998. Maximum Binary Tree II 最大二叉树 II

@TOC

# 题目描述

We are given the `root` node of a maximum tree: a tree where every node has a value greater than any other value in its subtree.

Just as in the `previous problem`, the given tree was constructed from an list `A (root = Construct(A))` recursively with the following `Construct(A)` routine:

• If `A` is empty, return `null`.
• Otherwise, let `A[i]` be the largest element of `A`. Create a root node with value `A[i]`.
• The left child of root will be `Construct([A[0], A[1], ..., A[i-1]])`
• The right child of root will be `Construct([A[i+1], A[i+2], ..., A[A.length - 1]])`
• Return `root`.

Note that we were not given A directly, only a root node `root = Construct(A)`.

Suppose B is a copy of A with the value val appended to it. It is guaranteed that B has unique values.

Return `Construct(B)`.

Example 1:

``````Input: root = [4,1,3,null,null,2], val = 5
Output: [5,4,null,1,3,null,null,2]
Explanation: A = [1,4,2,3], B = [1,4,2,3,5]
``````

Example 2:

``````Input: root = [5,2,4,null,1], val = 3
Output: [5,2,4,null,1,null,3]
Explanation: A = [2,1,5,4], B = [2,1,5,4,3]
``````

Example 3:

``````Input: root = [5,2,3,null,1], val = 4
Output: [5,2,4,null,1,3]
Explanation: A = [2,1,5,3], B = [2,1,5,3,4]
``````

Note:

1. `1 <= B.length <= 100`

# 解题方法

# 递归

1. 如果原来的A不存在，那么很简单要返回该新节点。
2. 如果A存在，在A的数组表示的最后新添加了一个val，两种情况：
• 如果val > root.val，已知root.val是数组中最大的元素了，所以，此时会形成一个新的根节点，并把原来的A当做该根节点的左子树
• 如果val < root.val，那么仍然要记住该节点是在最大元素的右边，所以根节点的右子树变成了在根节点的右子树插入val的新子树。

C++代码如下：

``````/**
* 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:
TreeNode* insertIntoMaxTree(TreeNode* root, int val) {
if (!root) return new TreeNode(val);
if (val > root->val) {
TreeNode* newRoot = new TreeNode(val);
newRoot->left = root;
return newRoot;
} else {
root->right = insertIntoMaxTree(root->right, val);
}
return root;
}
};
``````

# 日期

2019 年 2 月 24 日 —— 周末又结束了