I am reading the solution of this problem

solution

int traverse(TreeNode* r, int &moves) {
  if (r == nullptr) return 0;
  int left = traverse(r->left, moves), right = traverse(r->right, moves);
  moves += abs(left) + abs(right); <----- do not understand
  return r->val + left + right - 1;
}
int distributeCoins(TreeNode* r, int moves = 0) {
  traverse(r, moves);
  return moves;
}

I have hard time to understand that

• why move = move + abs(left) + abs(right) in current subtree?
• why we don’t involve curr_node? e.g move = move + abs(curr_node) + abs(left) + abs(right)?
• does it mean in each sub tree the move abs(left) + abs(right) equal moves of left subtree and right subtree only?
• in the top root subtree, move = abs(left) + abs(right), so there is no move for the root node? Looks like abs(left) OR abs(right) cover the move of root node?