1) What is the primary purpose of template functions? 2) Suppose bag is a template class, what is the syntax for declaring a bag b of integers?

Transcription

1 Review for Final (Chapter 6 13, 15) 6. Template functions & classes 1) What is the primary purpose of template functions? A. To allow a single function to be used with varying types of arguments B. To hide the name of the function from the linker (preventing duplicate symbols) C. To implement container classes D. To permit the use of the debugger 2) Suppose bag is a template class, what is the syntax for declaring a bag b of integers? A. bag b; B. bag<int> b; C. bag of int b; D. int bag b; 7. Stack (LIFO) & its application 1. Stack overflow & underflow 2. Implementation: partially filled array & linked list 3. Applications: reverse string, backtracking 1) Which of the following applications may use a stack? A. A parentheses balancing program. B. Keeping track of local variables at run time. C. Syntax analyzer for a compiler. D. All of the above. 2) Consider the usual algorithm for determining whether a sequence of parentheses is balanced. What is the maximum number of parentheses that will appear on the stack AT ANY ONE TIME when the algorithm analyzes: (()(())(()))? A. 1 B. 2 C. 3 D. 4 E. 5 or more

2 3) In the linked list implementation of the stack class, where does the push member function place the new entry on the linked list? A. At the head B. At the tail C. After all other entries that are greater than the new entry. D. After all other entries that are smaller than the new entry. 8. Queue (FIFO) & its application 1. Application: buffer data 2. Implementation: partially filled circular array & linked list 1) One difference between a queue and a stack is: A. Queues require dynamic memory, but stacks do not. B. Stacks require dynamic memory, but queues do not. C. Queues use two ends of the structure; stacks use only one. D. Stacks use two ends of the structure, queues use only one. 2) In the linked list implementation of the queue class, where does the push member function place the new entry on the linked list? A. At the head B. At the tail C. After all other entries that are greater than the new entry. D. After all other entries that are smaller than the new entry. 3) If data is a circular array of CAPACITY elements, and last is an index into that array, what is the formula for the index after last? A. (last % 1) + CAPACITY B. last % (1 + CAPACITY) C. (last + 1) % CAPACITY D. last + (1 % CAPACITY)

3 9. Recursion 1. Base case & recursive case 2. Infinite recursion 1) What is the importance of the stopping case in recursive functions? 2) Implement the following function. Do not use any local variables or loops. void pattern(unsigned int n) // Precondition: n > 0; // Postcondition: The output consists of lines of integers. The first line is the number n. The next line is the number 2n. The next line is the number 4n, and so on until you reach a number that is larger than This list of numbers is then repeated backward until you get back to n. /* Example output with n = 840: */ 3) Consider the following function: void super_write_vertical(int number) // Postcondition: The digits of the number have been written, stacked vertically. If number is negative, then a negative sign appears on top. Library facilities used: iostream.h, math.h if (number < 0) cout << '-' << endl; super_write_vertical(abs(number)); else if (number < 10) cout << number << endl; else super_write_vertical(number/10); cout << number % 10 << endl;

4 What values of number are directly handled by the stopping case? A. number < 0 B. number < 10 C. number >= 0 && number < 10 D. number > 10 4) Consider this function declaration: void quiz(int i) if (i > 1) quiz(i / 2); quiz(i / 2); cout << "*"; How many asterisks are printed by the function call quiz(5)? A. 3 B. 4 C. 7 D. 8 E. Some other number 10. Tree 1. General trees nodes leaves parent, children, sibling depth 2. full/complete trees 3. Binary trees How to build? Traversing: inorder, preorder, postorder Using recursion 4. Binary search trees Definitions Efficient trees vs. inefficient trees Search strategy for binary trees Insertion Deletion

5 1. Here is a small binary tree: 14 / \ 2 11 / \ / \ / / 7 40 Circle all the leaves. Put a square box around the root. Draw a star around each ancestor of the node that contains 10. Put a big X through every descendant of the node contains Using the binary_tree_node from textbook, write a function to meet the following specification. Check as much of the precondition as possible. No recursion is needed. template <class Item> void subswap(binary_tree_node<item>* root_ptr) // Precondition: root_ptr is the root pointer of a non-empty binary tree. // Postcondition: The original left subtree has been moved and is now the right // subtree, and the original right subtree is now the left subtree. // Example original tree: Example new tree: // 1 1 // / \ / \ // // / \ / \ // Using the binary_tree_node from textbook, write a recursive function to meet the following specification. Check as much of the precondition as possible. template <class Item> void flip(binary_tree_node<item>* root_ptr) // Precondition: root_ptr is the root pointer of a non-empty binary tree. // Postcondition: The tree is now the mirror image of its original value. // Example original tree: Example new tree: // 1 1 // / \ / \ // // / \ / \ //

6 4. Here is a small binary tree: 14 / \ 2 11 / \ / \ / / 7 40 Write the order of the nodes visited in: A. An in-order traversal: B. A pre-order traversal: C. A post-order traversal: 5. Here is a small binary tree: 14 / \ 2 11 / \ / \ / / 7 40 A. The tree is neither complete nor full. B. The tree is complete but not full. C. The tree is full but not complete. D. The tree is both full and complete. 11. Balanced Tree 1. Heaps Definition how to build a heap Be able to describe and/or draw the results of searching, insertion and deletion 2. AVL tree Definition how to build a AVL tree 3. B-trees Definition Trace the path of a search Be able to describe and/or draw the results of insertion 4. Time complexity of all kinds of trees operations (binary, binary search, heap, AVL tree, b-tree) 12. Searching 1. Linear searching

7 2. Binary searching 3. Hashing 1. Open-address: linear probing, double hashing, quadratic probing 2. Chained hashing 4. Time complexity analysis 13. Sorting 1. Selection sort 2. Insertion sort 3. Merge sort 4. Quick sort 5. Heap sort 6. Time complexity analysis 1) Here is an array of ten integers: Draw this array after the FIRST iteration of the large loop in a selection sort (sorting from smallest to largest). 2) Describe a case where quicksort will result in quadratic behavior. 3) Here is an array of ten integers: Suppose we partition this array using quicksort's partition function and using 5 for the pivot. Draw the resulting array after the partition finishes. 4) Suppose we are sorting an array of eight integers using heapsort, and we have just finished one of the reheapifications downward. The array now looks like this: How many reheapifications downward have been performed so far? A. 1 B. 2 C. 3 or 4 D. 5 or 6 5) When is insertionsort a good choice for sorting an array? A. Each component of the array requires a large amount of memory.

8 B. Each component of the array requires a small amount of memory. C. The array has only a few items out of place. D. The processor speed is fast. 15. Graphs 1. Graph representations: adjacency matrix, adjacency list 2. Graph traversal: DFS, BFS 3. Single source shortest path problem: Dijstrak s aglorithm