Alternating edges

You are given a weighted tree consisting of $n$ vertices numbered from $1$ to $n$. A tree is a connected undirected graph without cycles. If $w_1, w_2...w_m$ are the weights of the edges lying on the simple path starting from node $a$ and ending at node $b$, then we define the alternating-distance from $a$ to $b$, $altdist(a,b)$ as the sum of weights of alternate edges starting from $w_1$ (i.e $w