Hello everyone. I participated in the lowe's coding round and there was this question I was not able to solve completely. I did brute force and passed some test cases though.

The problem says, You are given a connected undirected graph. It has n nodes and m edges. Each node has some sweetness value that will be given to us.

The game is as follows:

1. Alice moves first and she may break a node. Each edge connected to this node will vanish.
2. Bob will pick any connected component(containing all or some nodes)
3. Alice will pick any remaining connected components if there are any

The game ends in three steps. Both of them want to maximize their score by collecting maximum possible sweetness. They are not trying to minimize each other' score.

Determine the maximum score of Alice and Bob respectively. Assume both plays the game optimally.

Graph nodes index starts from 1. If no connected component left, alice gets 0

Input: number of test cases then n, m and then sweetness of each node and then the edges.

Example:

1

6 7

4 3 7 5 9 2

1 2

2 3

1 3

3 4

4 5

5 6

4 6

For this answer is 11 14

I tried to construct a spanning tree and also strongly connected components but couldn't understand.

How to solve this problem? I did this with DFS and max heap. Brute force. What is optimal way of doing this problem