Assignment 1

Deadline

14 September, 2018 (Friday), 6:00pm.

Prerequisite

You are able to access the CS1010 programming environment.
You are familiar with basic UNIX CLI and using terminal-based editor vim.
You have gone through Exercise 1 and have already setup your .gitconfig.
You are familiar with the steps of accepting, downloading, and submitting your exercise and assignment.
You are familiar with the directory structure and the common files included in your assignment skeleton.

Learning Outcomes

Be comfortable writing simple C programs that involves arithmetic operations, long, double, and bool types, and conditional if/else statements.
Be comfortable breaking down a problem into smaller subproblems which can be resolved using functions, including reusing existing functions written for other programs (with a tweak), writing a function that calls itself, designing what should the inputs and return values/types of a function be.

Setup

Click on this link to accept the assignment.
Login to one of the hosts of CS1010 programming environment
Run:

~cs1010/get-as01

You should see the folder as01-<github id> in your home directory with the assignment skeleton inside.

Solving The Assignments

Edit the files invest.c, box.c, digits.c, and taxi.c to solve the corresponding question as described below.
To compile and run tests with the sample inputs and outputs:

make

The test cases are given in the inputs and outputs subdirectory. You can use cat or less to look at the content of these test cases. You can add more test cases or edit the given ones if needed.

Submission

When you are ready, run the following command to submit:

~cs1010/submit-as01

The four files invest.c, box.c, digits.c, and taxi.c will be uploaded to GitHub. You can submit multiple times, but only the last submission will be graded.

Identifying Yourself

In every C file that you submit to CS1010, you need to identify yourself by writing your name and tutorial group. Marks will be deducted if you fail to do so. You need to edit the line:

@author XXXX (Group YYYY)

and change it to something like:

@author Hermione Granger (Group 9)

Grading

This assignment contributes towards 3% of your final grade. The total marks for this assignment is 30. For Programming Assignment 1, the sole criteria for grading is correctness.

Question 1: Invest (5 marks)

If you invest $m$ dollars at $r$ % interest rate compounded annually, after $n$ years, your investment will grow to $\frac{m(1 - (r/100)^{n+1})}{1 - r/100}$ dollars.

Write a program invest.c that accepts three integers as input: principal $m$ , rate $r$ , and number of years $n$ , and computes the amount of money earned after $n$ years.

You may assume that ~~r <= 100~~ $r < 100$ .

Sample Run

ooiwt@pe111:~/as01-skeleton$ ./invest
100 10 5
111.1110
ooiwt@pe111:~/as01-skeleton$ ./invest
20000 5 10
21052.6316

Question 2: Box (5 marks)

Write a program box.c that reads three positive integers representing the length, width, and height of a box, and output (i) its surface area, and (ii) the length of the diagonal between two vertices of the box that are furthest apart (see figure).

diagonal of a box

You may assume that the surface area of the box does not exceed the maximum value representable in the long data type.

You should break down the problem into smaller ones:

Write a new method area_of_rectangle that computes the area of a rectangle given the width and height of the rectangle, then use it to compute the surface area.
Modify the method hypotenuse_of seen in Unit 5 to compute the diagonal of the box. (hint: pay attention to the type of the parameter and the return value).

Sample Run

ooiwt@pe111:~/as01-skeleton$ ./box 
12 3 10
372 15.9060
ooiwt@pe111:~/as01-skeleton$ ./box 
10 20 30
2200 37.4166

Question 3: Digits (5 marks)

Write a program digits.c that reads in a non-negative integer, and prints the sum of the individual digits in this integer.

For instance, if the input is 1933091, then the sum is 1 + 9 + 3 + 3 + 0 + 9 + 1 = 26.

You should not use a loop to solve this, but rather, you should write a function sum_of_digits that takes in an integer and return the sum of the digits of that integer, that calls itself:

if the input to sum_of_digits has only one digit, return this digit.
Otherwise, use the modulo operator % and integer division / to extract the last digit (e.g., 1) and the rest of the digits (e.g., 193309) respectively, and call sum_of_digits on the rest of the digits to find its sum (e.g., 1+9+3+3+0+9 = 25). Finally we add the last digit to this sum to get the total we seek (e.g., 1 + 25 = 26).

Sample Run

ooiwt@pe111:~/as01-skeleton$ ./digits 
1933091
26
ooiwt@pe111:~/as01-skeleton$ ./digits 
0
0

Question 4: Taxi Fare (15 marks)

The taxi fare structure in Singapore must be one of the most complex in the world! Check out: http://www.taxisingapore.com/taxi-fare/.

For the purpose of this exercise, we will just use the following simpliﬁed fare structure:

Basic Fare
The first 1 km or less (Flag Down)	$3.40
Every 400 m thereafter or less, up to 10.2 km	$0.22
Every 350 m thereafter or less, after 10.2 km	$0.22

Surcharge
Monday to Friday	6:00 to 9:29	25% of metered fare
Daily	18:00 to 23:59	25% of metered fare
Daily	0:00 (midnight) to 5:59	50% of metered fare

Note that the surcharge is applicable based on the boarding time. For instance, if the trip started at 17:50 and ended at 18:10, then no surcharged is incurred.

Write a program taxi.c that computes the taxi fare. The program, called taxi, takes in four integers as inputs:

The first is the day of the week. It can only be the value 1 to 7, 1 being Monday, 7 being Sunday.
The second and the third is the starting time of the trip: the second input indicates the hours since midnight of the stated day, the third input indicates the minutes since the beginning of the stated hours.
The forth and final input is the distance of the trip, in meters.

Your program should print a single floating point number, which is the cost of the fare in dollars.

Examine the following examples for more details:

Example 1

ooiwt@pe111:~/as01-skeleton$ ./taxi 
1 17 59 1000
3.4000

Start: Mon 17:59
Distance: 1,000 m

The metered fare is $3.40 since the distance travelled is 1km. The boarding time is before 18:00 so there is no surcharge. The total fare is $3.40.

Example 2

ooiwt@pe111:~/as01-skeleton$ ./taxi 
1 17 57 2000
4.0600

Start: Mon 17:57
Distance: 2,000 m

The metered fare for the first 1,000 m (1km) is $3.40. The next 1,000 m is charged $0.22 for every 400 m (or less) travelled. The pessengar is charged an additional 3 x $0.22, giving the total of metered fare of $4.06.
The boarding time is before 18:00 so there is no surcharge.

Example 3

ooiwt@pe111:~/as01-skeleton$ ./taxi 
1 5 50 15000
17.3100

Start: Mon 05:50
Distance: 15,000 m

The metered fare for the first 1,000 m (1km) is $3.40. The next 9,200 m is charged $0.22 for every 400 m travelled. The pessengar is charged an additional 23 x $0.22 = $5.06. The remaining 4,800 m is charged $0.22 for every 350 m (or less) travelled). The pessengar is charged an additional 14 x $0.22 = $3.08. The total metered fare is $11.54.

The boarding time is before 6:00 so there is a 50% surcharge. Total fare is $17.31.

Hints

You can break down this problem into multiple subproblems, each can be solved by a function. Write one function to answer each question below:
- given the day of the week, is it a weekday?
- given the time of boarding, does it fall under the morning peak hour (6:00 - 9:29)?
- given the time of boarding, does it fall under the evening peak hour (18:00 - 23:59)?
- given the time of boarding, does it fall under the midnight peak hour (0:00 - 5:59)?
You can further breakdown the calculation of fare into two parts: the basic metered fare and the surcharge. Each of these can be its own function. Think about the four inputs to the taxi program. Which one is needed to compute the metered fare? Which ones are used to compute the surcharge? Pass in the appropriate arguments to the function that computes the metered fare and the function that computes the surcharge.