All Possible Full Binary Trees

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 have node.val = 0.

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

题目理解：

每个节点含有0个或者2个节点的二叉树称为FBT。给定节点数目，返回所有可能的FBT

解题思路：

运用递归解决。每一棵FBT一定含有奇数个节点，其左右孩子也一定都含有奇数个节点，这样就可以将问题分解为求左右子树的问题。遍历所有可能的子树节点数目，然后将左右子树连接都根节点返回即可。

代码如下：

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;
    }
}