1. This question concerns the dynamic programming algorithm for computing a binary tree, discussed in class in and in the notes. Suppose we are given the following data, consisting of 8 key values and the frequency with which each key is accessed: i 1 2 3 4 5 6 7 8 Data Pi A B D E F G H 0.09 0.17 0.26 0.05 0.06 0.12 0.10 0.15 (a) For each i and j in the appropriate range, give the values of E[i, j] and root[i, j]. (b) Draw the optimal binary tree for the data given above. (c) What is the weighted lookup cost of the optimal binary tree? Explain briefly how you computed it.