2003 - Smallest Missing Genetic Value in Each Subtree.

Hard

There is a family tree rooted at 0 consisting of n nodes numbered 0 to n - 1. You are given a 0-indexed integer array parents, where parents[i] is the parent for node i. Since node 0 is the root , parents[0] == -1.

There are <code>10⁵</code> genetic values, each represented by an integer in the inclusive range <code>1, 10⁵</code>. You are given a 0-indexed integer array nums, where nums[i] is a distinct genetic value for node i.

Return an array ans of length n where ans[i] is the smallest genetic value that is missing from the subtree rooted at node i.

The subtree rooted at a node x contains node x and all of its descendant nodes.

Example 1:

Input: parents = -1,0,0,2, nums = 1,2,3,4

Output: 5,1,1,1

Explanation: The answer for each subtree is calculated as follows:

• 0: The subtree contains nodes 0,1,2,3 with values 1,2,3,4. 5 is the smallest missing value.

• 1: The subtree contains only node 1 with value 2. 1 is the smallest missing value.

• 2: The subtree contains nodes 2,3 with values 3,4. 1 is the smallest missing value.

• 3: The subtree contains only node 3 with value 4. 1 is the smallest missing value.

Example 2:

Input: parents = -1,0,1,0,3,3, nums = 5,4,6,2,1,3

Output: 7,1,1,4,2,1

Explanation: The answer for each subtree is calculated as follows:

• 0: The subtree contains nodes 0,1,2,3,4,5 with values 5,4,6,2,1,3. 7 is the smallest missing value.

• 1: The subtree contains nodes 1,2 with values 4,6. 1 is the smallest missing value.

• 2: The subtree contains only node 2 with value 6. 1 is the smallest missing value.

• 3: The subtree contains nodes 3,4,5 with values 2,1,3. 4 is the smallest missing value.

• 4: The subtree contains only node 4 with value 1. 2 is the smallest missing value.

• 5: The subtree contains only node 5 with value 3. 1 is the smallest missing value.

Example 3:

Input: parents = -1,2,3,0,2,4,1, nums = 2,3,4,5,6,7,8

Output: 1,1,1,1,1,1,1

Explanation: The value 1 is missing from all the subtrees.

Constraints:

• n == parents.length == nums.length

• <code>2 <= n <= 10⁵</code>

• 0 <= parents[i] <= n - 1 for i != 0

• parents[0] == -1

• parents represents a valid tree.

• <code>1 <= numsi<= 10⁵</code>

• Each nums[i] is distinct.