Minimum Flips in Binary Tree to Get Result

Given a binary tree that encodes a boolean expression (leaves are 0/1 and internal nodes are AND/OR gates, with some gates allowed to be changed), find the minimum number of flips — toggling leaf values or changing gate types where permitted — required so the root evaluates to a specified target value. Core challenge: combine gate semantics and flip options bottom-up to compute the minimal flips for each subtree.