There exists an undirected and unrooted tree with
n nodes indexed from
n - 1. You are given an integer
n and a 2D integer array edges of length
n - 1, where
edges[i] = [ai, bi] indicates that there is an edge between nodes
bi in the tree. You are also given an array
coins of size
coins[i] can be either
1 indicates the presence of a coin in the vertex
Initially, you choose to start at any vertex in the tree. Then, you can perform the following operations any number of times:
2from the current vertex, or
Find the minimum number of edges you need to go through to collect all the coins and go back to the initial vertex.
Note that if you pass an edge several times, you need to count it into the answer several times.
Input: coins = [1,0,0,0,0,1], edges = [[0,1],[1,2],[2,3],[3,4],[4,5]] Output: 2 Explanation: Start at vertex 2, collect the coin at vertex 0, move to vertex 3, collect the coin at vertex 5 then move back to vertex 2.
Input: coins = [0,0,0,1,1,0,0,1], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[5,6],[5,7]] Output: 2 Explanation: Start at vertex 0, collect the coins at vertices 4 and 3, move to vertex 2, collect the coin at vertex 7, then move back to vertex 0.
n == coins.length
1 <= n <= 3 * 104
0 <= coins[i] <= 1
edges.length == n - 1
edges[i].length == 2
0 <= ai, bi < n
ai != bi
edgesrepresents a valid tree.