# All algorithms in R

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The Breadth-first search algorithm is an algorithm used to solve the shortest path problem in a graph without edge weights (i.e. a graph where all nodes are the same “distance” from each other, and they are either connected or not). This means that given a number of nodes and the edges between them, the Breadth-first search algorithm is finds the shortest path from the specified start node to all other nodes. Nodes are sometimes referred to as vertices (plural of vertex) - here, we’ll call them nodes.

#### A Star in R

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The A star (A*) algorithm is an algorithm used to solve the shortest path problem in a graph. This means that given a number of nodes and the edges between them as well as the “length” of the edges (referred to as “weight”) and a heuristic (more on that later), the A* algorithm finds the shortest path from the specified start node to all other nodes. Nodes are sometimes referred to as vertices (plural of vertex) - here, we’ll call them nodes.

#### DFS in R

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The Depth-First Search (also DFS) algorithm is an algorithm used to find a node in a tree. This means that given a tree data structure, the algorithm will return the first node in this tree that matches the specified condition (i.e. being equal to a value). Nodes are sometimes referred to as vertices (plural of vertex) - here, we’ll call them nodes. The edges have to be unweighted. This algorithm can also work with unweighted graphs if a mechanism to keep track of already visited nodes is added.

#### Dijkstra in R

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The Dijkstra algorithm is an algorithm used to solve the shortest path problem in a graph. This means that given a number of nodes and the edges between them as well as the “length” of the edges (referred to as “weight”), the Dijkstra algorithm is finds the shortest path from the specified start node to all other nodes. Nodes are sometimes referred to as vertices (plural of vertex) - here, we’ll call them nodes.

#### Greatest Common Divisor in R

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The greatest common divisor of two numbers (in this case a and b) is the biggest number which both numbers can be divided by without a rest. This greatest common divisor algorithm, called the euclidean algorithm, determines this number. The greatest common divisor is also often abbreviated as gcd.

#### Iterative Deepening A Star in R

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The Iterative Deepening A Star (IDA*) algorithm is an algorithm used to solve the shortest path problem in a tree, but can be modified to handle graphs (i.e. cycles). It builds on Iterative Deepening Depth-First Search (ID-DFS) by adding an heuristic to explore only relevant nodes.

#### Iterative Deepening DFS in R

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The Iterative Deepening Depth-First Search (also ID-DFS) algorithm is an algorithm used to find a node in a tree. This means that given a tree data structure, the algorithm will return the first node in this tree that matches the specified condition. Nodes are sometimes referred to as vertices (plural of vertex) - here, we’ll call them nodes. The edges have to be unweighted. This algorithm can also work with unweighted graphs if mechanism to keep track of already visited nodes is added.

#### Point in Polygon in R

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The Point in Polygon (PIP) problem is the problem of determining whether a point is any arbitrary polygon. This might sound trivial for a simple polygon like a square or a triangle, but gets more complex with more complex polygons like the one in the example below. In this post, the even-odd algorithm, also called crossing number algorithm or Jordan’s algorithm (since it can be proven using the Jordan curve theorem), will be introduced.

# R

R is an interpreted language first released in 1993 with a significant increase in popularity in recent years. It is primarily used for data mining and -science as well as statistics, and is a popular language in non-computer science disciplines ranging from Biology to Physics. R is dynamically typed, and has one of the widest variety of libraries for statistics, machine learning, data mining etc.

## Getting to “Hello World” in R

The most important things first - here’s how you can run your first line of code in R.

2. Open a terminal, make sure the `R` command is working, and that the command your’re going to be using is referring to the version you just installed by running `R --version`. If you’re getting a “command not found” error (or similar), try restarting your command line, and, if that doesn’t help, your computer. If the issue persists, here are some helpful StackOverflow questions for Windows, Mac and Linux.
3. As soon as that’s working, you can run the following snippet: `print("Hello World")`. You have two options to run this: 3.1 Run `R` in the command line, just paste the code snippet and press enter (Press `CTRL + D` and type `n` followed by enter to exit). 3.2 Save the snippet to a file, name it something ending with `.R`, e.g. `hello_world.R`, and run `Rscript hello_world.R`. Tip: use the `ls` command (`dir` in Windows) to figure out which files are in the folder your command line is currently in.

That’s it! Notice how printing something to the console is just a single line in R - this low entry barrier and lack of required boilerplate code is a big part of the appeal of R.

## Fundamentals in R

To understand algorithms and technologies implemented in R, one first needs to understand what basic programming concepts look like in this particular language.

### Variables and Arithmetic

Variables in R are really simple, no need to declare a datatype or even declare that you’re defining a variable; R knows this implicitly. R is also able to easily define objects and their property, in multiple different ways.

``````some_value = 10
my_object <- list(my_value = 4)
attr(my_object, 'other_value') <- 3

print((some_value + my_object\$my_value + attr(my_object, 'other_value'))) # Prints 17``````

### Arrays

Working with arrays is similarly simple in R:

``````# Create 2 vectors of length 3
vector1 <- c(1,2,3)
vector2 <- c(4,5,6)

# Create names for rows and columns (optional)
column.names <- c("column_1","column_2","column_3")
row.names <- c("row_1","row_2")

# Concatenate the vectors (as rows) to form an array, providing dimensions and row/column names
result <- array(c(vector1,vector2), dim = c(2,3), dimnames = list(row.names, column.names))

print(result)
# Prints:
#       column_1 column_2 column_3
# row_1        1        3        5
# row_2        2        4        6``````

As those of you familiar with other programming language like Java might have already noticed, those are not native arrays, but rather lists dressed like arrays. This means that arrays in R are considerably slower than in lower level programming languages. This is a trade off R makes in favor of simplicity. There are, however, packages which implement real arrays that are considerably faster.

### Conditions

Just like most programming languages, R can do `if-else` statements:

``````value = 1
if(value==1){
print("Value is 1")
} else if(value==2){
print("Value is 2")
} else {
print("Value is something else")
}``````

R can also do switch statements, although they are implemented as a function, unlike in other languages like Java:

``````x <- switch(
1,
"Value is 1",
"Value is 2",
"Value is 3"
)

print(x)``````

Note that this function is pretty useless, but there are other functions for more complex use cases.

### Loops

R supports both `for` and `while` loops as well as `break` and `next` statements (comparable to `continue` in other languages). Additionally, R supports `repeat`-loops, which are comparable to `while(true)` loops in other languages, but simplify the code a little bit.

``````value <- 0
repeat {
value <- value + 1
if(value > 10) {
break
}
}
print(value)

value <- 0
while (value <= 10) {
value = value + 1
}
print(value)

value <- c("Hello","World","!")
for ( i in value) {
print(i)
}

for(i in 1:10){
print(i)
}``````

### Functions

Functions in R are easily defined and, for better or worse, do not require specifying return or arguments types. Optionally, a default for arguments can be specified:

``````my_func <- function (
a = "World"
) {
print(a)
return("!")
}

my_func("Hello")
print(my_func())``````

(This will print “Hello”, “World”, and then ”!“)

### Syntax

R requires the use of curly brackets (`{}`) to surround code blocks in conditions, loops, functions etc.; While this can lead to some annoying syntax errors, it also means the use of whitespace for preferred formatting (e.g. indentation of code pieces) does not affect the code.