3949. Subtree Inversion Sum II

Root the tree at 0. Do not track only inverted ancestors; the constraint is between any two inverted nodes, including nodes in different child subtrees.

Use DP by distance. Let mx[u][d] and mn[u][d] be the maximum/minimum possible subtree sum of u, assuming every inverted node inside this subtree is at distance at least d from u. Cap distances at k.

When merging child subtrees, if one inverted node is in one child at distance a from that child, and another is in a different child at distance b, their distance through u is a + b + 2, so it must be at least k.

Store both max and min because inverting u negates the whole subtree. So the best value after inverting u comes from negating the minimum compatible child sum, and the worst comes from negating the maximum compatible child sum.