even-odd-tree

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Algorithms

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

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

Given the <code>root</code> of a binary tree, return <code>true</code> if the binary tree is Even-Odd, otherwise return <code>false</code>.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/15/sample_1_1966.png" style="width: 362px; height: 229px;" />
<pre>
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.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/15/sample_2_1966.png" style="width: 363px; height: 167px;" />
<pre>
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 level 2 must be in strictly increasing order, so the tree is not Even-Odd.
</pre>

Example 3:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/22/sample_1_333_1966.png" style="width: 363px; height: 167px;" />
<pre>
Input: root = [5,9,1,3,5,7]
Output: false
Explanation: Node values in the level 1 should be even integers.
</pre>

&nbsp;
Constraints:

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 105]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 106</code></li>
</ul>

isEvenOddTree

Even Odd Tree

Tree

Breadth-First Search

Binary Tree

如果一棵二叉树满足下述几个条件，则可以称为 奇偶树 ：

<ul>
	<li>二叉树根节点所在层下标为 <code>0</code> ，根的子节点所在层下标为 <code>1</code> ，根的孙节点所在层下标为 <code>2</code> ，依此类推。</li>
	<li>偶数下标 层上的所有节点的值都是 奇 整数，从左到右按顺序 严格递增</li>
	<li>奇数下标 层上的所有节点的值都是 偶 整数，从左到右按顺序 严格递减</li>
</ul>

给你二叉树的根节点，如果二叉树为 奇偶树 ，则返回 <code>true</code> ，否则返回 <code>false</code> 。

 

示例 1：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/10/04/sample_1_1966.png" style="height: 229px; width: 362px;" />

<pre>
输入：root = [1,10,4,3,null,7,9,12,8,6,null,null,2]
输出：true
解释：每一层的节点值分别是：
0 层：[1]
1 层：[10,4]
2 层：[3,7,9]
3 层：[12,8,6,2]
由于 0 层和 2 层上的节点值都是奇数且严格递增，而 1 层和 3 层上的节点值都是偶数且严格递减，因此这是一棵奇偶树。
</pre>

示例 2：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/10/04/sample_2_1966.png" style="height: 167px; width: 363px;" />

<pre>
输入：root = [5,4,2,3,3,7]
输出：false
解释：每一层的节点值分别是：
0 层：[5]
1 层：[4,2]
2 层：[3,3,7]
2 层上的节点值不满足严格递增的条件，所以这不是一棵奇偶树。
</pre>

示例 3：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/10/04/sample_1_333_1966.png" style="height: 167px; width: 363px;" />

<pre>
输入：root = [5,9,1,3,5,7]
输出：false
解释：1 层上的节点值应为偶数。
</pre>

示例 4：

<pre>
输入：root = [1]
输出：true
</pre>

示例 5：

<pre>
输入：root = [11,8,6,1,3,9,11,30,20,18,16,12,10,4,2,17]
输出：true
</pre>

 

提示：

<ul>
	<li>树中节点数在范围 <code>[1, 105]</code> 内</li>
	<li><code>1 <= Node.val <= 106</code></li>
</ul>