Smallest Missing Genetic Value in Each Subtree

arraydynamic programmingtree

Problem Statement

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 10 ^5 genetic values, each represented by an integer in the inclusive range [1, 10 ^5 ] . 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.

Examples

Example 1

Input: parents = [-1,0,0,2], nums = [1,2,3,4]
Output: [5,1,1,1]
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]
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]
The value 1 is missing from all the subtrees.

Constraints

n == parents.length == nums.length

2 <= n <= 10 ^5

0 <= parents[i] <= n - 1 for i != 0

parents[0] == -1

parents represents a valid tree.

1 <= nums[i] <= 10 ^5

Each nums[i] is distinct.

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming