Maximum Points After Collecting Coins From All Nodes
There exists an undirected tree rooted at node 0 with n nodes labeled from 0 to n - 1. 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 array coins of size n where coins[i] indicates the number of coins in vertex i, and an integer k.
Starting from the root, you have to collect all the coins such that the coins at a node can only be collected if the coins of its ancestors have already been collected.
Coins at node_i can be collected in one of the following ways:
- Collect all the coins, but you will get
coins[i] - kpoints. Ifcoins[i] - kis negative, then you will loseabs(coins[i] - k)points. - Collect all the coins, but you will get
floor(coins[i] / 2)points. If this way is used, then for all thenode_jpresent in the subtree ofnode_i,coins[j]will get reduced tofloor(coins[j] / 2).
Return the maximum points you can get after collecting the coins from all the tree nodes.
Example 1
Input
edges = [[0,1],[1,2],[2,3]], coins = [10,10,3,3], k = 5Output
11Using the first way at nodes 0 and 1 and the second way at nodes 2 and 3 gives a total of 11 points, which is the maximum possible.
Example 2
Input
edges = [[0,1],[0,2]], coins = [8,4,4], k = 0Output
16Coins will be collected from all the nodes using the first way, so the total points are (8 - 0) + (4 - 0) + (4 - 0) = 16.
Constraints
- n == coins.length
- 2 <= n <= 10^5
- 0 <= coins[i] <= 10^4
- edges.length == n - 1
- 0 <= edges[i][0], edges[i][1] < n
- 0 <= k <= 10^4