方法一：递归

/**
 * 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) {
        if(N % 2 == 0) return {};
        if(N == 1) return {new TreeNode(0)};
        
        vector<TreeNode*> ans;
        for(int i = 1;i < N;i += 2)
        {
            for(auto l:allPossibleFBT(i))
            {
                for(auto r:allPossibleFBT(N-i-1))
                {
                    TreeNode* root = new TreeNode(0);
                    root->left = l;
                    root->right = r;
                    
                    ans.push_back(root);
                }
            }
        }
        
        return ans;
    }
};

方法二 递归加记忆化

/**
 * 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) {
        if(N % 2 == 0) return {};
        if(N == 1) return {new TreeNode(0)};
        
        vector<TreeNode*> ans;
        for(int i = 1;i < N;i += 2)
        {
            for(auto l:allPossibleFBT(i))
            {
                for(auto r:allPossibleFBT(N-i-1))
                {
                    TreeNode* root = new TreeNode(0);
                    root->left = l;
                    root->right = r;
                    
                    ans.push_back(root);
                }
            }
        }
        
        return ans;
    }
};

方法三 动态规划