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一、Description
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
.
题目大意:
给定一个数N,找出所有结点数为N的满数。满树指的是每个结点的子节点数要么为0要么为2。
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:
二、Analyzation
首先,对于N为偶数,不可能存在一个满足条件的满树,因此N必须为奇数。除开根结点,一棵满树可以分解为有i(i为奇数)个结点的左子树和n-i-1(n-i-1为奇数)个结点的右子树,所以只需遍历i的取值。
三、Accepted code
class Solution {
public List<TreeNode> allPossibleFBT(int N) {
List<TreeNode> list = new ArrayList<>();
if (N % 2 == 0 || N <= 0) {
return list;
}
if (N == 1) {
list.add(new TreeNode(0));
return list;
}
for (int i = 1; i < N; i += 2) {
List<TreeNode> left = allPossibleFBT(i);
List<TreeNode> right = allPossibleFBT(N - i - 1);
for (TreeNode l : left) {
for (TreeNode r : right) {
TreeNode node = new TreeNode(0);
node.left = l;
node.right = r;
list.add(node);
}
}
}
return list;
}
}