Now let's look at a cell \\(x\\), and consider the cost of continually supplying it with fluid, along the whole line of pipes leading from the root to \\(x\\).

Part of this cost would be accounted for by summing \\(w(e)^\alpha \cdot L(e)\\), for all edges \\(e\\) on the path from the root to \\(x\\).

Part of this cost would be accounted for by summing \\(w(e)^\alpha \cdot L(e)\\), for all edges \\(e\\) on the path from the root to \\(x\\).