Problem 3: Label Internal Philosophy Suites (20+ pts) Put a dark circle around True or False as appropriate for the following statements. Then, prove why the False statements are not True.

3.1 True False The order in which keys are inserted has no impact on the shape of the corresponding binary search tree. 3.2 True False A static array of size n has non-empty keys in all the entries. 3.3 True False One goal of asymptotic analysis is to determine the growth rate of the execution time of an algorithm with respect to an increase in the size of the problem. 1.4 True False An algorithm with execution time in (log n) must examine at least (a log n) nodes, for some positive constant a. 3.5 True False Delete in a BST is in 12(1). 3.6 True False All full 4-ary trees with the leaves at the same level are complete. 3.7 True False The number of nodes in a complete binary tree with levels numbered from 0 to p, also known as p+1 levels is given by 2i = 2P+1 -1 2 IM i=0 3.8 True False The time to build a binary search tree with n unique keys is in O(na). 3.9 True False All priority queues maintain the keys in order of some predefined rank. 3.10 True False O(na) The amount of space required to store a graph with n vertices and n2 3 edges is in