# 1609. Even Odd Tree

<https://leetcode.com/problems/even-odd-tree>

## Description

A binary tree is named **Even-Odd** if it meets the following conditions:

* The root of the binary tree is at level index `0`, its children are at level index `1`, their children are at level index `2`, etc.
* For every **even-indexed** level, all nodes at the level have **odd** integer values in **strictly increasing** order (from left to right).
* For every **odd-indexed** level, all nodes at the level have **even** integer values in **strictly decreasing** order (from left to right).

Given the `root` of a binary tree, *return* `true` *if the binary tree is **Even-Odd**, otherwise return* `false`*.*

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/09/15/sample_1_1966.png)

```
**Input:** root = [1,10,4,3,null,7,9,12,8,6,null,null,2]
**Output:** true
**Explanation:** The node values on each level are:
Level 0: [1]
Level 1: [10,4]
Level 2: [3,7,9]
Level 3: [12,8,6,2]
Since levels 0 and 2 are all odd and increasing, and levels 1 and 3 are all even and decreasing, the tree is Even-Odd.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/09/15/sample_2_1966.png)

```
**Input:** root = [5,4,2,3,3,7]
**Output:** false
**Explanation:** The node values on each level are:
Level 0: [5]
Level 1: [4,2]
Level 2: [3,3,7]
Node values in the level 2 must be in strictly increasing order, so the tree is not Even-Odd.
```

**Example 3:**

![](https://assets.leetcode.com/uploads/2020/09/22/sample_1_333_1966.png)

```
**Input:** root = [5,9,1,3,5,7]
**Output:** false
**Explanation:** Node values in the level 1 should be even integers.
```

**Example 4:**

```
**Input:** root = [1]
**Output:** true
```

**Example 5:**

```
**Input:** root = [11,8,6,1,3,9,11,30,20,18,16,12,10,4,2,17]
**Output:** true
```

**Constraints:**

* The number of nodes in the tree is in the range `[1, 105]`.
* `1 <= Node.val <= 106`

## ac

```java
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://jaywin.gitbook.io/leetcode/solutions/1609-even-odd-tree.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.