Leetcode 2646. Minimize the Total Price of the Trips

Given a tree and many trips (each traversing any path between two nodes), you must minimize the total sum of node prices across all trips by halving the prices of a chosen set of non-adjacent nodes. Core challenge: compute how often each node is used across all trip paths, then run a tree DP over the independent-set constraint (pick/skip each node) to maximize savings and hence minimize total cost.