Decomposition

breaking down a complex problem or system into smaller parts

Pattern Recognition

looking for similarities among and within problems

Abstraction

focusing on the important parts only, ignoring irrelevant detail

Algorithms

developing a step-by-step solution to the problem

To draw a star, you decompose in these steps:

• put the cat at coordinates (0,150)
• hide the cat
• clear any existing drawing
• put the pen down
• point in direction 130 degrees
• repeat 40 times
  • move 200 steps
  • turn right 130 degrees

Let’s forget about specific numbers.

In other words, let’s make an abstraction

• N: How many sides we will draw
• angle: how do you turn after each side
• R: radius, distance from the center to each peak
• initial_angle: initial angle
• size: length of each side

Assuming that you know the input values, you need to:

• Move R steps to the first corner
• Point in the direction initial_angle
• repeat N times
  • draw a line of length size
  • turn right angle degrees

In this case it is easy to see a pattern:

• draw a line of length size
• turn right angle degrees

This pattern is repeated N times

You can do this easily with a loop

You already have seen a first algorithmic structure: loops

repeat (10)

which in R we write as

for(i in 1:10) {
  ...
}

The second algorithmic structure you can use are

Procedures

A group of specific steps grouped together

In R we represent procedures with functions

In Math and Informatics, a function is a “black box”

A rule to transform the input elements into an output

• e.g. logarithm of a number, length of a vector

The same input should produce always the same output

Notice that there may be more than one input element

newFunc <- function(input) {
  commands
  commands
  return(output)
}

The keyword return can be omitted

In that case the output is the result of the last command

my_func()

Error in my_func(): argument "a" is missing, with no default

my_func(1,2,3,4)

Error in my_func(1, 2, 3, 4): unused arguments (3, 4)

Before writing the function we need to decide:

• the name of the function (it’s harder than it seems)
• which are the inputs
• what is the output

Then we can start writing the code

Let’s write a function to draw stars

Hint

initial_angle must be 90+angle/2

size must be 2*R*sin(angle*pi/360)

Last semester we used RMarkdown

This semester we will use R Scripts

Be sure of understanding the difference