Tree Rerooting DP: When to Use It

Start with the idea

A problem is a good match for Tree Rerooting DP when it asks for all-node distance sums and per-root tree answers. Here the concrete task is: Return sum of distances from every node in the tree. The visible input n=4 edges=(0,1),(1,2),(1,3) is an example, not a definition of the whole problem. Ask what operations the solution must support and what the input guarantees. Look for hierarchy and parent-child structure; a plain sequence algorithm loses the branching relationships. The right choice follows from those guarantees, not from a familiar noun in the prompt.

The decisive invariant is: Compute child-to-parent contributions, then propagate the outside contribution while changing the root. Try to say why it applies to the task without quoting the implementation. Which fact becomes known after one update, and which possible answers remain? A tree result is built from a node and its children. Decide whether information flows downward, upward, or in level order. If that claim cannot be maintained on a legal input, the pattern is wrong or one of its preconditions is missing. A counterexample is more useful than a vague warning: change one property of the sample, trace the first two steps, and identify the exact claim that fails.

Compare costs before committing. The advertised bound is O(n) time · O(n) space; identify the operation responsible for it and the extra memory it needs.