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 Data pi 1 A 0.09 2 B 0.17 3 C 0.26 4 D 0.05 5 E 0.06 6 F 0.12 7 G 0.10 8 H 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