Computer Engineering 1 (1E3)

Transcription

1 Faculty of Engineering, Mathematics and Science School of Computer Science & Statistics Engineering Trinity Term 2017 Junior Freshman Examinations Computer Engineering 1 (1E3) DD MMM YYYY Venue Dr Lucy Hederman Instructions to Candidates: Attempt three questions. All questions carry equal marks. Each question is scored out of a total of 33 marks. You may not start this examination until you are instructed to do so by the invigilator. Materials Permitted for this examination: Non-programmable calculators are permitted for this examination please indicate the make and model of your calculator on each answer book used.

2 1. (a) The Fibonacci series starts with 0, 1, Thereafter each term is the sum of the two previous terms (i) (ii) Write a C++ program to print out the first 20 fibonacci numbers, separated by a space. (7 marks) Write a second C++ program to print out the fibonacci series, separated by spaces, up to but not including any number beyond 2000, and then report how many terms were printed. (9 marks) (b) Write a program for a number guessing game. The program generates a random number (see function below) between 0 and 99, and then asks the user to guess that number. For each guess the program replies Correct, Too low, or Too high. If the number is correct, the program prints the number of guesses it took. If not, the program asks the user to guess again. For example: Guess a number between 0 and 99: 50 Too low. Guess again: 75 Too high. Guess again: 60 Too high. Guess again: 54 Correct. It took you 4 guesses. Use the following function to choose the random number: int random (int n); //returns a random integer between 0 and n-1 (17 marks) Page 2 of 6

3 2. (a) Write a function sort2 which takes two integer variables a and b, and swaps the values of a and b if a is greater than b, and otherwise leaves a and b unchanged. For example int u = 2; v = 3; w = 4; x = 1; sort2(u, v); // u is still 2, v is still 3 sort2(w, x); // w is now 1, x is now 4 (8 marks) (b) The C++ program on the next page computes the real roots of a quadratic equation and tests the accuracy of those roots. In this question you will rewrite the program using functions. (i) Write a function to compute the discriminant. This function is to be used by the qroots function (part ii). (3 marks) (ii) Write a function qroots that determines whether and how many real roots there are and computes any real roots. The declaration of this function is void qroots (double a, double b, double c, int& status, double& r1, double& r2); The status value should be set by this function as follows: 0 no real roots; 1 one real root; 2 two real roots; 3 not a quadratic at all (10 marks) (iii) Write a function to compute the value of the quadratic at a given point, which is used to test the accuracy of the computed roots. (3 marks) (iv) Rewrite main so that it behaves like the original but uses the functions of part (ii) and part (iii). (9 marks) Page 3 of 6

4 int main() { double a, b, c, discriminant, root1, root2; cout << "Enter a, b and c:"; cin >> a >> b >> c; if (a == 0) cout << "\nthat is not a quadratic.\n"; else //a is not 0 { discriminant = b*b - 4*a*c; if (discriminant < 0) cout << "\nthe equation has no real roots.\n"; else if (discriminant == 0) { root1 = -b/(2*a); cout << "\nthe equation's only root is "; cout << root1 << endl; if ((a*root1*root1 + b*root1 + c) == 0) cout << " which is accurate.\n"; } else //discriminant is > 0 { root1 = (-b + sqrt(discriminant)) / (2*a); root2 = (-b - sqrt(discriminant)) / (2*a); cout << "\nthe roots are \n" << root1; if ((a*root1*root1 + b*root1 + c) == 0) cout << " which is accurate\n"; cout << " and " <<root2; if ((a*root2*root2 + b*root2 + c) == 0) cout << " which is accurate.\n"; } } //end of else a is not 0 } return 0; Page 4 of 6

5 3. Write a program to process weekly payroll records. The input is a file of records each consisting of staffid (a string), surname, first name, hours worked, hourly rate, tax credit. The first line of the input is an integer specifying how many records there are in the file. The output for each input record should give all the input data, plus the gross pay, tax to be paid and the net pay. Additionally the program should print the total weekly pay bill (sum of each employee s gross pay) and the total tax to be paid by the employer (sum of each employee s net tax). An employee s gross pay is the amount the employer pays for the hours worked, inclusive of tax. Employees are paid their hourly rate for all hours up to 40 in a week, and an overtime rate of 1.5 times their hourly rate for all hours in a week over 40. Net pay is gross pay minus tax. Tax is 25% of gross pay, reduced by the employee s tax credit, to a minimum of 0. For example if gross pay is 400, gross tax at 25% is 100; if this employee has a tax credit of 80, they would pay net tax of 20; if their tax credit is 120, they would pay net tax of 0. Use appropriate functions to read in each record, print out details for each employee, compute gross pay, and compute tax. Page 5 of 6

6 4. Write a C++ program to compute the mean, variance, standard deviation and number of zero crossings for a sequence of numbers. You must use a separate function to compute each of the statistical measures, given an array and its size, as well as to read the number sequence into an array. The input sequence is terminated by a sentinel value of Your program should handle up to 1000 numbers, but must not crash if the sequence has more than 1000 numbers in it. The standard deviation is the square root of the variance. The variance, denoted σ 2, is the average squared deviation from the mean: Σ (x i - µ) 2 (N-1) where µ, the mean, is the sum of all the numbers divided by N, the number of numbers in the sequence. The number of zero crossings is the number of times in the sequence that x i and x i-1 are opposite sides of zero i.e. their product is negative. Page 6 of 6