-
Notifications
You must be signed in to change notification settings - Fork 226
Expand file tree
/
Copy pathBinarySearchTre.py
More file actions
434 lines (341 loc) · 12.3 KB
/
BinarySearchTre.py
File metadata and controls
434 lines (341 loc) · 12.3 KB
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
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun Oct 2 11:36:12 2022
@author: rik
"""
class Tree():
class Position():
def element(self):
raise NotImplementedError('must be implemented by a subclass')
def __eq__(self):
raise NotImplementedError('must be implemented by a subclass')
def __ne__(self,other):
return not(self==other)
def root(self):
raise NotImplementedError('must be implemented by a subclass')
def parent(self,p):
raise NotImplementedError('must be implemented by a subclass')
def num_children(self,p):
raise NotImplementedError('must be implemented by a subclass')
def children(self,p):
raise NotImplementedError('must be implemented by a subclass')
def __len__(self):
raise NotImplementedError('must be implemented by a subclass')
def __iter__(self):
for p in self.positions():
yield p.element()
def is_root(self,p):
return self.root()==p
def is_leaf(self,p):
return self.num_children(p)==0
def is_empty(self):
return len(self)==0
def depth(self,p):
if self.is_root(p):
return 0
else:
return 1+self.depth(self.parent(p))
def _height2(self,p):
if self.is_leaf(p):
return 0
else:
return 1+max(self._height2(c) for c in self.children(p))
def height(self,p=None):
if p is None:
p=self.root()
return self._height2(p)
def preorder(self):
if not self.is_empty():
for p in self._subtree_preorder(self.root()):
yield p
def postorder(self):
if not self.is_empty():
for p in self._subtree_postorder(self.root()):
yield p
def _subtree_postorder(self,p):
for c in self.children(p):
for other in self._subtree_postorder(c):
yield other
yield p
def _subtree_preorder(self,p):
yield p
for c in self.children(p):
for other in self._subtree_preorder(c):
yield other
def positions(self):
return self.preorder()
class BinaryTree(Tree):
def left(self,p):
raise NotImplementedError('must be implemented by a subclass')
def right(self,p):
raise NotImplementedError('must be implemented by a subclass')
def sibling(self,p):
parent=self.parent(p)
if parent is None:
return None
else:
if p==self.left(parent):
return self.right(parent)
else:
return self.left(parent)
def children(self,p):
if self.left(p) is not None:
yield self.left(p)
if self.right(p) is not None:
yield self.right(p)
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Oct 1 20:18:16 2022
@author: rik
"""
class LinkedBinaryTree(BinaryTree):
class _Node():
__slots__='_element','_parent','_right','_left'
def __init__(self,element,parent,right,left):
self._element=element
self._parent=parent
self._right=right
self._left=left
class Position(BinaryTree.Position):
def __init__(self,container,node):
self._container=container
self._node=node
def element(self):
return self._node._element
def __eq__(self,other):
return type(other) is type(self) and other._node is self._node
def _validate(self,p):
if not isinstance(p,self.Position):
raise TypeError(' p must be proper position type')
if p._container is not self:
raise ValueError(' p does not belong to this container')
if p._node._parent is p._node:
raise ValueError('p is deprecated')
return p._node
def _make_position(self,node):
return self.Position(self,node) if node is not None else None
def __init__(self):
self._root=None
self._size=0
def __len__(self):
return self._size
def root(self):
return self._make_position(self.root)
def parent(self,p):
node=self._validate(p)
return self._make_position(node._parent)
def left(self,p):
node=self._validate(p)
return self._make_position(node._left)
def right(self,p):
node=self._validate(p)
return self._make_position(node._right)
def num_children(self,p):
node=self._validate(p)
count=0
if node._left is not None:
count+=1
if node._right is not None:
count+=1
return count
def _add_root(self,e):
if self._root is not None: raise ValueError('root already exists')
self._size=1
self._root=self._Node(e)
return self._make_position(self._root)
def _add_left(self,e):
node=self._validate(e)
if node._left is not None: raise ValueError('left child already exists')
self._size+=1
node._left=self._Node(e,node)
return self._make_position(node._left)
def _add_right(self,e):
node=self._validate(e)
if node._right is not None: raise ValueError('right child already exists')
self._size+=1
node._right=self._Node(e,node)
return self._make_position(node._right)
def _replace(self,p,e):
node=self._validate(p)
old=node._element
node._element=e
return old
def _delete(self,p):
node=self._validate(p)
if self.num_children(p)==2: raise ValueError('p has two children')
child=node._left if node._left else node._right
if child is not None:
child._parent=node._parent
if node is self._root:
self._root=child
else:
parent=node._parent
if node is parent._left:
parent._left=child
else:
parent._right=child
self._size-=1
node._parent=node
return node._element
def _attach(self, p, t1,t2):
node=self._validate(p)
if not self.is_leaf(p): raise ValueError('position must be leaf')
if not type(self) is type(t1) is type(t2):
raise TypeError('all trees must be concordant types')
self._size+=len(t1)+len(t2)
if not t1.is_empty():
t1._root._parent=node
node._left=t1._root
t1._root=None
t1._size=0
if not t2.is_empty():
t2._root._parent=node
node._left=t1._root
t2._root=None
t2._size=0
from collections import MutableMapping
class Mapbase(MutableMapping):
class _Item:
__slots__='_key','_value'
def __init__(self,k,v):
self._key=k
self._value=v
def __eq__(self,other):
return self._key==other._key
def __ne__(self,other):
return not(self==other)
def __It__(self,other):
return self._key<other._key
class BinarySearchTree(Mapbase,LinkedBinaryTree):
class Position(LinkedBinaryTree.Position):
def key(self):
return self.element()._key
def value(self):
return self.element()._value
def _subtree_search(self,p,k):
if k==p.key():
return p
elif k<p.key():
if self.left(p) is not None:
return self._subtree_search(self.left(p),k)
else:
if self.right(p) is not None:
return self._subtree_search(self.right(p),k)
return p
def _subtree_first_position(self,p):
walk=p
while self.left(walk) is not None:
walk=self.left(walk)
return walk
def _subtree_last_position(self,e):
walk=e
while self.right(walk) is not None:
walk=self.right(walk)
return walk
def first(self):
return self._subtree_first_position(self.root()) if len(self)>0 else None
def last(self):
return self._subtree_last_position(self.root()) if len(self)>0 else None
def before(self,p):
self._validate(p)
if self.left(p):
return self._subtree_last_position(self.left(p))
else:
walk=p
above=self.parent(walk)
while above is not None and walk==self.left(above):
walk=above
above=self.parent(walk)
return above
def after(self,p):
self.validate(p)
if self.right(p):
return self._subtree_last_position(self.left(p))
else:
walk=p
above=self.parent(walk)
while above is not None and walk==self.left(above):
walk=above
above=self.parent(walk)
return above
def find_position(self,k):
if self.is_empty():
return None
else:
p=self._subtree_search(self.root(),k)
self._rebalance_access(p)
return p
def find_min(self):
if self.is_empty():
return None
else:
p=self.first()
return (p.key(),p.value())
def find_ge(self,k):
if self.is_empty():
return None
else:
p=self.find_position(k)
if p.key()<k:
p=self.after(p)
return (p.key(),p.value()) if p is not None else None
def find_range(self,start,stop):
if self.is_empty():
if start is None:
p=self.first()
else:
p=self.find_position(start)
if p.key()<start:
p=self.after(p)
while p is not None and (stop is None or p.key()<stop):
yield (p.key(),p.value())
p=self.after(p)
def __getitem__(self,k):
if self.is_empty():
raise KeyError('Key Error'+repr(k))
else:
p=self._subtree_search(self.root(),k)
self._rebalance_access(p)
if k!=p.key():
raise KeyError('Key Error'+repr(k))
return p.value()
def __setitem__(self,k,v):
if self.is_empty():
leaf=self._add_root(self._Item(k,v))
else:
p=self._subtree_search(self.root(),k)
if p.key()==k:
p.element()._value=v
self._rebalance_access(p)
return
else:
item=self._Item(k,v)
if p.key()<k:
leaf=self._add_right(p,item)
else:
leaf=self._add_left(p,item)
self._rebalance_insert(leaf)
def __iter__(self):
p=self.first()
while p is not None:
yield p.key()
p=self.after(p)
def delete(self,p):
self._validate(p)
if self.left(p) and self.right(p):
replacement=self._subtree_last_position(self.left(p))
self._replace(p,replacement.element())
p=replacement
parent=self._parent(p)
self.delete(p)
self._rebalance_delete(parent)
def __delitem__(self,k):
if not self.is_empty():
p=self._subtree_search(self.root(),k)
if k==p.key():
self.delete(p)
return
self._rebalance_access(p)
raise KeyError('Key Erro'+repr(k))