TreeAndCycle

You are given an undirected tree with n vertices numbered 0 through n-1. For each i between 0 and n-2, inclusive, the vertices (i+1) and pre[i] are connected by an edge. We ensure pre[i] < i+1, so the edges are guaranteed to form a tree.
A cycle graph is an undirected graph with n vertices and n edges in which the edges form a single cycle through all vertices. Formally, a graph with n vertices and n edges is a cycle graph if there exists a permutation p[0], p[1],..., p[n-1] of its vertices such that the n edges are the edges (p[0],p[1]), (p[1],p[2]), (p[2],p[3]), ..., (p[n-2],p[n-1]), and (p[n-1],p[0]).
You want to transform the given tree into an arbitrary cycle graph by adding and/or removing edges. Removing the edge (i+1,pre[i]) costs costE[i]. Each vertex x has an associated weight costV[x]. The cost of adding a new edge (x,y) is costV[x]+costV[y]. The edges added in this way cannot be removed. Note that all the edges are undirected.
You are given the following int[]s:

• The int[] costV with n elements that contains the weight of each vertex. Remember that these weights are used to compute the costs of adding new edges.
• The int[] pre with n-1 elements that describes the shape of the tree.
• The int[] costE with n-1 elements: the costs of removing the edges described by pre.

Compute and return the smallest total cost of changing the given tree into some cycle graph.