1. Binary search trees find their widely use in many applications. Answer the following short questions about binary search tress. ( 2 O % )
(a) Define a binary search tree. (5%)
(b) Using data sequence: (40, 20, 60, 10, 30, 50, 70, 45, 55, 521, construct a binary search tree. (5%)
(c) Write a recursive search function for binary search trees, assuming that the input arguments are the root pointer and an integer key. The return value is the pointer of the node containing the key or null. (5%)
(d) Explain how t o use binary search trees to sort sequences. What is the time coinplexity of it? (5%)
2. Queues and priority queues are two widely used data structures. Answer the following short questions. (20 d/b)
(a) Describe the differences between queues and priority queues. (5%) (b) Define a min-priority queue. (5%)
(c) What are the time complexities of insertion and deletion operations when a min- prority queue is represented in terms of the following data structures: a n unordered array, an unordered linked list, a sorted array, a sorted linked list, and a rnin heap?
(10%)
3. Answer the followillg two short questions about stack and min-priority queue. ( ( I=, %)
(a) T h e stack is also a data structure. Describe its main features. (5%)
(b) Can a inin-priority queue be used as a stack? If yes, please explain how to do this.
(5%)
4. (20%)
(a) Briefly explain the hashing technique and discuss its advantages. (5%)
(b) Discuss the advantages and disadvantages of the two clash (collision) resolution strategies: open addressing and chaining. (5%)
(c) What are the key points for designing a good hash function? (5%)
(d) What would be a good hash function for license plates that is a string of numbers and letters of the form " * ic 000 * ic "', where an ''0" represents a digit and
an " * " represents a letter? Why? (5%)
5 (20%)
(a) Write an algorithm that checks if a complete binary tree is a heap. Analyze your algorithm and show the result using order notation. (1 0%)
(b) Design a sorting algorithm based on a ternary heap. A ternary heap is like an ordinary heap except that each internal node has three children. (10%)
6. (10%)
Write a C/C+t function that takes an integer array and its size as arguments and finds the minimum and the maximum of the numbers. This can be done by using no more than 3n/2 comparisons where n is the size of the array.
