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merged 1 commit into from
Apr 23, 2024
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feat: add solutions to lc/lcci problems #2647

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265 changes: 146 additions & 119 deletions lcci/04.05.Legal Binary Search Tree/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -9,36 +9,38 @@

## 解法

### 方法一
### 方法一：递归

我们可以对二叉树进行递归中序遍历，如果遍历到的结果是严格升序的，那么这棵树就是一个二叉搜索树。

因此，我们使用一个变量 $\textit{prev}$ 来保存上一个遍历到的节点，初始时 $\textit{prev} = -\infty$，然后我们递归遍历左子树，如果左子树不是二叉搜索树，直接返回 $\text{False}$，否则判断当前节点的值是否大于 $\textit{prev}$，如果不是，返回 $\text{False}$，否则更新 $\textit{prev}$ 为当前节点的值，然后递归遍历右子树。

时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 是二叉树的节点个数。

<!-- tabs:start -->

```python
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None


# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution:
res, t = True, None
def isValidBST(self, root: Optional[TreeNode]) -> bool:
def dfs(root: Optional[TreeNode]) -> bool:
if root is None:
return True
if not dfs(root.left):
return False
nonlocal prev
if prev >= root.val:
return False
prev = root.val
return dfs(root.right)

def isValidBST(self, root: TreeNode) -> bool:
self.isValid(root)
return self.res

def isValid(self, root):
if not root:
return
self.isValid(root.left)
if self.t is None or self.t < root.val:
self.t = root.val
else:
self.res = False
return
self.isValid(root.right)
prev = -inf
return dfs(root)
```

```java
Expand All @@ -48,29 +50,34 @@ class Solution:
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class Solution {
private boolean res = true;
private Integer t = null;
private TreeNode prev;

public boolean isValidBST(TreeNode root) {
isValid(root);
return res;
return dfs(root);
}

private void isValid(TreeNode root) {
private boolean dfs(TreeNode root) {
if (root == null) {
return;
return true;
}
isValid(root.left);
if (t == null || t < root.val) {
t = root.val;
} else {
res = false;
return;
if (!dfs(root.left)) {
return false;
}
if (prev != null && prev.val >= root.val) {
return false;
}
isValid(root.right);
prev = root;
return dfs(root.right);
}
}
```
Expand All @@ -82,54 +89,59 @@ class Solution {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
bool isValidBST(TreeNode* root) {
TreeNode* pre = nullptr;
TreeNode* cur = root;
stack<TreeNode*> stk;
while (cur || !stk.empty()) {
if (cur) {
stk.push(cur);
cur = cur->left;
} else {
cur = stk.top();
stk.pop();
if (pre && pre->val >= cur->val) {
return false;
}
pre = cur;
cur = cur->right;
TreeNode* prev = nullptr;
function<bool(TreeNode*)> dfs = [&](TreeNode* root) {
if (!root) {
return true;
}
}
return true;
if (!dfs(root->left)) {
return false;
}
if (prev && prev->val >= root->val) {
return false;
}
prev = root;
return dfs(root->right);
};
return dfs(root);
}
};
```

```go
/**
* Definition for a binary tree node.
* type TreeNode struct {
* Val int
* Left *TreeNode
* Right *TreeNode
* }
*/
func isValidBST(root *TreeNode) bool {
stack := make([]*TreeNode, 0)
var prev *TreeNode = nil
node := root
for len(stack) > 0 || node != nil {
for node != nil {
stack = append(stack, node)
node = node.Left
var prev *TreeNode
var dfs func(*TreeNode) bool
dfs = func(root *TreeNode) bool {
if root == nil {
return true
}
node = stack[len(stack)-1]
stack = stack[:len(stack)-1]
if prev == nil || node.Val > prev.Val {
prev = node
} else {
if !dfs(root.Left) {
return false
}
node = node.Right
if prev != nil && prev.Val >= root.Val {
return false
}
prev = root
return dfs(root.Right)
}
return true
return dfs(root)
}
```

Expand All @@ -149,17 +161,19 @@ func isValidBST(root *TreeNode) bool {
*/

function isValidBST(root: TreeNode | null): boolean {
let pre = -Infinity;
const dfs = (root: TreeNode | null) => {
if (root == null) {
let prev: TreeNode | null = null;
const dfs = (root: TreeNode | null): boolean => {
if (!root) {
return true;
}
const { val, left, right } = root;
if (!dfs(left) || val <= pre) {
if (!dfs(root.left)) {
return false;
}
pre = val;
return dfs(right);
if (prev && prev.val >= root.val) {
return false;
}
prev = root;
return dfs(root.right);
};
return dfs(root);
}
Expand Down Expand Up @@ -187,19 +201,19 @@ function isValidBST(root: TreeNode | null): boolean {
use std::rc::Rc;
use std::cell::RefCell;
impl Solution {
fn dfs(root: &Option<Rc<RefCell<TreeNode>>>, pre: &mut Option<i32>) -> bool {
fn dfs(root: &Option<Rc<RefCell<TreeNode>>>, prev: &mut Option<i32>) -> bool {
if root.is_none() {
return true;
}
let root = root.as_ref().unwrap().borrow();
if !Self::dfs(&root.left, pre) {
if !Self::dfs(&root.left, prev) {
return false;
}
if pre.is_some() && pre.unwrap() >= root.val {
if prev.is_some() && prev.unwrap() >= root.val {
return false;
}
*pre = Some(root.val);
Self::dfs(&root.right, pre)
*prev = Some(root.val);
Self::dfs(&root.right, prev)
}

pub fn is_valid_bst(root: Option<Rc<RefCell<TreeNode>>>) -> bool {
Expand All @@ -208,59 +222,72 @@ impl Solution {
}
```

<!-- tabs:end -->

### 方法二

<!-- tabs:start -->

```go
func isValidBST(root *TreeNode) bool {
return check(root, math.MinInt64, math.MaxInt64)
}

func check(node *TreeNode, lower, upper int) bool {
if node == nil {
return true
}
if node.Val <= lower || node.Val >= upper {
return false
}
return check(node.Left, lower, node.Val) && check(node.Right, node.Val, upper)
}
```js
/**
* Definition for a binary tree node.
* function TreeNode(val, left, right) {
* this.val = (val===undefined ? 0 : val)
* this.left = (left===undefined ? null : left)
* this.right = (right===undefined ? null : right)
* }
*/
/**
* @param {TreeNode} root
* @return {boolean}
*/
var isValidBST = function (root) {
let prev = null;
const dfs = root => {
if (!root) {
return true;
}
if (!dfs(root.left)) {
return false;
}
if (prev && prev.val >= root.val) {
return false;
}
prev = root;
return dfs(root.right);
};
return dfs(root);
};
```

```ts
```cs
/**
* Definition for a binary tree node.
* class TreeNode {
* val: number
* left: TreeNode | null
* right: TreeNode | null
* constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
* this.val = (val===undefined ? 0 : val)
* this.left = (left===undefined ? null : left)
* this.right = (right===undefined ? null : right)
* public class TreeNode {
* public int val;
* public TreeNode left;
* public TreeNode right;
* public TreeNode(int val=0, TreeNode left=null, TreeNode right=null) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
public class Solution {
private TreeNode prev;

function isValidBST(root: TreeNode | null): boolean {
if (root == null) {
return true;
public bool IsValidBST(TreeNode root) {
return dfs(root);
}
const { val, left, right } = root;
const dfs = (root: TreeNode | null, min: number, max: number) => {

private bool dfs(TreeNode root) {
if (root == null) {
return true;
}
const { val, left, right } = root;
if (val <= min || val >= max) {
if (!dfs(root.left)) {
return false;
}
return dfs(left, min, Math.min(val, max)) && dfs(right, Math.max(val, min), max);
};
return dfs(left, -Infinity, val) && dfs(right, val, Infinity);
if (prev != null && prev.val >= root.val) {
return false;
}
prev = root;
return dfs(root.right);
}
}
```

Expand Down
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