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
use ;
use ;
/// ## Description
///
/// When writing the nodes you need to start from the lowest ones and make your way up to the root
/// one.
///
/// There's no guarantees that this Binary Tree is balanced (this is important for optimizations.)
///
/// The struct signature is entirely 1:1 with LeetCode with additional optional features like
/// serde.
///
/// ## Examples
///
/// Example 1 - balanced tree:
///
/// ```rust
/// use std::{cell::RefCell, rc::Rc};
/// use leetcode_trees_rs::utils::TreeNode;
///
/// let left_node = TreeNode::new(42);
/// let right_node = TreeNode::new(42);
/// let root_node = TreeNode {
/// val: 100,
/// left: Some(Rc::from(RefCell::from(left_node))),
/// right: Some(Rc::from(RefCell::from(right_node))),
/// };
/// ```
///
/// Result:
///
/// ```markdown
/// Some(100) // Root Node
/// / \
/// Some(42) Some(42) // Left and Right nodes respectively
/// / \ / \
/// None None None None
/// ```
///
/// **NOTE:** Simplified `Option<Rc<RefCell<TreeNode>>>` to `Option<TreeNode.val>`.
///
/// Example 2 - unbalanced tree:
///
/// ```rust
/// use std::{cell::RefCell, rc::Rc};
/// use leetcode_trees_rs::utils::TreeNode;
///
/// let left_node = TreeNode::new(42);
/// let right_node = TreeNode::new(21);
/// let root_node = TreeNode {
/// val: 100,
/// left: Some(Rc::from(RefCell::from(left_node))),
/// right: Some(Rc::from(RefCell::from(right_node))),
/// };
/// ```
///
/// Result:
///
/// ```markdown
/// Some(100) // Root Node
/// / \
/// Some(42) Some(21) // Left and Right nodes respectively
/// / \ / \
/// None None None None
/// ```
///
/// Example 3 - unbalanced tree:
///
/// ```rust
/// use std::{cell::RefCell, rc::Rc};
/// use leetcode_trees_rs::utils::TreeNode;
///
/// // let left_node = TreeNode::new(42); // Removing the left node.
/// let right_node = TreeNode::new(21);
/// let root_node = TreeNode {
/// val: 100,
/// left: None, // Setting the left node to None.
/// right: Some(Rc::from(RefCell::from(right_node))),
/// };
/// ```
///
/// Result:
///
/// ```markdown
/// Some(100) // Root Node
/// / \
/// None Some(21) // Left and Right nodes respectively
/// / \
/// None None
/// ```
///
/// The second example is unbalanced because the depths of both sides don't match.
///
/// Example 4 - unbalanced tree:
///
/// ```rust
/// use std::{cell::RefCell, rc::Rc};
/// use leetcode_trees_rs::utils::TreeNode;
///
/// let left_right_node = TreeNode::new(16);
/// let left_node = TreeNode {
/// val: 42,
/// left: None,
/// right: Some(Rc::from(RefCell::from(left_right_node))),
/// };
/// let right_node = TreeNode::new(21);
/// let root_node = TreeNode {
/// val: 100,
/// left: Some(Rc::from(RefCell::from(left_node))),
/// right: Some(Rc::from(RefCell::from(right_node))),
/// };
/// ```
///
/// Result:
///
/// ```markdown
/// Some(100) // Root Node
/// / \
/// Some(42) Some(21) // Left and Right nodes respectively
/// / \ / \
/// None Some(16) None None // Left->Left; Left->Right;
/// / \ // Right->Left; Right->right
/// None None
/// ```
///
/// Example 5 - balanced tree:
///
/// ```rust
/// use std::{cell::RefCell, rc::Rc};
/// use leetcode_trees_rs::utils::TreeNode;
///
/// let left_left_node = TreeNode::new(16);
/// let right_right_node = TreeNode::new(16);
/// let left_node = TreeNode {
/// val: 42,
/// left: Some(Rc::from(RefCell::from(left_left_node))),
/// right: None,
/// };
/// let right_node = TreeNode {
/// val: 42,
/// left: None,
/// right: Some(Rc::from(RefCell::from(right_right_node))),
/// };
/// let root_node = TreeNode {
/// val: 100,
/// left: Some(Rc::from(RefCell::from(left_node))),
/// right: Some(Rc::from(RefCell::from(right_node))),
/// };
/// ```
///
/// Result:
///
/// ```markdown
/// Some(100) // Root Node
/// / \
/// Some(42) Some(42) // Left and Right nodes respectively
/// / \ / \
/// Some(16) None None Some(16) // Left->Left; Left->Right;
/// / \ / \ // Right->Left; Right->right
/// None None None None
/// ```
///
/// If root->right.val != root->left.val then the tree wouldn't be balanced.
///
/// The same is the case if root->left->left.val != root->right->right.val.
///
/// ## Big O
///
/// Traversal (postorder, preorder and inorder) -> O(n)
///
/// Insertion at the start (above the old root) -> O(1)
///
/// Any other insertion:
/// - balanced -> O(log n)
/// - unbalanced -> O(n)
///
/// Searching:
/// - balanced -> O(log n)
/// - unbalanced -> O(n)
///
/// Deletion:
/// - balanced -> O(log n)
/// - unbalanced -> O(n)
///
/// Finding successor/predecessor:
/// - balanced -> O(log n)
/// - unbalanced -> O(n)