:
return list(set(self.find(key) for key in self._parent))
def getGroups(self) -> DefaultDict[T, List[T]]:
groups = defaultdict(list)
for key in self._parent:
root = self.find(key)
groups[root].append(key)
return groups
def getSize(self, key: T) -> int:
return self._rank[self.find(key)]
def __repr__(self) -> str:
return "\n".join(f"{root}: {member}" for root, member in self.getGroups().items())
def __len__(self) -> int:
return self.part
def __contains__(self, key: T) -> bool:
return key in self._parent
class UnionFindGraph:
"""并查集维护无向图每个连通块的边数和顶点数"""
__slots__ = ("n", "part", "_parent", "vertex", "edge")
def __init__(self, n: int):
self.n = n
self.part = n
self.vertex = [1] * n # 每个联通块的顶点数
self.edge = [0] * n # 每个联通块的边数
self._parent = list(range(n))
def find(self, x: int) -> int:
while x != self._parent[x]:
self._parent[x] = self._parent[self._parent[x]]
x = self._parent[x]
return x
def union(self, x: int, y: int) -> bool:
rootX = self.find(x)
rootY = self.find(y)
if rootX == rootY:
self.edge[rootX] += 1 # !两个顶点已经在同一个连通块了,这个连通块的边数+1
return False
if self.vertex[rootX] > self.vertex[rootY]:
rootX, rootY = rootY, rootX
self._parent[rootX] = rootY
self.vertex[rootY] += self.vertex[rootX]
self.edge[rootY] += self.edge[rootX] + 1
self.part -= 1
return True
def getSize(self, x: int) -> int:
return self.vertex[self.find(x)]
def getEdge(self, x: int) -> int:
return self.edge[self.find(x)]
def isConnected(self, x: int, y: int) -> bool:
return self.find(x) == self.find(y)
def getGroups(self) -> DefaultDict[int, List[int]]:
groups = defaultdict(list)
for key in range(self.n):
root = self.find(key)
groups[root].append(key)
return groups
def __repr__(self) -> str:
return "\n".join(f"{root}: {member}" for root, member in self.getGroups().items())