CS2 Final Study Guide


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1 CS2 Final Study Guide  Know how to write an assignment operator, copy constructor and destructor for a simple class that has dynamically allocated memory. Trees 1. Define the following terms o binary search tree o leaf of a tree o degree of a tree node o degree of a tree o path in a tree o length of a path in a tree o descendents of a node in a tree o ancestors of a node in a tree o depth of a node in a tree o height of a node in a tree o height of a tree 2. Draw the expression tree for the expression a*(b+c)(d+(ef)*g) 3. For the tree 1. What is the height of node A? 2. What is the height of the tree? 3. What is the depth of node E? 4. What is the parent of node F? 5. Name the descendent(s) of node B. 6. Name the leaves in the tree. 4. Write a C++ function TreeNode* copy_tree(treenode* T) that returns a copy of binary tree T
2 5. Write a C++ function TreeNode* expand_leaf(treenode* node, ItemType x, ItemType y) that returns a new binary tree that is identical to the binary tree T except that every leaf in T now has a left child and a right child whose values are equal to x and y, respectively. For example, invoking expand_leaf(t, 9, 12) on the tree on the left produces the tree on the right. 6. Write a C++ function int height(treenode* T) that returns the height of the binary tree T. 7. Write a C++ function bool same_tree(treenode* T1, TreeNode* T2) that returns true if binary trees T1 and T2 are exactly the same (same values, same structure), and returns false otherwise. You may assume that values of tree_item_type can be compared by means of the == operator. 8. Write a C++ function TreeNode* bst_insert(itemtype item, TreeNode* T) that inserts item into the binary search tree T. After the insertion, T must remain a binary search tree. You may assume that tree_item_type values are comparable using the ==, <, and > C operators. Draw the binary search tree resulting from sequentially calling bst_insert on an initially empty binary tree with the values 9,12,5,15,7,10,18.
3 Tree Traversal 1. For the tree Write the node labels in preorder order 2. Write the node labels in inorder order 3. Write the node labels in postorder order 1. Write C++ code, using the ADT operations for binary tree, to construct this binary tree of char 2. Write a function void Foo(TreeNode* T) that takes a binary tree, T, of char and performs some function (your choice) on the tree. Briefly describe what the function does in your own words.
4 Search Functions for DFS and BFS of binary trees from the notes will be given to you in the exam, if needed. 1. Let tree T be this tree 1. Draw the subtree returned by depth_first_search(t, 'B'); 2. Draw the subtree returned by bfs_queue(t, 'B'); 2. Given an array containing the sequence 1,5,29,45,67,76,92,104,187,234 (in that order) 1. state each comparison made in finding the number 234 using linear search. (For example, 234:1 is a comparison of 234 with 1.) 2. state each comparison made in determining that the number 48 is not present using linear search. 3. Given an array containing the sequence 1, 5,29,45,67,76,92,104,187,234 (in that order) 1. state each comparison made in finding the number 234 using binary search. (For example, 234:1 is a comparison of 234 with 1.) 2. state each comparison made in determining that the number 48 is not present using binary search. 4. Given the following sequence of integers (for example, integers received from the keyboard) 29,234,1,45,92,76,67,187,104,5 (in that order)
5 1. draw the binary search tree that would result from inserting the integers in the order given. 2. state each comparison made in finding the number 234 in the tree (For example, 234:1 is a comparison of 234 with 1.) 3. state each comparison made in determining that the number 48 is not present in the tree. 4. write the integers as they would be encountered in an inorder traversal of the tree. 5. Linear search can be done on data in an array or in a list. Name an advantage and a disadvantage of the list implementation over the array implementation. 6. Binary search can be done on data in a sorted array or in a binary search tree. Name an advantage and a disadvantage of the array implementation over the BST implementation. Sorting 1. How many permutations of N distinct items are there? 2. Explain: selection sort is an algorithm on average. 3. Explain: quicksort is an algorithm on average, but is an algorithm worst case. 4. Given an array containing the integers (in that order), 1. Show the array as it is sorted by the function selectionsort. 2. Show the array as it is sorted by the function mergesort 3. Show the array as it is sorted by the function insertionsort 4. Show the array as it is sorted by the function bubblesort 5. Write a templated version of both bubble and selection sort. 1. As the numbers of elements to be sorted increases how do the two sorts compare to one another?
6 Asymptotic Analysis 1. Fill in the following in increasing order from the set 2. Linear search can be done on data in an array or in a list. What is the average time complexity for successful search using an array? Using a list? Name an advantage of the list implementation. Name an advantage of the array implementation. 3. Binary search can be done on data in a sorted array or in a binary search tree. What is the average time complexity for successful search using the array? Using the BST? What is the worst case time complexity for each? Name an advantage of the BST implementation. Name an advantage of the sorted array implementation. Graphs 1. Is every graph a binary tree? If so why, it not, why not? 2. Draw the adjacency matrix for the following graph. Draw the adjacency list for the graph. When is one representation better than the other? How do you represent an undirected graph in an adjacency matrix?
7 3. Starting at Start Room label nodes in the order visited via a depth first search 4. Starting at Start Room label nodes (1,2,3,4,..) in the order visited via breadth first search. Heaps 1. Be able to identify a heap. 2. Show a maxheap after inserting each of the following numbers: 13,9,4,5,2,8,3,0,12 3. Remove the two biggest numbers, showing the heap structure after each deletion.
8 Previous Exam Topics 1. What will be the output of the program? #include <iostream> using namespace std; int main () { int nums[] = {2, 4, 6, 1, 2, 5}; int *p = nums + 5; } while (p >= nums) { if (*p % 3 == 0) { *p = *p + 1; p++; } else if(*p % 2 == 0) { *p += 2; p++; } p = p  2; } for (int i=0; i<6; i++) cout << nums[i] << " "; 2. Write the code fragment that appropriately deletes the node pointed to by p (data value 14) in the doubly linked list shown in the diagram. Write the code fragment to insert a node between 14 and Write code for an abstract base class called SeaCreature. This base class should have at least 2 member functions, not including any constructors/destructors. Write a derived concrete subclass called Fish. Remember to use good programming habits when writing these classes.
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