<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) {}
 * };
 */

vector<TreeNode*> ans[16];

TreeNode* Copy(const TreeNode* x) {
  if (x == nullptr) {
    return nullptr;
  }
  TreeNode* ret = new TreeNode();
  if (x->left != nullptr) {
    ret->left = Copy(x->left);
  }
  if (x->right != nullptr) {
    ret->right = Copy(x->right);
  }
  return ret;
}

void AddLeaves(TreeNode* x) {
  if (x->left == nullptr) {
    x->left = new TreeNode();
  } else {
    AddLeaves(x->left);
  }
  if (x->right == nullptr) {
    x->right = new TreeNode();
  } else {
    AddLeaves(x->right);
  }
}

void Init() {
  ans[0].push_back(nullptr);
  for (int i = 1; i < 10; ++i) {
    for (int j = 0; j < i; ++j) {
      int p = j, q = i - 1 - j;
      for (const TreeNode* l : ans[p]) {
        for (const TreeNode* r : ans[q]) {
          TreeNode* cur = new TreeNode();
          cur->left = Copy(l);
          cur->right = Copy(r);
          ans[i].push_back(cur);
        }
      }
    }
  }
  ans[0][0] = new TreeNode();
  for (int i = 1; i < 10; ++i) {
    for (TreeNode* x : ans[i]) {
      AddLeaves(x);
    }
  }
}

class Solution {
public:
    vector<TreeNode*> allPossibleFBT(int n) {
      static bool init = []() {
        Init();
        return true;
      }();

      return (n & 1) ? ans[(n - 1) / 2] : vector<TreeNode*>();
    }
};
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