Maximum Score After Applying Operations on a Tree
There is an undirected tree with n nodes labeled from 0 to n - 1, rooted at node 0. You are given a 2D integer array edges of length n - 1, where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.
You are also given a 0-indexed integer array values of length n, where values[i] is the value associated with the i^th node.
You start with a score of 0. In one operation, you can:
- Pick any node
i. - Add
values[i]to your score. - Set
values[i]to0.
A tree is healthy if the sum of values on the path from the root to any leaf node is different than zero.
Return the maximum score you can obtain after performing these operations on the tree any number of times so that it remains healthy.
Example 1
Input
edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1]Output
11Choosing nodes 1, 2, 3, 4, and 5 leaves the root value non-zero, so every root-to-leaf path has a nonzero sum and the score is 11.
Example 2
Input
edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5]Output
40Choosing nodes 0, 2, 3, and 4 leaves all root-to-leaf path sums nonzero, producing the maximum score 40.
Constraints
- 2 <= n <= 2 * 10^4
- edges.length == n - 1
- edges[i].length == 2
- 0 <= ai, bi < n
- values.length == n
- 1 <= values[i] <= 10^9
- The input is generated such that edges represents a valid tree.