-
Notifications
You must be signed in to change notification settings - Fork 0
/
AVL_tree.py
257 lines (209 loc) · 7.57 KB
/
AVL_tree.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
# import random, math
outputdebug = False
def debug(msg):
if outputdebug:
print msg
class Node ():
def __init__(self, key):
self.key = key
self.left = None
self.right = None
class AVLTree ():
def __init__(self, *args):
self.node = None
self.height = -1
self.balance = 0;
if len ( args ) == 1:
for i in args[0]:
self.insert ( i )
def height(self):
if self.node:
return self.node.height
else:
return 0
def is_leaf(self):
return (self.height == 0)
def insert(self, key):
tree = self.node
newnode = Node ( key )
if tree == None:
self.node = newnode
self.node.left = AVLTree ()
self.node.right = AVLTree ()
debug ( "Inserted key [" + str ( key ) + "]" )
elif key < tree.key:
self.node.left.insert ( key )
elif key > tree.key:
self.node.right.insert ( key )
else:
debug ( "Key [" + str ( key ) + "] already in tree." )
self.rebalance ()
def rebalance(self):
'''
Rebalance a particular (sub)tree
'''
# key inserted. Let's check if we're balanced
self.update_heights ( False )
self.update_balances ( False )
while self.balance < -1 or self.balance > 1:
if self.balance > 1:
if self.node.left.balance < 0:
self.node.left.lrotate () # we're in case II
self.update_heights ()
self.update_balances ()
self.rrotate ()
self.update_heights ()
self.update_balances ()
if self.balance < -1:
if self.node.right.balance > 0:
self.node.right.rrotate () # we're in case III
self.update_heights ()
self.update_balances ()
self.lrotate ()
self.update_heights ()
self.update_balances ()
def rrotate(self):
# Rotate left pivoting on self
debug ( 'Rotating ' + str ( self.node.key ) + ' right' )
A = self.node
B = self.node.left.node
T = B.right.node
self.node = B
B.right.node = A
A.left.node = T
def lrotate(self):
# Rotate left pivoting on self
debug ( 'Rotating ' + str ( self.node.key ) + ' left' )
A = self.node
B = self.node.right.node
T = B.left.node
self.node = B
B.left.node = A
A.right.node = T
def update_heights(self, recurse=True):
if not self.node == None:
if recurse:
if self.node.left != None:
self.node.left.update_heights ()
if self.node.right != None:
self.node.right.update_heights ()
self.height = max ( self.node.left.height,
self.node.right.height ) + 1
else:
self.height = -1
def update_balances(self, recurse=True):
if not self.node == None:
if recurse:
if self.node.left != None:
self.node.left.update_balances ()
if self.node.right != None:
self.node.right.update_balances ()
self.balance = self.node.left.height - self.node.right.height
else:
self.balance = 0
def delete(self, key):
# debug("Trying to delete at node: " + str(self.node.key))
if self.node != None:
if self.node.key == key:
debug ( "Deleting ... " + str ( key ) )
if self.node.left.node == None and self.node.right.node == None:
self.node = None # leaves can be killed at will
# if only one subtree, take that
elif self.node.left.node == None:
self.node = self.node.right.node
elif self.node.right.node == None:
self.node = self.node.left.node
# worst-case: both children present. Find logical successor
else:
replacement = self.logical_successor ( self.node )
if replacement != None: # sanity check
debug ( "Found replacement for " + str ( key ) + " -> " + str ( replacement.key ) )
self.node.key = replacement.key
# replaced. Now delete the key from right child
self.node.right.delete ( replacement.key )
self.rebalance ()
return
elif key < self.node.key:
self.node.left.delete ( key )
elif key > self.node.key:
self.node.right.delete ( key )
self.rebalance ()
else:
return
def logical_predecessor(self, node):
'''
Find the biggest valued node in LEFT child
'''
node = node.left.node
if node != None:
while node.right != None:
if node.right.node == None:
return node
else:
node = node.right.node
return node
def logical_successor(self, node):
'''
Find the smallese valued node in RIGHT child
'''
node = node.right.node
if node != None: # just a sanity check
while node.left != None:
debug ( "LS: traversing: " + str ( node.key ) )
if node.left.node == None:
return node
else:
node = node.left.node
return node
def check_balanced(self):
if self == None or self.node == None:
return True
# We always need to make sure we are balanced
self.update_heights ()
self.update_balances ()
return ((abs ( self.balance ) < 2) and self.node.left.check_balanced () and self.node.right.check_balanced ())
def inorder_traverse(self):
if self.node == None:
return []
inlist = []
l = self.node.left.inorder_traverse ()
for i in l:
inlist.append ( i )
inlist.append ( self.node.key )
l = self.node.right.inorder_traverse ()
for i in l:
inlist.append ( i )
return inlist
def display(self, level=0, pref=''):
'''
Display the whole tree. Uses recursive def.
TODO: create a better display using breadth-first search
'''
self.update_heights () # Must update heights before balances
self.update_balances ()
if (self.node != None):
print '-' * level * 2, pref, self.node.key, "[" + str ( self.height ) + ":" + str (
self.balance ) + "]", 'L' if self.is_leaf () else ' '
if self.node.left != None:
self.node.left.display ( level + 1, '<' )
if self.node.left != None:
self.node.right.display ( level + 1, '>' )
# Usage example
if __name__ == "__main__":
a = AVLTree ()
print "----- Inserting -------"
# inlist = [5, 2, 12, -4, 3, 21, 19, 25]
inlist = [7, 5, 2, 6, 3, 4, 1, 8, 9, 0]
for i in inlist:
a.insert ( i )
a.display ()
print "----- Deleting -------"
a.delete ( 3 )
a.delete ( 4 )
# a.delete(5)
a.display ()
print
print "Input :", inlist
print "deleting ... ", 3
print "deleting ... ", 4
print "Inorder traversal:", a.inorder_traverse ()