1. Use "<" and "=" to order the following functions by asymptotic growth rate, please give your justifications.

     3n² + n + 4, 2¹⁰⁰⁰, 5n(logn)³, 2^logn, n^logn, (logn)ⁿ,

2. Consider the following array java codes.

int[][][] x = {{{1,2},{3,4}},{{5,6},{7,8}}};

int[][][] y = new int[2][2][];

y[0] = x[0].clone();

y[1][1] = x[1][1].clone();

x[0][0][0] = 100;

x[1][1][1] = 200;

System.out.println(y[0][0][0]+" "+y[1][1][1]);

Please answer what will be printed and explain what will happen in the memory (why).

3.Insert into an empty binary search tree entries with keys: 30, 40, 24, 58, 48, 26, 11, 13 (in this order).  Draw a tree after each insertion.

4.The next two questions are based on the tree below:

a. Draw the resulting AVL tree resulting from the insertion of an entry with key 52.

b. Draw the resulting AVL tree resulting from the removal of the entry with key 62 (use the original tree).

5. Illustrate the process of inserting an initial empty 2-3-4 tree with the sequence of keys (5, 16, 22, 45, 2, 10, 18, 30, 50, 12, 1).