Afull binary tree has 24 leaves. deduce a lower bound for its height. (b) let t be a full 4-ary tree of height h, where h > 0. assume that t has 78 internal vertices. i. how many vertices does t have? ii. deduce a lower bound h for the height of t. iii. assume t is balanced and of height precisely this lower bound h computed in ii. for each level of t, identify the total number of internal vertices and the number of leaves.

A-12.3 an american spy is deep undercover in the hostile country of phonemia. in order not to waste scarce resources, any time he wants to send a message back home, he removes all the punctuation from his message and converts all the letters to uppercase. so, for example, to send the message, “abort the plan! meet at the dark cabin.” he would transmit given such a string, s, of n uppercase letters, describe an efficient way of breaking it into a sequence of valid english words. you may assume that you have a function, valid(s), which can take a character string, s, and return true if and only if s is a valid english word. what is the running time of your algorithm, assuming each call to the function, valid, runs in o(1) time?