Module Contact: Dr Pierre Chardaire, CMP Copyright of the University of East Anglia Version 1

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1 UNIVERSITY OF EAST ANGLIA School of Computing Sciences Main Series UG Examination 2015/16 INTRODUCTORY PROGRAMMING CMP-0005B Time allowed: 2 hours. Answer BOTH questions from section A and ONE question from section B. Notes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator. CMP-0005B Module Contact: Dr Pierre Chardaire, CMP Copyright of the University of East Anglia Version 1

2 Page 2 SECTION A 1. (a) The following C++ function contains eight syntax errors. Describe [16 marks] each of them using the line numbers to identify them. If you mention more than eight errors only the first eight will be considered for marking. 1 # include < iostream > 2 #include <vector > 3 4 using namespace std ; 5 6 bool isprime ( i n t n ) 7 { 8 i f ( n == 1) return false ; 9 i f ( n == 2) return true ; 10 double sqx = s q r t ( n ) ; 11 for ( i n t i =2; i =< f l o o r ( sqx ), i ++) 12 i f ( n mod i == 0) 13 return false ; 14 return true void printupto ( i n t n ) 18 { 19 for ( i n t i =2; i <n ; i ++) 20 i f isprime ( i ) 21 cout << i << endl ; i n t main ( ) 25 { 26 i n t n ; 27 cout >> Enter a p o s i t i v e number > ; 28 c i n << n ; 29 n = printupto ( n ) ; 30 return 0; 31

3 Page 3 (b) Trace the execution of the following function for the input n = [8 marks] using the line numbers to indicate when changes in the states of the variables occur. 1 bool t e s t 7 d i v ( i n t n ) 2 { 3 i n t r, q ; 4 while ( n > 0) 5 { 6 r = n % 10; 7 q = n / 10; 8 n = q 2 r ; 9 10 i f ( ( n==0) ( n== 7) ( n== 14) ) 11 return true ; 12 else 13 return false ; 14 (c) What is the following function supposed to do? Clearly justify your [8 marks] answer. You may want to trace the code with some of the inputs BARBER, BAOBAB, BERBER. bool t o i s t a a ( s t r i n g &s ) { i f ( s. l e n g t h ( ) % 2 == 1) return false ; i n t j = s. l e n g t h ( ) / 2 ; for ( i n t i = 0; i < s. length ( ) / 2 ; i ++) i f ( s [ i ]!= s [ i + j ] ) return false ; return true ; TURN OVER

4 Page 4 (d) What is the purpose of the following function? Clearly justify your [8 marks] answer. 1 void j a r j e s t e l l a ( i n t &a, i n t &b, i n t &c ) 2 { 3 i n t temp =0; 4 i f ( b>c ) { temp=b ; b=c ; c=temp ; 5 i f ( a>b ) { temp=a ; a=b ; b=temp ; 6 i f ( b>c ) { temp=b ; b=c ; c=temp ; 7 2. There is no requirement to test for input ranges or carry out other validation in the following parts of this question. Comments should only be included if they are required to add clarity to the code. (a) Write a C++ code fragment to ask the user to enter an integer number, and output all non-negative integer numbers whose squares are less than or equal to the input number. (b) The conversion formulas between temperatures in degrees [15 marks] Fahrenheit (F) and temperatures in degrees Celsius (C) are: F = C 9/ and C = (F 32) 5/9. Write a program that repeatedly ask a user to enter a temperature. The user inputs a number followed by the letter F or by the letter C. After each temperature input the program should output the conversion of the temperature into the other unit. The program should terminate when the same temperature is entered twice in succession.

5 Page 5 (c) A palindrome is a word which reads the same forward and [15 marks] backward. A sentence is called palindromic if after removing spaces, punctuation and changing lower case letters into upper case letters a palindrome is obtained. For example, the sentence Was it a car or a cat I saw? is palindromic. Write one or more functions to determine if a sentence is palindromic. To do so you may want to use the function ispunct that takes a character as input and returns true if the character is a punctuation sign and false otherwise, and the function toupper that returns the upper case letter associated with a letter. TURN OVER

6 Page 6 SECTION B Answer ONE question from this section. 3. A class for storing and returning consecutive primes is declared as [40 marks] follows: #include <vector > using namespace std ; class Primes { public : s t a t i c i n t f i r s t P r i m e ( ) ; s t a t i c i n t nextprime ( ) ; s t a t i c i n t previousprime ( ) ; / / r e t u r n s 0 i f no previous prime private : / / I n i t i a l i s e the data members s t a t i c i n t i n i t P r i m e s ( ) ; / / Adds a new prime t o t h e sequence o f primes s t a t i c void addprime ( ) ; / / Helper f o r addprime : r e t u r n s t r u e i f n i s d i v i s i b l e / / by a prime i n t h e sequence o f primes memorised s t a t i c bool composite ( i n t n ) ; / / memorises consecutive prime numbers 2, 3, 5... s t a t i c v e c t o r <int > primes ; / / index i n v e c t o r primes of the prime l a s t returned / / by a c a l l to f i r s t P r i m e, lastprime or nextprime s t a t i c i n t index ; ;

7 Page 7 For example the class may be used by the following program: # include < iostream > #include " Primes. h " using namespace std ; i n t main ( ) { cout << Primes : : f i r s t P r i m e ( ) ; for ( i n t i =0; i <10; i ++) cout <<, << Primes : : nextprime ( ) ; cout << endl ; the execution of which produces: 2,3,5,7,11,13,17,19,23,29,31 Press any key t o continue... The start of the implementation of the class is as follows: vector <int > Primes : : primes ; i n t Primes : : index = Primes : : i n i t P r i m e s ( ) ; Implement the rest of the class. An equal number of marks will be awarded for each of the methods correctly implemented. Reminder: If the first n primes are known, the n + 1 th prime is the first number that follows the n th prime and is not divisible by any of the first n primes. TURN OVER

8 Page 8 4. An integer y is a factor or divisor of an integer x if x/y is an integer number. An integer number is prime if it is greater than one and its only factors are one and itself. Any number can be written as a product of prime factors, called its prime factorization. This product is unique up to the order of the factors. For example = 2 {{ {{ {{ 11 = , = , 143 = , 43 = (a) You are given a function firstprime() that returns the first prime number and a function nextprime() that returns the first prime number that follows the number obtained by the last call to firstprime() or nextprime(). Write a function that takes a non-negative integer n as input and returns the smallest prime greater than n. (b) Write a function that takes two non-negative integers n and p as input and returns true if p is a factor of n and false otherwise. (c) Using the function of question 4b write a function that takes two non-negative integers p and q as input and returns p/q m where m is the largest integer such that q m is a divisor of p and sets an output variable to m. If q is less than two then p should be returned and the output variable set to zero. You are reminded that x 0 = 1 for any integer x.

9 Page 9 (d) Using the functions of questions 4a and 4c write a main program that repeatedly ask for an integer number until a zero or a one is entered. For each number entered the program should output its prime factorisation, representing consecutive primes with their exponents as consecutive pairs. An example of execution is as follows: Enter number > = ( 2, 2 ) ( 3, 4 ) ( 1 1, 2 ) Enter number > = ( 2, 7 ) ( 3, 3 ) Enter number > 0 Press any key t o continue... END OF PAPER