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

Return a list of all possible full binary trees with N nodes.  Each element of the answer is the root node of one possible tree.

Each node of each tree in the answer must

You may return the final list of trees in any order.

Example 1:

Input: 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]]
Explanation:

Note:

• 1 <= N <= 20

題目理解：

每個節點含有0個或者2個節點的二叉樹稱為FBT。給定節點數目，返回所有可能的FBT

解題思路：

運用遞迴解決。每一棵FBT一定含有奇數個節點，其左右孩子也一定都含有奇數個節點，這樣就可以將問題分解為求左右子樹的問題。遍歷所有可能的子樹節點數目，然後將左右子樹連線都根節點返回即可。

程式碼如下：

class Solution {
    public List<TreeNode> allPossibleFBT(int N) {
        List<TreeNode> res = new ArrayList<TreeNode>();
        if(N % 2 == 0)
        	return res;
        if(N == 1) {
        	res.add(new TreeNode(0));
        	return res;
        }
        for(int num_l = 1, num_r = N - 2; num_r > 0; num_l += 2, num_r -= 2) {
        	List<TreeNode> nodes_l = allPossibleFBT(num_l);
        	List<TreeNode> nodes_r = allPossibleFBT(num_r);
        	for(TreeNode l : nodes_l) {
        		for(TreeNode r : nodes_r) {
        			TreeNode root = new TreeNode(0);
        			root.left = l;
        			root.right = r;
        			res.add(root);
        		}
        	}
        }
        return res;
    }
}