## Part 1: Converting Currencies

Write a program (note: name the source code file part1.cpp) that converts between Dollars, Euros and Pounds. The program reads input from the user in the following format: Convert amount currency_1 to currency_2 and prints results in the obvious way. Here are a couple of sample runs:
~$./part1 Convert 3.50 Euros to Dollars document.write((3.5/toEUR).toFixed(5)) ~$ ./part1
Convert 3.50 Euros to Pounds
document.write((3.5/toEUR*toGBP).toFixed(5))
Here are the conversion rates you'll need: 1.00 Dollar is Euros and 1.00 Dollar is Pounds.

Important: do not write if statements for every single pairwise combination (e.g., dol-euro, dol-pound, euro-dol, euro-...). Instead, always convert the first given currency to Dollars, and then convert Dollars to the second currency. This avoids an explosion of if statements as you move to Part 2 when another currency is added to the mix. Instead of n^2 if statements, you'll only need n*2 statements (n is the number of possible currencies).

Submission: If you're finished before lab ends, please demo for your instructor. Also submit via the class submit script as follows:
~/bin/submit -c=SI204 -p=lab03 part1.cpp

## Part 2: More Currencies

Extend your program from Part 1 (note: name the source code file part2.cpp) to allow for Canadian dollars as well (1.00 Dollars US is Dollars Canadian). Now the user can't simply put "Dollars" in the input, it must be either "Dollars US" or "Dollars Canadian". Here are a couple of sample runs:
~$./part2 Convert 3.50 Euros to Dollars Canadian document.write((3.5/toEUR*toCAD).toFixed(5)) ~$ ./part2
Convert 11.72 Dollars US to Dollars Canadian
document.write((11.72*toCAD).toFixed(4))

Hint: you'll probably need to break up your cin statements from Part 1. There are now some currencies that are only one word (euro), but others need a second word to be input based on the first word you read in (Dollars US).

Submission: If you're finished before lab ends, please demo for your instructor. Also submit via the class submit script as follows:

~/bin/submit -c=SI204 -p=lab03 part1.cpp part2.cpp

## Part 3: Going further, Creating output for plotting

It's often nice to write programs that produce output that's intended for other programs. You will write a program (note: name the source code file part3.cpp) that reads in three points from the user and prints output that the user can put in a file to give the program "gnuplot" to produce a plot showing the triangle defined by the three user-input points along with its bounding box, i.e. the smallest rectangle aligned with the coordinate axes that contains the triangle.

Gnuplot is a standard tool for creating plots. Its input is simply a text file of points, one per line, given by the point's x-coordinate, followed by a space, followed by its y-coordinate. Gnuplot will draw a mark at each point, and connect successive points with segments, as long as they are not separated by blank lines. Note: this means that drawing a closed figure (like a triangle) requires repeating the first point at the end of the input.

Here's a sample of running the program and using gnuplot to plot the results. Note: please print the lines defining the bounding box before the lines defining the input triangle. This is for automatic grading purposes, not because gnuplot cares.

 sample run ~/$./part3 (-1.1,-0.5) (1,3.3) (2.7,-1.1) -1.1 -1.1 -1.1 3.3 2.7 3.3 2.7 -1.1 -1.1 -1.1 -1.1 -0.5 1 3.3 2.7 -1.1 -1.1 -0.5 after copy&pasting output into a new file named tmp ... [copy&paste the output into a new file named tmp...] ~/$ gnuplot G N U P L O T Version 4.4 patchlevel 3 last modified March 2011 System: Linux 3.5.0-54-generic Copyright (C) 1986-1993, 1998, 2004, 2007-2010 Thomas Williams, Colin Kelley and many others gnuplot home: http://www.gnuplot.info faq, bugs, etc: type "help seeking-assistance" immediate help: type "help" plot window: hit 'h' Terminal type set to 'wxt' gnuplot> plot "tmp" with linespoints; gnuplot's output
Submission: If you're finished before lab ends, please demo for your instructor. Also submit via the class submit script as follows:
~/bin/submit -c=SI204 -p=lab03 part1.cpp part2.cpp part3.cpp

## Part 4: Going even further, Classifying triangles

There are two common ways of classifying a triangle:

This is an acute isosceles triangle.
1. By describing its interior angles
• Acute triangles have three interior angles that are all less than 90 degrees
• Right triangles have an interior angle that is exactly 90 degrees
• Obtuse triangles have an interior angle that is greater than 90 degrees
2. By describing the lengths of the sides in relation to each other
• Equilateral triangles have three sides that are all of equal length
• Isosceles triangles have two sides that are of equal length
• Scalene triangle have all three sides of different lengths
A well known property of all triangles is that the sum of any two sides will always be greater than the third. Given a set of three lengths it is possible to determine if they can form a triangle by adding two lengths together and comparing them to the third. Given the three lengths of the sides of a triangle, a, b and c, it is also possible to calculate the area of a triangle using Heron's formula. $$\Delta = \sqrt{s(s-a)(s-b)(s-c)} \mbox{, where } s = \frac{1}{2}(a + b + c)$$ Also, from the side lengths $a$, $b$ and $c$, it is possible to calculate the three interior angles, $A$, $B$ and $C$, of the triangle using the law of sines: $$\frac{sin{A}}{a} = \frac{sin{B}}{b} = \frac{sin{C}}{c} = \frac{2\Delta}{abc}.$$ Your job: write a program (note: name the source code file part4.cpp) that reads three lengths from the user displays the type of triangle that is formed by the input according to both kinds of classification. E.g. "This is a obtuse scalene triangle"
Tip: The cmath library has a function asin() that computes the arcsine of an angle. Enter
man asin
on the command line for documentation.

We have a bit of a problem in that for any positive angle $\theta$ less than $\pi/2$, we have that $\sin(\theta) = \sin(\pi - \theta)$. Thus, when we use $\theta$ = asin(w) for positive w, we don't know whether we really want the angle $\theta$ or $\pi - \theta$.

In our triangle case, we cans fix things like this: if the three angles we calculate (A, B and C) sum up to a lot less than $\pi$ (in fact, we should probably check that the sum is less than 3), we replace the angle opposite the longest side with $\pi$ minus that angle. So, for example, if $A$ is opposite the longest side, then we replace $A$ with $\pi - A$.

BTW: as long as you're including cmath, the constant M_PI gives you a high-precision double representation of $\pi$.

Also, the function sqrt( ) computes square roots.

Example executions are shown below:
~/$./part4 Enter side lengths: 1 2 3 Error! these lengths violate the triangle inequality! ~/$ ./part4
Enter side lengths: 1.5 2 3
This is a obtuse scalene triangle.
~/$./part4 Enter side lengths: 2 2 3 This is a obtuse isosceles triangle. ~/$ ./part4
Enter side lengths: 2 2 2
This is a acute equilateral triangle.
~/\$ ./part4
Enter side lengths: 2 2 1.5
This is a acute isosceles triangle.

Submission: If you're finished before lab ends, please demo for your instructor. Also submit via the class submit script as follows:

~/bin/submit -c=SI204 -p=lab03 part1.cpp part2.cpp part3.cpp part4.cpp