18. Consider a set of 6 nodes 1, 2, 3, 4, 5, 6 and their corresponding weights: 2, 3, 4, 4, 5, 6.
(a) (5%) Build a binary tree with these nodes appearing in the leaves such that the maximum of w[il x (1/2)^d[i] is minimized, where w[i] is the weight and d[i] is the depth of node i in the tree. Note that the root has depth 0. What is the optimal value?