| comments | difficulty | edit_url | tags | |||||
|---|---|---|---|---|---|---|---|---|
true |
中等 |
|
给你一个整数 n ，请你找出所有可能含 n 个节点的 真二叉树 ，并以列表形式返回。答案中每棵树的每个节点都必须符合 Node.val == 0 。
答案的每个元素都是一棵真二叉树的根节点。你可以按 任意顺序 返回最终的真二叉树列表。
真二叉树 是一类二叉树，树中每个节点恰好有 0 或 2 个子节点。
示例 1：
输入：n = 7 输出：[[0,0,0,null,null,0,0,null,null,0,0],[0,0,0,null,null,0,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,null,null,null,null,0,0],[0,0,0,0,0,null,null,0,0]]
示例 2：
输入：n = 3 输出：[[0,0,0]]
提示：
1 <= n <= 20
如果
如果
此过程可以用记忆化搜索，避免重复计算。
时间复杂度
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution:
def allPossibleFBT(self, n: int) -> List[Optional[TreeNode]]:
@cache
def dfs(n: int) -> List[Optional[TreeNode]]:
if n == 1:
return [TreeNode()]
ans = []
for i in range(n - 1):
j = n - 1 - i
for left in dfs(i):
for right in dfs(j):
ans.append(TreeNode(0, left, right))
return ans
return dfs(n)/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* 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 List<TreeNode>[] f;
public List<TreeNode> allPossibleFBT(int n) {
f = new List[n + 1];
return dfs(n);
}
private List<TreeNode> dfs(int n) {
if (f[n] != null) {
return f[n];
}
if (n == 1) {
return List.of(new TreeNode());
}
List<TreeNode> ans = new ArrayList<>();
for (int i = 0; i < n - 1; ++i) {
int j = n - 1 - i;
for (var left : dfs(i)) {
for (var right : dfs(j)) {
ans.add(new TreeNode(0, left, right));
}
}
}
return f[n] = ans;
}
}/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* 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:
vector<TreeNode*> allPossibleFBT(int n) {
vector<vector<TreeNode*>> f(n + 1);
function<vector<TreeNode*>(int)> dfs = [&](int n) -> vector<TreeNode*> {
if (f[n].size()) {
return f[n];
}
if (n == 1) {
return vector<TreeNode*>{new TreeNode()};
}
vector<TreeNode*> ans;
for (int i = 0; i < n - 1; ++i) {
int j = n - 1 - i;
for (auto left : dfs(i)) {
for (auto right : dfs(j)) {
ans.push_back(new TreeNode(0, left, right));
}
}
}
return f[n] = ans;
};
return dfs(n);
}
};/**
* Definition for a binary tree node.
* type TreeNode struct {
* Val int
* Left *TreeNode
* Right *TreeNode
* }
*/
func allPossibleFBT(n int) []*TreeNode {
f := make([][]*TreeNode, n+1)
var dfs func(int) []*TreeNode
dfs = func(n int) []*TreeNode {
if len(f[n]) > 0 {
return f[n]
}
if n == 1 {
return []*TreeNode{&TreeNode{Val: 0}}
}
ans := []*TreeNode{}
for i := 0; i < n-1; i++ {
j := n - 1 - i
for _, left := range dfs(i) {
for _, right := range dfs(j) {
ans = append(ans, &TreeNode{0, left, right})
}
}
}
f[n] = ans
return ans
}
return dfs(n)
}/**
* 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)
* }
* }
*/
function allPossibleFBT(n: number): Array<TreeNode | null> {
const f: Array<Array<TreeNode | null>> = new Array(n + 1).fill(0).map(() => []);
const dfs = (n: number): Array<TreeNode | null> => {
if (f[n].length) {
return f[n];
}
if (n === 1) {
f[n].push(new TreeNode(0));
return f[n];
}
const ans: Array<TreeNode | null> = [];
for (let i = 0; i < n - 1; ++i) {
const j = n - 1 - i;
for (const left of dfs(i)) {
for (const right of dfs(j)) {
ans.push(new TreeNode(0, left, right));
}
}
}
return (f[n] = ans);
};
return dfs(n);
}// Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
// pub val: i32,
// pub left: Option<Rc<RefCell<TreeNode>>>,
// pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
// #[inline]
// pub fn new(val: i32) -> Self {
// TreeNode {
// val,
// left: None,
// right: None
// }
// }
// }
use std::cell::RefCell;
use std::rc::Rc;
impl Solution {
pub fn all_possible_fbt(n: i32) -> Vec<Option<Rc<RefCell<TreeNode>>>> {
let mut f: Vec<Option<Vec<Option<Rc<RefCell<TreeNode>>>>>> = vec![None; (n + 1) as usize];
Self::dfs(n, &mut f)
}
fn dfs(
n: i32,
f: &mut Vec<Option<Vec<Option<Rc<RefCell<TreeNode>>>>>>,
) -> Vec<Option<Rc<RefCell<TreeNode>>>> {
if let Some(ref result) = f[n as usize] {
return result.clone();
}
let mut ans = Vec::new();
if n == 1 {
ans.push(Some(Rc::new(RefCell::new(TreeNode::new(0)))));
return ans;
}
for i in 0..n - 1 {
let j = n - 1 - i;
for left in Self::dfs(i, f).iter() {
for right in Self::dfs(j, f).iter() {
let new_node = Some(Rc::new(RefCell::new(TreeNode {
val: 0,
left: left.clone(),
right: right.clone(),
})));
ans.push(new_node);
}
}
}
f[n as usize] = Some(ans.clone());
ans
}
}/**
* Definition for a binary tree node.
* 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 List<TreeNode>[] f;
public IList<TreeNode> AllPossibleFBT(int n) {
f = new List<TreeNode>[n + 1];
return Dfs(n);
}
private IList<TreeNode> Dfs(int n) {
if (f[n] != null) {
return f[n];
}
if (n == 1) {
return new List<TreeNode> { new TreeNode() };
}
List<TreeNode> ans = new List<TreeNode>();
for (int i = 0; i < n - 1; ++i) {
int j = n - 1 - i;
foreach (var left in Dfs(i)) {
foreach (var right in Dfs(j)) {
ans.Add(new TreeNode(0, left, right));
}
}
}
f[n] = ans;
return ans;
}
}