1609 - Even Odd Tree.

Medium

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:

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:

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.

Example 3:

Input: root = 5,9,1,3,5,7

Output: false

Explanation: Node values in the level 1 should be even integers.

Constraints:

• The number of nodes in the tree is in the range <code>1, 10⁵</code>.

• <code>1 <= Node.val <= 10⁶</code>