# All algorithms in Javascript

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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 Javascript

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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 Javascript

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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 Javascript

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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 Javascript

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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 Javascript

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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 Javascript

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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 Javascript

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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.

# JavaScript

JavaScript is an interpreted scripting language previously primarily used in web pages (executed in browsers) that has since found popularity for back-end and other tasks as well through node.js

While it borrows a lot of its syntax from Java, it is a very different language and should not be confused.

## Getting to “Hello World” in JavaScript

The most important things first - here’s how you can run your first line of code in JavaScript. If you want to use JavaScript for backend, follow the chapter on how to print Hello World using Node.js. If you want to use JavaScript in the frontend (i.e. in web pages), follow the chapter on how print Hello World in the browser.

### Getting to “Hello World” in JavaScript using the browser

1. Create a file named hello_world.html
2. Open it using a text editor (e.g. Sublime Text, or just the default Windows editor)
3. Paste the following code snippet:

``````<html>
<script type="application/javascript">
// This prints to the browsers console
console.log("Hello World")
// This opens a popup
</script>
<body>
(Website content)
</body>
</html>``````
4. Open this file using your browser (by typing the location into the address bar)
5. You should see a pop-up saying “Hello World”
6. If you use your browsers console (e.g. in Chrome: right-click -> inspect), you will see it printed there as well.

The reason we’re wrapping the script in HTML is that the browser will otherwise not execute the JavaScript, but just show it’s contents.

### Getting to “Hello World” in JavaScript using Node.js

2. Open a terminal, make sure the `node` command is working. 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 each platform:

3. As soon as that’s working, copy the following snippet into a file named hello_world.js:

``console.log("Hello World");``
4. Change directory by typing `cd path/to/hello_world`, then run `node hello_world.js`. This should print “Hello World” to your Terminal.

That’s it! Notice that the entry barrier is similarly low as it is for Python and many other scripting languages.

## Fundamentals in JavaScript

To understand algorithms and technologies implemented in JavaScript, one first needs to understand what basic programming concepts look like in this particular language. Each of the following snippets can be executed using Node.js on its own, as no boilerplate is required. In the browser, the code needs to be surrounded by HTML just like the Hello World example for the browser shown above.

### Variables and Arithmetic

Variables in JavaScript are dynamically typed, meaning the content of a variable is determined at runtime and does not need to be specified when writing the code.

``````var number = 5;
var decimalNumber = 3.25;
var result = number * decimalNumber;
var callout = "The number is ";
// In this instance, the values are concatenated rather than added because one of them is a String.
console.log(callout + result);``````

This will print ‘The number is 16.25’.

### Arrays

Arrays in JavaScript are implemented as objects, with the index just being the name of the property. This makes them dynamically sized. The whole concepts of objects and arrays are merged in JavaScript, as demonstrated by the following snippet.

``````var integers = {}; // initialized as object
integers[3] = 42; // assigned using array index
console.log(integers["3"]); // Accessed using property name, prints "42"

var strings = ["Hello"]; // strings[0] is now Hi
strings[2] = "World"; // index 1 skipped
strings.beautiful = "Beautiful" // Assigned using property name

console.log(strings[0] + " " + strings["beautiful"] + " " + strings[2]); // Prints "Hello World"``````

### Conditions

Just like most programming languages, JavaScript can do `if-else` statements. Additionally, JavaScript can also do `switch-case` statements.

``````var value = 5;
if(value === 5){
console.log("Value is 5");
} else if(value < 5){
console.log("Value is less than 5");
} else {
console.log("Value is something else");
}

switch (value){
case 1:
console.log("Value is 1");
break; // Don't go further down the cases
case 2:
console.log("Value is 2");
break; // Don't go further down the cases
case 3:
console.log("Value is 3");
break; // Don't go further down the cases
case 4:
console.log("Value is 4");
break; // Don't go further down the cases
case 5:
console.log("Value is 5");
break; // Don't go further down the cases
default:
console.log("Value is something else");
}``````

The above JavaScript code will print “Value is 5” twice.

### Loops

JavaScript supports `for`, `while` as well as `do while` loops. `break` and `continue` statements are also supported. The below example illustrates the differences:

``````var value = 2;
for (var i = 0; i < value; i++) {
console.log(i);
}
while (value > 0) {
console.log(value);
value--;
}
do {
console.log(value);
value--;
} while (value > 0);``````

This will print the following to the terminal:

``````0
1
2
1
0``````

Note the last `0`: it is printed because in the `do-while`-loop, compared to the `while`-loop. the code block is executed at least once before the condition is checked.

### Functions

Functions in JavaScript can be declared using many different syntaxes, for example as object properties, as variables, or, in more recent JavaScript versions, as part of a class.

Here’s an example of a JavaScript function as a variable:

``````var my_function = function(){
console.log("Hello World")
}

my_function()``````

Here’s an example of a JavaScript function as an object property:

``````var function_object = {}
function_object.my_function = function(){
console.log("Hello World")
}

function_object.my_function()``````

And here’s an example of calling a function of an object of a class:

``````class FunctionClass {
my_function(){
console.log("Hello World")
}
}

new FunctionClass().my_function();``````

(all of these examples print “Hello World”.)

### Syntax

As previously mentioned, JavaScript shares much of its Syntax with Java. JavaScript requires the use of curly brackets (`{}`) to surround code blocks in conditions, loops, functions etc.; It doesn’t always require semicolons at the end of statements, but their use is encouraged, as their usage means the use of whitespace for preferred formatting (e.g. indentation of code pieces) does not affect the code.