Input: A max binomial heap $H$, and a pointer to a node $V$.
Output: A max binomial heap, where all the children of $V$ are multiplied by 2.
I have tried solving this by taking out the node $V$ together with it's sub-tree, multiplying all the children of V by $2$, rearranging the heap to close the hole, and adding V's children to the heap.
It sums up to $O(k\log n )$, where $k$ is the number on nodes in the tree containing $V.$
Can I do better than this? I'm sure I can but I don't know how.