Maximum Score After Applying Operations on a Tree

Select a subset of nodes in a rooted tree to collect their positive values (setting them to zero) to maximize total collected value subject to the constraint that no root-to-leaf path becomes entirely collected (i.e., you must leave at least one node on every root-to-leaf path). This reduces to choosing a minimum-weight set of “kept” nodes that hits every root-to-leaf path and is typically solved with a tree DP.