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

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

<p>A <strong>full binary tree</strong> is a binary tree where each node has exactly <code>0</code> or <code>2</code> children.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/22/fivetrees.png" style="width: 700px; height: 400px;" />
<pre>
<strong>Input:</strong> n = 7
<strong>Output:</strong> [[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]]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> [[0,0,0]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 20</code></li>
</ul>

/**
 * 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:
    unordered_map<int, vector<TreeNode*>> dp;

    TreeNode* makeCopy(TreeNode* node) {
        if(node == nullptr) return nullptr;
        TreeNode* newNode = new TreeNode();
        TreeNode* left = makeCopy(node->left);
        TreeNode* right = makeCopy(node->right);
        newNode->left = left;
        newNode->right = right;
        return newNode;
    }

    vector<TreeNode*> getAllPossibleFBTForN(int n) {
        auto it = dp.find(n);
        if(it != dp.end()) {
            vector<TreeNode*> newCopiedNodesForN;
            for(auto node : it->second) {
                newCopiedNodesForN.push_back(makeCopy(node));
            }
            return newCopiedNodesForN;
        }
        vector<TreeNode*> results;
        for(int i = 1; i <= n - 2; i += 2) {
            auto leftAllPossibleFBT = getAllPossibleFBTForN(i);
            auto rightAllPossibleFBT = getAllPossibleFBTForN(n - 1 - i);
            for(auto leftNode : leftAllPossibleFBT) {
                for(auto rightNode : rightAllPossibleFBT) {
                    TreeNode* newRoot = new TreeNode();
                    newRoot->left = leftNode;
                    newRoot->right = rightNode;
                    results.push_back(newRoot);
                }
            }
        }
        dp[n] = results;
        return results;
    }

    vector<TreeNode*> allPossibleFBT(int n) {
        if(n % 2 == 0) return {};
        dp[1] = {new TreeNode()};
        return getAllPossibleFBTForN(n);
    }
};
36371