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;
}
}