/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    vector<TreeNode*> allPossibleFBT(int N) {
        mem.clear();
        return dfs(N);
    }
    
    vector<TreeNode*> dfs(int n) {
        if (mem.find(n) != mem.end() ) return mem[n];
        vector<TreeNode*> ret;
        if (n == 1) {
            ret.push_back(new TreeNode(0));
            mem[n] = ret;
            return ret;
        }
        for (int i = 1; i < n; i+=2) {
            vector<TreeNode*> left = dfs(i);
            vector<TreeNode*> right = dfs(n-i-1);
            for (int j = 0; j < left.size(); j++) {
                for ( int k = 0; k < right.size(); k++ ) {
                    TreeNode* root = new TreeNode(0);
                    root->left = left[j];
                    root->right = right[k];
                    ret.push_back(root);
                }
            }
        }
        return ret;
    }

private:
    map< int, vector<TreeNode*> > mem;
    
};