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 p_{i}
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? Explain briefly how you computed it.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.