# 894. All Possible Full Binary Trees

## Description

Given an integer n, return a list of all possible full binary trees with n nodes. Each node of each tree in the answer must have Node.val == 0.

Each element of the answer is the root node of one possible tree. You may return the final list of trees in any order.

A full binary tree is a binary tree where each node has exactly 0 or 2 children.

Example 1:

Input: n = 7
Output: [[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]]


Example 2:

Input: n = 3
Output: [[0,0,0]]


Constraints:

• 1 <= n <= 20

## Solutions

• /**
* 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)) {
}
}
}
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.
# 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.
* 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
//     }
//   }
// }

impl TreeNode {
pub fn new_with_node(
left: Option<Rc<RefCell<TreeNode>>>,
right: Option<Rc<RefCell<TreeNode>>>
) -> Self {
Self {
val: 0,
left,
right,
}
}
}

use std::rc::Rc;
use std::cell::RefCell;
impl Solution {
pub fn all_possible_fbt(n: i32) -> Vec<Option<Rc<RefCell<TreeNode>>>> {
let mut record_vec = vec![vec![]; n as usize + 1];
Self::dfs(n, &mut record_vec)
}

fn dfs(
n: i32,
record_vec: &mut Vec<Vec<Option<Rc<RefCell<TreeNode>>>>>
) -> Vec<Option<Rc<RefCell<TreeNode>>>> {
if record_vec[n as usize].len() != 0 {
return record_vec[n as usize].clone();
}
if n == 1 {
// Just directly return a single node
return vec![Some(Rc::new(RefCell::new(TreeNode::new(0))))];
}
// Otherwise, need to construct return vector
let mut ret_vec = Vec::new();

// Enumerate the node number for left subtree from 0 -> n - 1
for i in 0..n - 1 {
// The number of right subtree node
let j = n - i - 1;
for left in Self::dfs(i, record_vec) {
for right in Self::dfs(j, record_vec) {
// Construct the ret vector
ret_vec.push(
Some(
Rc::new(
RefCell::new(TreeNode::new_with_node(left.clone(), right.clone()))
)
)
);
}
}
}

record_vec[n as usize] = ret_vec;

record_vec[n as usize].clone()
}
}


• /**
* 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)) {
}
}
}
f[n] = ans;
return ans;
}
}