1-2. * Recursion:*

- Write a recursive method (code) for computing the sum of all the elements of a linked list.
- Trace your method on the example of a list consisting of elements 12, 10, and 20.
- Describe advantages and disadvantages of recursion vs. iteration in solving a problem, from the viewpoint of easiness to write, easiness to understand, and running time.

3.

- Write a method for checking whether all the elements of a matrix
are positive. For example, for the matrix
1 2 3 4 5 6 7 8 9

the answer should be "true", while for the matrix1 -2 3 4 5 6 7 8 9

the answer should be "false". - Trace your method on the example of the second matrix.
- Using big-oh notation, give the worst-case running time for your algorithm.

4.

- Rewrite the expression 12 - 10 * (20 - 1) in postfix form.
- Show, step by step, how a stack can be used to compute the value of the resulting postfix expression.

5.

- Show, step by step, the state of a queue -- implemented as an 3-element array - when we first add 12, 10, and 20, then dequeue twice and after that add 1 and 0.
- Write a method for enqueuing an element in a queue represented as an array.
- Using big-oh notation, what is the worst-case running time for your enqueue method?

6-7.

- Show, step by step, how bubble sort, selection sort, insertion sort, mergesort, quicksort, and heapsort will sort a list consisting of the elements 12, 10, 20, 1, 0.
- Write code for
**one**of these sorting algorithms (clearly specify which one). - Draw a table listing the worst-case and average-case complexity for each of the six sorting algorithms.
- True or False: It is possible to implement a sorting algorithm that is much faster than heapsort. Justify your answer.

8.

- Suppose you start with an empty AVL binary search tree. Show step by step what will happen if you add elements 12, 10, 20, 1, and 0 to the binary search tree in that order. Balance at each step where it is necessary.
- Show how the resulting tree will look like in an array-based implementation of trees (leave blank spaces for any nodes that do not exist in the tree).
- In 1-2 sentences, what is the purpose of balancing?
- State the condition that every node in a binary search tree must satisfy.

9.

- Show, step by step, how sequential search and binary search will look for an element 9 in the sorted list 0, 1, 10, 11, and 20.
- What is the worst-case and average-case number complexity of each search?
- What are relative advantages and disadvantages of these two search algorithms?
- Write down a method implementing sequential search and another implementing binary search. Assume that the list is implemented as an array.

10.

- Show, step by step, how a hash table with six "buckets" will look if we
sequentially add to it elements 12, 10, 20, 0, and 1. Assume that
as a hash function, we take remainder modulo 6:

h(n) = n % 6. - What are advantages and disadvantages of hash tables?
- List two properties of a good hash function.