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algorithm-pattern-cpp/advanced_algorithm/binary_search_tree.md at master · da183/algorithm-pattern-cpp · GitHub
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# 二叉搜索树
## 定义
- 每个节点中的值必须大于（或等于）存储在其左侧子树中的任何值。
- 每个节点中的值必须小于（或等于）存储在其右子树中的任何值。
## 应用
[validate-binary-search-tree](https:
//
leetcode-cn.com/problems/validate-binary-search-tree/)
> 验证二叉搜索树
```c++
struct
Result
{
TreeNode *maxNode;
TreeNode *minNode;
bool
isValidate;
Result
(
bool
validate =
true
, TreeNode *max =
nullptr
, TreeNode *min =
nullptr
)
: isValidate(validate), maxNode(max), minNode(min) {
}
};
bool
isValidBST
(TreeNode *root) {
if
(!root) {
return
true
;
}
return
helper
(root).
isValidate
;
}
Result
helper
(TreeNode *root) {
if
(!root) {
return
{};
}
auto
left =
helper
(root->
left
);
auto
right =
helper
(root->
right
);
if
(!(left.
isValidate
&& right.
isValidate
)) {
return
{
false
};
}
if
(left.
maxNode
&& left.
maxNode
->
val
>= root->
val
) {
return
{
false
};
}
if
(right.
minNode
&& right.
minNode
->
val
<= root->
val
) {
return
{
false
};
}
return
{
true
,
right.
maxNode
? right.
maxNode
: root,
left.
minNode
? left.
minNode
: root,
};
}
```
[insert-into-a-binary-search-tree](https:
//
leetcode-cn.com/problems/insert-into-a-binary-search-tree/)
> 给定二叉搜索树（
BST
）的根节点和要插入树中的值，将值插入二叉搜索树。 返回插入后二叉搜索树的根节点。 保证原始二叉搜索树中不存在新值。
```c++
TreeNode *
insertIntoBST
(TreeNode *root,
int
val) {
if
(root ==
nullptr
) {
return
new
TreeNode
(val);
}
if
(root->
val
> val) {
root->
left
=
insertIntoBST
(root->
left
, val);
}
else
{
root->
right
=
insertIntoBST
(root->
right
, val);
}
return
root;
}
```
[
delete
-node-in-a-bst](https:
//
leetcode-cn.com/problems/delete-node-in-a-bst/)
> 给定一个二叉搜索树的根节点 root 和一个值 key，删除二叉搜索树中的 key 对应的节点，并保证二叉搜索树的性质不变。返回二叉搜索树（有可能被更新）的根节点的引用。
```c++
//
注意二叉搜索树的概念！
//
如果当前节点是其父节点的左子节点，则当前节点底下任何一个节点都要比该父节点小
//
反之亦然
TreeNode*
deleteNode
(TreeNode* root,
int
key) {
if
(root ==
nullptr
) {
return
root;
}
if
(root->
val
< key) {
root->
right
=
deleteNode
(root->
right
, key);
return
root;
}
if
(root->
val
> key) {
root->
left
=
deleteNode
(root->
left
, key);
return
root;
}
//
每个节点中的值必须大于（或等于）存储在其左侧子树中的任何值。
//
所以压根不需要考虑啥当前节点的父节点，必定当前节点的左右子树！
if
(root->
left
==
nullptr
) {
return
root->
right
;
}
if
(root->
right
==
nullptr
) {
return
root->
left
;
}
auto
iter = root->
right
;
while
(iter->
left
!=
nullptr
) {
iter = iter->
left
;
}
iter->
left
= root->
left
;
return
root->
right
;
}
```
[balanced-binary-tree](https:
//
leetcode-cn.com/problems/balanced-binary-tree/)
> 给定一个二叉树，判断它是否是高度平衡的二叉树。
```c++
struct
ResultType
{
int
height;
bool
valid;
};
bool
isBalanced
(TreeNode *root) {
return
dfs
(root).
valid
;
}
type ResultType
struct
{
height
int
valid
bool
}
func
isBalanced
(root *TreeNode) bool {
return
dfs
(root).
valid
}
func
dfs
(root *TreeNode)(result ResultType){
if
root==nil{
result.
valid
=
true
result.
height
=
0
return
}
left:=
dfs
(root.
Left
)
right:=
dfs
(root.
Right
)
//
满足所有特点：二叉搜索树&&平衡
if
left.
valid
&&right.
valid
&&
abs
(left.
height
,right.
height
)<=
1
{
result.
valid
=
true
}
result.
height
=
Max
(left.
height
,right.
height
)+
1
return
}
func
abs
(a,b
int
)int{
if
a>b{
return
a-b
}
return
b-a
}
func
Max
(a,b
int
)int{
if
a>b{
return
a
}
return
b
}
```
## 练习
- [ ] [validate-binary-search-tree](https:
//
leetcode-cn.com/problems/validate-binary-search-tree/)
- [ ] [insert-into-a-binary-search-tree](https:
//
leetcode-cn.com/problems/insert-into-a-binary-search-tree/)
- [ ] [
delete
-node-in-a-bst](https:
//
leetcode-cn.com/problems/delete-node-in-a-bst/)
- [ ] [balanced-binary-tree](https:
//
leetcode-cn.com/problems/balanced-binary-tree/)
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