1. Draw an AVL tree of height 0,1,2,3, 4 with a minimum number of nodes 2. (a) The minimum number of nodes S(h) of the AVL tree of height h is given by the recurrence S(h) = S(h-1) + S(h-2) + 1 with S(0) = 1 and S(1) = 2 . Tabulate the values for h 1, . . . , 20. (b) Try to find a value a > 1, such that s(h) ah for all the values in the table. (a) For 100 items? (b) For 500 items? 4. There are 300 elements which need to be stored in an AVL tree. (a) What is the height of the AVL tree in the worst case? (b) What is the height of the AVL tree in the best case? 5. There are 300 elements which need to be stored in a 2-3 tree. (a) What is the height of the 2-3 tree in the worst case? (b) What is the height of the 2-3 tree in the best case? 6. Consider a 2-3 Tree of height 10. What is the minimum and maximum number of elements which can be stored? 7. Consider a B tree of order 5 with height 3. What is the minimum and maximum number of elements which can be stored? 1. Draw an AVL tree of height 0,1,2,3, 4 with a minimum number of nodes 2. (a) The minimum number of nodes S(h) of the AVL tree of height h is given by the recurrence S(h) = S(h-1) + S(h-2) + 1 with S(0) = 1 and S(1) = 2 . Tabulate the values for h 1, . . . , 20. (b) Try to find a value a > 1, such that s(h) ah for all the values in the table. (a) For 100 items? (b) For 500 items? 4. There are 300 elements which need to be stored in an AVL tree. (a) What is the height of the AVL tree in the worst case? (b) What is the height of the AVL tree in the best case? 5. There are 300 elements which need to be stored in a 2-3 tree. (a) What is the height of the 2-3 tree in the worst case? (b) What is the height of the 2-3 tree in the best case? 6. Consider a 2-3 Tree of height 10. What is the minimum and maximum number of elements which can be stored? 7. Consider a B tree of order 5 with height 3. What is the minimum and maximum number of elements which can be stored