Subtree answers (bottom-up) (Tree DFS Sub-pattern)

// Bottom-up: each call returns a summary of its subtree; the global answer is
// updated while combining the two children. Here: diameter (longest path, in edges).
int best = 0;

int height(TreeNode* node) {                             // returns: nodes on the longest downward path
    if (!node) return 0;
    int lh = height(node->left);
    int rh = height(node->right);
    best = max(best, lh + rh);                           // the longest path that bends at this node
    return 1 + max(lh, rh);                              // a parent can only extend ONE side
}

int diameterOfBinaryTree(TreeNode* root) {
    best = 0;
    height(root);
    return best;
}