Test 2: CPS Owen Astrachan. November 17, Name: Honor code acknowledgement (signature)

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1 Test 2: CPS 53.2 Owen Astrachan November 17, 1993 Name: Honor code acknowledgement (signature) Problem 1 value 12 pts. grade Problem 2 16 pts. Problem 3 10 pts. Problem 4 13 pts. Problem 5 14 pts. TOTAL: 65 pts. 1

2 PROBLEM 1 : (Vocabulary) For each of the words/phrases below, circle the definition that is the best description as it pertains in the context of computer science, programming, and C/C array (a) a heterogeneous aggregate in which, by default, everything is public (b) a contiguous collection of homogeneous elements supporting random access (c) the member function called to initialize an object when the object is defined 2. constructor (a) a form of polymorphism in which multiple instances of a function with one name, but with different types of parameters, are used in the same program (b) the member function called to initialize an object when the object is defined (c) a form of graphics image that is accessible under both UNIX and DOS operating systems 3. binary search (a) the process of determining the binary representation of an integer using two s complement to represent negative numbers (b) the process of dividing a range to be searched in half with each comparison that is made (c) the process of adding two elements to a database at the same time cutting in half the time needed to add a new author and title, for example 4. strlen (a) the C function used to determine the number of characters in a string represented as a null-character terminated array of char (b) the C++ member function applied to objects of the class String to determine the number of characters in the string (c) A form of I/O stream that can be bound to a particular file when a program is run 2

3 PROBLEM 2 : (Fragments) Part A (6 points) The elements of an array a are to be shifted one position to the right so that a new element can be inserted into a[0]. You are to complete the function Insert given below so that val is inserted into a[0] as indicated by the pre- and post-conditions. Assume that there is room for the insertion to take place: void Insert(int a[], int val, int & numelts) // precondition: numelts = number of elements in a // there is room in a for val to be inserted // postcondition: a[0] = val, other array elements shifted right // numelts updated to reflect addition of val int k; for(k = ; ; ) a[0] = val; 3

4 Part B (10 points) The mean of a set of numbers is the average of the numbers, the mode is the number that occurs more often than any other number. For example, for the sequence of numbers: the mean is 3.5 and the mode is 4 (4 occurs more often than any other number). The function Stats below correctly calculates the mean of all numbers read. You are to modify it so that the mode is calculated as well. Assume that the mode is unique, i.e., one number will occur more often than any other number. You should also assume that all numbers read are between 0 and 100 (for example, the numbers might represent test scores.) void Stats() // postcondition: mean and mode printed int num; // number entered int sum = 0; // sum of all numbers entered int numnums = 0; // number of numbers entered while (cin >> num) sum += num; numnums++; // loop while number entered if (numnums > 0) // check for no numbers entered double average = double(sum)/numnums; cout << "mean = " << average << endl; else cout << "no numbers entered, no stats calculated" << endl; 4

5 PROBLEM 3 : (Database Redux) ThecodeforthefunctionFindIndex given below is taken from a working version of a database program like the one written in class: int FindIndex(const Collection & coll, const Item & item) // postcondition: returns index of item in coll // if item not in coll returns -1 int k; for(k=0; k < coll.numitems; k++) if (item == coll.list[k]) return k; return -1; Part A (6 points) If the collection coll stores 1,000 entries and takes (on the average) seconds to search using FindIndex, approximately how many seconds will it take to search if coll stores 1,000,000 entries? Briefly justify your answer. If the list of items is maintained in sorted order, within 3 seconds how many seconds will it take to search a list of 1,000,000 entries if binary search is used instead of the sequential method shown above? Briefly justify your answer. Part B (4 points) The lines String s; cout << "file "; ReadString(cin,s); ofstream output(s); occur in a student s database program. Briefly describe their purpose. 5

6 PROBLEM 4 : (Population Density) For each of the 50 states that make up the United States, an array is maintained of the ten most populous cities and the population of each of these cities, with the most populous city as the first entry in the array, the second most populous city as the second entry, and so on. The eleventh entry in each array represents all people NOT living in one of the ten most populous cities, i.e., everyone else. Consider the C/C++ definitions below: const int STATE_ENTRIES = 11; struct City String name; // name of the city int pop; // number of people in the city ; A state is considered urban if a majority of the people in the state live in one of the five most populous cities. Part A (6 points) Write the body of the function IsUrban whose header is given below. IsUrban returns 1 if the information in parameter statelist represents an urban state and returns 0 otherwise. int IsUrban(City statelist[]) // precondition: statelist contains STATE_ENTRIES entries // postcondition: returns 1 if statelist represents an urban state // else returns 0 Part B (7 points) You are to write the function UrbanStates whose header is given below. UrbanStates prints the names of all urban states (as defined above). Assume that information for all states in the U.S. is stored in a two-dimensional array USinfo, where USinfo[k] is an array (of 11 City entries) for the k th state (0 k<50). Further assume that the name of each state is stored in 6

7 astringarraystatename (with the k th state s name stored in position k). In writing UrbanStates, you may call the function IsUrban of Part A. Assume that IsUrban works as specified regardless of what you wrote in Part A. void UrbanStates(City USinfo[][STATE_ENTRIES], String statename[]) // precondition: USinfo[k] = info for kth state whose name is // stored in statename[k] // postcondition: names of all urban states printed 7

8 PROBLEM 5 : (Sets) A set of integers is a collection of integers in which no integer is repeated. For example 1, 3, 2, 6 is a set of four integers, whereas the collection 3, 2, 5, 3, 7 is not a set because the element 3 is repeated. A C++ class for implementing sets uses the following declarations: const int MAX_SET_SIZE = 500; // max number of elements in the set class Set private: int elements[max_set_size]; // elements stored in this set int numelements; // number of elements in set public: Set(); // constructor, makes set initially empty int IsEmpty(); // returns 1 if set is empty, else returns 0 int IsElement(int elt); // returns 1 if elt is in set, else returns 0 void Insert(int elt); // inserts elt into set (if room and not there) int NumElts(); // return number of elements in set int KthElt(int k); // return k -th element in set (0 <= k < numelements) ; where new items in a set are added to the end of the array elements (as a new item was added to the end of the array in the database program). For example, to create a set of the numbers 1 200, either of the code fragments below could be used: Set first; //initially empty int k; for(k=1; k <= 200; k++) first.insert(k); Set second; //initially empty int k; for(k=200; k >= 1; k--) second.insert(k); Note that first and second represent the same set although the numbers are inserted in different orders. The value of first.kthelt(0) is 1, and the value of second.kthelt(0) is 200 (since, for example, 200 is added to second before any other element). Part A (3 points) The constructor for the class Set is written as follows: Set::Set() numelements = 0; // intially no elements in the set Complete the body of the member function IsEmpty int Set::IsEmpty() // postcondition: returns 1 if set is empty, else returns 0 8

9 Part B (4 points) Complete the member function Insert below. In writing Insert you may call the member function IsElement. void Set::Insert(int elt) // postcondition: if elt not already in set then elt added to set // (provided there is room for a new element) Part C (3 points) One limitation of the this representation is that a set can contain no more than 500 elements, a limit set at compile time. Describe how to make a change so that the number of elements in a set could be set at runtime, by an argument to the constructor. For example, the definitions Set bigset(1000); Set smallset(10); could result in sets capable of storing 1,000 and 10 elements respectively. You just need to describe how the size of elements could be set at run time. Part D (4 points) If the array elements is kept sorted, which of the functions IsEmpty, IsElement, Insert, andnumelts could execute more quickly (assuming the functions are rewritten to take advantage of the sorted order) and why? Part E: Extra Credit (5 points) Write the function Intersect whose header is given below. This function should store in set C all elements that are in both A and B, i.e., should set C to the intersection of A and B. void Intersect(const Set & A, const Set & B, Set & C) // precondition: C represents an empty set // postcondition: C represents the set A intersect B 9

PROBLEM 1 : (Vocabulary: 8 points) For each of the words/phrases below, circle the denition that is the best description as it pertains in the context

PROBLEM 1 : (Vocabulary: 8 points) For each of the words/phrases below, circle the denition that is the best description as it pertains in the context Test 1: CPS 100 Owen Astrachan February 12, 1996 Name: Honor code acknowledgement (signature) Problem 1 Problem 2 Problem 3 Problem 4 Extra TOTAL: value 8 pts. 18 pts. 13 pts. 16 pts. 6 pts. 57 pts. grade