cs109: Programming Paradigms C++ FS 2014

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1 UNIVERSITÄT BASEL Thorsten Möller Alexander Haesen Valentino Rugolo cs109: Programming Paradigms C++ FS 2014 Exercise 1 Deadline: :59:59 Note: Please upload answers to the questions and source code before the deadline via courses.cs.unibas.ch. Running programs have to be demonstrated during the exercise slot on or Modalities of work: The exercise can be done in groups of at most 2 persons. Do not forget to provide the full name of all group members together with the submitted solution. Question 1: Declarations & Definitions (9 points) a) Consider the following lines: double d1 = ; extern double d2 ; d1 = d2 ; Are these definitions, declarations, a combination of both, or neither a definition nor a declaration? Explain. b) Given the following C++ source code, explain each line (i.e., what it does). Imagine a source code file that contains line 1 to 6 in this order. Would it compile? If there are errors, explain what must be changed. 1 double magic ( int x, double y ) ; 2 double magic ( int x, float y ) ; 3 float s p e l l ( int x, double y ) ; 4 double magic ( int x, double y ) { return s p e l l ( x, y ) ; } 5 double magic ( int x=1, double y = ); 6 double s p e l l ( int x, double y ) { return ( float ) ( x/y ) ; } Question 2: Function Prototypes (5 points) Define the prototype for the following functions. Parameter names may be freely chosen if not specified. Choose types that are appropriate in the specified context. 1

2 a) A function named isinrange that has a minimum and a maximum value as parameters and returns whether a third parameter x is within that range or not. b) A function named drawnextframe that draws the next frame (the frames are stored globally). c) A function named drawnextpoint that draws the next point (the points are stored locally). d) A function named ultrapow that computes a very large number given from a single parameter x. e) A function named divide that returns a division of two parameters and that defaults the denominator to a non-zero value. Question 3: Input & Output (8 points) a) Write a C++ program called guess-the-number.cpp. This program calculates a random number between 1 and 999 and invites the user to guess this number. If the user make a too large guess the program answers with too large, and vice versa with too small. After 10 wrong guesses, the program ends with a message that says that the user lost the game. If the user found the right number, output the number of guesses needed. Hint: Generting a random number between 0 and : Include stdlib.h Set a random generator seed with srand(time(null)) Generate the random number with rand() b) Write a C++ program called guess-the-number v2.cpp, based on the previous program. Instead of making the user guess the number, implement an algorithm that finds the right number; i.e., the lines in the source code where the user inputs a guess should be replaced by a calculation it is not difficult to see that this can be done in a systematic way. Question 4: Structures and sizeof Operator (6 points) The instruction in the first line of the C/C++ source code listed below is an advanced feature that can be used to adjust the memory alignment of data. Provided that the hardware supports non-aligned memory access (i.e., an access of an address that is not a multiple of the architecture s word size), which is the case for x86 architectures, one can, for instance, instruct the compiler to use a one-byte alignment (which is precisely what is done in the source code). #pragma pack ( 1 ) struct foo { char c1 ; 2

3 } ; long l ; char c2 ; char c3 ; a) First, explain what kind of instruction it is. Second, given the foo structure, if one would compile with a one-byte, a four-byte, and an eight-byte alignment (#pragma pack(1), #pragma pack(4), or #pragma pack(8), respectively), the sizeof operator would return 11, 16, and 24 bytes, respectively, on a 64 bit x86 architecture (verify this on such an architecture). Explain the different results! What tradeoff is being made between the different settings? b) Is the foo structure optimally designed in terms of memory consumption regarding a four and eight-byte alignment? If not, find an optimal layout. Question 5: Enumerations (5 points) Given the structure and enumeration below, write a C++ program that does the following: The users enters a string and a number first. If the number is positive, a new Person is instantiated, the string is assigned to the name field and the number to the age field; otherwise an error message is printed and the program terminates with a return value 1. The field t is initialized with a value depending on the following indications: a baby is aged 0 to 1 (inclusive) a child is aged 2 to 18 (inclusive) an adult is aged 19 to 60 (inclusive) an elder is aged 61 and upwards Afterwards, the program prints out following statement: [p.name] is a [p.type]. Make use of a switch statement to achieve this. enum VehicleType { BABY, CHILD, ADULT, ELDER } ; struct Person { int age ; s t r i n g name ; Type type ; } ; Question 6: The Collatz conjecture (12 points) The so-called hailstone sequence is a sequence of natural numbers, with initial value n, obtained by the following algorithm: a i = { n for i = 0 f(a i 1 ) for i < 0 3

4 where f(x) = { x/2 if x mod 2 = 0 3x + 1 if x mod 2 = 1. The Collatz conjecture states that this sequence will eventually reach the number 1, regardless of which n is chosen initially. In this exercise, you will write a C++ program that will verify this conjecture for start values up to a) Write a program, collatz v1.cpp, with the following two functions: int collatz(int n), which computes the value f(n) for the input value n as described above. void sequence(int start), which computes the hailstone sequence up to the value 1, starting with initial value start. Test these functions by outputting the hailstone sequence for a given initial value in the main function; e.g., the output for sequence(6) would be: 6,3,10,5,16,8,4,2,1. b) Write a program, collatz v2.cpp, that computes the hailstone sequence up to the value 1 for initial values ranging between 1 and , and outputs the initial value for the sequence with the longest iteration. In order to achieve this, change the function void sequence(int start) so that it returns the number of iterations to reach the value 1. c) Write a program, collatz v3.cpp, that computes the distribution of iteration lengths of the sequences computed in collatz v2.cpp over intervals of 10. Since the maximum number of iterations is known (as computed above), you can create a static array representing the buckets (e.g. the first entry of the array counts the number of sequences with iteration length between 1 and 10, the second entry counts the number of sequences with iteration length between 11 and 20, etc...). Output the distribution of iteration lengths over all buckets. Question 7: Recursive Function 1 (0 points) Implement a C++ function that calculates the difference of the first n positive cubed numbers and returns the result as an integer. This difference is formally expressed as follows n The function should take n as a parameter of type unsigned int and return the result as an int. The method should furthermore not have any local variables other than formal parameters. Make sure to test the implementation; e.g., the result for n = 10 is There are two undesired phenomena that can occur at runtime. Which are these phenomena? Find values for n (analytically or experimentally) for which the phenomena occur. 1 Optional task. There is no need to solve this task nor is it graded if done. 4

5 What could be done to prevent/handle them (i.e., to make the implementation more robust)? 5

cs109: Programming Paradigms C++ FS 2015

UNIVERSITÄT BASEL Thorsten Möller Alexander Haesen Mihai Rapcea cs109: Programming Paradigms C++ FS 2015 Exercise 1 Deadline: 29.03.2015 23:59:59 Note: Please upload answers to the questions and source