-
Notifications
You must be signed in to change notification settings - Fork 0
/
avl-tree.go
306 lines (274 loc) · 7.51 KB
/
avl-tree.go
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
package datastructures
import (
"math"
)
// AvlTree represents an avl tree data structure.
type AvlTree struct {
root *AvlNode
size int
}
// AvlNode is the node used in the avl tree data structure.
type AvlNode struct {
bf int
height int
Left *AvlNode
Right *AvlNode
Data float64
}
// NewAvlTree returns a new avl tree data structure.
func NewAvlTree() *AvlTree {
return &AvlTree{}
}
// Add adds a new node to the avl tree.
func (avl *AvlTree) Add(elem float64) *AvlTree {
avl.root = avl.insert(avl.root, elem)
avl.size++
return avl
}
// insert is a helper method for inserting new nodes in the avl
// tree.
func (avl *AvlTree) insert(node *AvlNode, elem float64) *AvlNode {
if node == nil {
return &AvlNode{Data: elem}
}
if elem == node.Data {
return node // do nothing
}
if elem > node.Data {
node.Right = avl.insert(node.Right, elem)
}
if elem < node.Data {
node.Left = avl.insert(node.Left, elem)
}
avl.update(node)
return avl.balance(node)
}
// update is a helper method to update the height and balance factor
// of a node.
func (avl *AvlTree) update(node *AvlNode) {
leftHeight := -1
rightHeight := -1
if node.Left != nil {
leftHeight = node.Left.height
}
if node.Right != nil {
rightHeight = node.Right.height
}
node.bf = rightHeight - leftHeight
node.height = 1 + int(math.Max(float64(leftHeight), float64(rightHeight)))
}
// balance is the helper method to balance the avl tree if the balance
// factor not in {-1, 0, +1}.
func (avl *AvlTree) balance(node *AvlNode) *AvlNode {
// left heavy
if node.bf == -2 {
if node.Left.bf <= 0 {
return avl.leftLeftCaseRotation(node)
}
return avl.leftRightCaseRotation(node)
}
// right heavy
if node.bf == 2 {
if node.Right.bf >= 0 {
return avl.rightRightCaseRotation(node)
}
return avl.rightLeftCaseRotation(node)
}
return node
}
// leftLeftCaseRotation is a helper method to handle left-left
// case rotation.
func (avl *AvlTree) leftLeftCaseRotation(node *AvlNode) *AvlNode {
return avl.rotateRight(node)
}
// leftRightCaseRotation is a helper method to handle left-right
// case rotation.
func (avl *AvlTree) leftRightCaseRotation(node *AvlNode) *AvlNode {
node.Left = avl.rotateLeft(node.Left)
return avl.leftLeftCaseRotation(node)
}
// rightLeftCaseRotation is a helper method to handle right-left
// case rotation.
func (avl *AvlTree) rightLeftCaseRotation(node *AvlNode) *AvlNode {
node.Right = avl.rotateRight(node.Right)
return avl.rightRightCaseRotation(node)
}
// rightRightCaseRotation is a helper method to handle right-right
// case rotation.
func (avl *AvlTree) rightRightCaseRotation(node *AvlNode) *AvlNode {
return avl.rotateLeft(node)
}
// rotateRight is a helper method to do a right rotation on
// a node.
func (avl *AvlTree) rotateRight(node *AvlNode) *AvlNode {
leftNode := node.Left
node.Left = leftNode.Right
leftNode.Right = node
// updating the height and balance factor for the rotated
// nodes.
avl.update(node)
avl.update(leftNode)
return leftNode
}
// rotateLeft is a helper method to do a left rotation on
// a node.
func (avl *AvlTree) rotateLeft(node *AvlNode) *AvlNode {
rightNode := node.Right
node.Right = rightNode.Left
rightNode.Left = node
// updating the height and balance factor for the rotated
// nodes.
avl.update(node)
avl.update(rightNode)
return rightNode
}
// Search walks through the avl tree to look for
// the specified item.
//
// it returns nil if the item does not exist.
func (avl *AvlTree) Search(item float64) *AvlNode {
return avl.find(avl.root, item)
}
// find is a helper method to recursively find an item in
// the avl tree.
func (avl *AvlTree) find(node *AvlNode, item float64) *AvlNode {
if node == nil {
return nil
}
if item > node.Data {
return avl.find(node.Right, item)
}
if item < node.Data {
return avl.find(node.Left, item)
}
return node
}
// Size returns the size of the avl tree.
func (avl *AvlTree) Size() int {
return avl.size
}
// Remove removes an item from the avl tree.
func (avl *AvlTree) Remove(item float64) bool {
if avl.find(avl.root, item) == nil {
return false
}
avl.root = avl.removeItem(avl.root, item)
avl.size--
return true
}
// removeItem is a helper function to remove a node from the avl
// tree.
func (avl *AvlTree) removeItem(node *AvlNode, item float64) *AvlNode {
if item > node.Data {
node.Right = avl.removeItem(node.Right, item)
}
if item < node.Data {
node.Left = avl.removeItem(node.Left, item)
} else {
if node.Left == nil {
return node.Right
}
if node.Right == nil {
return node.Left
}
if node.Left.height > node.Right.height {
successor := avl.findMaxNode(node.Left)
node.Data = successor.Data
node.Left = avl.removeItem(node.Left, successor.Data)
} else {
successor := avl.findMinNode(node.Right)
node.Data = successor.Data
node.Right = avl.removeItem(node.Right, successor.Data)
}
}
avl.update(node)
return avl.balance(node)
}
// findMinNode is a helper function to find min child node by
// digging left in a subtree.
func (avl *AvlTree) findMinNode(node *AvlNode) *AvlNode {
if node.Left == nil {
return node
}
return avl.findMinNode(node.Left)
}
// findMaxNode is a helper function to find max child node in
// a subtree by digging right.
func (avl *AvlTree) findMaxNode(node *AvlNode) *AvlNode {
if node.Right == nil {
return node
}
return avl.findMaxNode(node.Right)
}
// GetRoot returns the root of the avl tree.
func (avl *AvlTree) GetRoot() *AvlNode {
return avl.root
}
// PreOrderTraversal runs a pre-order traversal on the avl tree
// and execute the callback function f for each iteration.
//
// pre-order traversal follows the order: <root>-<left>-<right>
func (avl *AvlTree) PreOrderTraversal(f func(node *AvlNode)) {
avl.runPreOrderTraversal(avl.root, f)
}
func (avl *AvlTree) runPreOrderTraversal(node *AvlNode, f func(node *AvlNode)) {
if node == nil {
return
}
f(node)
avl.runPreOrderTraversal(node.Left, f)
avl.runPreOrderTraversal(node.Right, f)
}
// InOrderTraversal runs an in-order traversal on the avl tree and
// execute the callback function f for each iteration.
//
// in-order traversal follows the order: <left>-<root>-<right>
func (avl *AvlTree) InOrderTraversal(f func(node *AvlNode)) {
avl.runInOrderTraversal(avl.root, f)
}
func (avl *AvlTree) runInOrderTraversal(node *AvlNode, f func(node *AvlNode)) {
if node == nil {
return
}
avl.runInOrderTraversal(node.Left, f)
f(node)
avl.runInOrderTraversal(node.Right, f)
}
// PostOrderTraversal runs a post-order traversal on the avl tree and
// execute the callback function f for each iteration.
//
// post-order traversal follows the order: <left>-<right>-<root>
func (avl *AvlTree) PostOrderTraversal(f func(node *AvlNode)) {
avl.runPostOrderTraversal(avl.root, f)
}
func (avl *AvlTree) runPostOrderTraversal(node *AvlNode, f func(node *AvlNode)) {
if node == nil {
return
}
avl.runPostOrderTraversal(node.Left, f)
avl.runPostOrderTraversal(node.Right, f)
f(node)
}
// LevelOrderTraversal runs a level-order traversal on the avl
// tree and execute the callback function f for each iteration.
func (avl *AvlTree) LevelOrderTraversal(f func(node *AvlNode)) {
avl.runLevelOrderTraversal(avl.root, f)
}
func (avl *AvlTree) runLevelOrderTraversal(node *AvlNode, f func(node *AvlNode)) {
if node == nil {
return
}
queue := NewQueue()
queue.Enqueue(node)
for !queue.IsEmpty() {
currentItem, _ := queue.Dequeue()
currentNode := currentItem.(*AvlNode)
f(currentNode)
if currentNode.Left != nil {
queue.Enqueue(currentNode.Left)
}
if currentNode.Right != nil {
queue.Enqueue(currentNode.Right)
}
}
}