Data Structures

All Code From This Writeup

"use strict";
class List {
  constructor() {
    this.memory = [];
    this.length = 0;
  }
  get(address) {
    return this.memory[address];
  }
 
  push(value) {
    this.memory[this.length] = value;
    this.length++;
  }
  pop() {
    if (this.length === 0) return;
    let lastAddress = this.length - 1;
    let value = this.memory[lastAddress];
    delete this.memory[lastAddress];
    this.length--;
    return value;
  }
  unshift(value) {
    let previous = value;
    for (let address = 0; address < this.length; address++) {
      let current = this.memory[address];
      this.memory[address] = previous;
      previous = current;
    }
    this.memory[this.length] = previous;
    this.length++;
  }
  shift() {
    if (this.length === 0) return;
    let value = this.memory[0];
    for (let address = 0; address < this.length - 1; address++) {
      this.memory[address] = this.memory[address + 1];
    }
    delete this.memory[this.length - 1];
    this.length--;
    return value;
  }
}
class HashTable {
  constructor() {
    this.memory = [];
  }
  hashKey(key) {
    let hash = 0;
    for (let index = 0; index < key.length; index++) {
      let code = key.charCodeAt(index);
      hash = ((hash << 5) - hash + code) | 0;
    }
    return hash;
  }
  get(key) {
    let address = this.hashKey(key);
    return this.memory[address];
  }
  set(key, value) {
    let address = this.hashKey(key);
    this.memory[address] = value;
  }
  remove(key) {
    let address = this.hashKey(key);
    if (this.memory[address]) {
      delete this.memory[address];
    }
  }
}
class Stack {
  constructor() {
    this.list = [];
    this.length = 0;
  }
  push(value) {
    this.length++;
    this.list.push(value);
  }
  pop() {
    if (this.length === 0) return;
    this.length--;
    return this.list.pop();
  }
  peek() {
    return this.list[this.length - 1];
  }
}
class Queue {
  constructor() {
    this.list = [];
    this.length = 0;
  }
  enqueue(value) {
    this.length++;
    this.list.push(value);
  }
  dequeue() {
    if (this.length === 0) return;
    this.length--;
    return this.list.shift();
  }
  peek() {
    return this.list[0];
  }
}
class Graph {
  constructor() {
    this.nodes = [];
  }
  addNode(value) {
    return this.nodes.push({
      value,
      lines: [],
    });
  }
  find(value) {
    return this.nodes.find((node) => {
      return node.value === value;
    });
  }
  addLine(startValue, endValue) {
    let startNode = this.find(startValue);
    let endNode = this.find(endValue);
    if (!startNode || !endNode) {
      throw new Error("Both nodes need to exist");
    }
    startNode.lines.push(endNode);
  }
}
class LinkedList {
  constructor() {
    this.head = null;
    this.length = 0;
  }
  get(position) {
    if (position >= this.length) {
      throw new Error("Position outside of list range");
    }
    let current = this.head;
    for (let index = 0; index < position; index++) {
      current = current.next;
    }
    return current;
  }
  add(value, position) {
    let node = {
      value,
      next: null,
    };
    if (position === 0) {
      node.next = this.head;
      this.head = node;
    } else {
      let prev = this.get(position - 1);
      let current = prev.next;
      node.next = current;
      prev.next = node;
    }
    this.length++;
  }
  remove(position) {
    if (!this.head) {
      throw new Error("Removing from empty list");
    }
    if (position === 0) {
      this.head = this.head.next;
    } else {
      let prev = this.get(position - 1);
      prev.next = prev.next.next;
    }
    this.length--;
  }
}
class Tree {
  constructor() {
    this.root = null;
  }
  traverse(callback) {
    function walk(node) {
      callback(node);
      node.children.forEach(walk);
    }
    walk(this.root);
  }
  add(value, parentValue) {
    let newNode = {
      value,
      children: [],
    };
    if (this.root === null) {
      this.root = newNode;
      return;
    }
    this.traverse((node) => {
      if (node.value === parentValue) {
        node.children.push(newNode);
      }
    });
  }
}
class BinarySearchTree {
  constructor() {
    this.root = null;
  }
  contains(value) {
    let current = this.root;
    while (current) {
      if (value > current.value) {
        current = current.right;
      } else if (value < current.value) {
        current = current.left;
      } else {
        return true;
      }
    }
    return false;
  }
  add(value) {
    let node = {
      value: value,
      left: null,
      right: null,
    };
    if (this.root === null) {
      this.root = node;
      return;
    }
    let current = this.root;
    while (true) {
      if (value > current.value) {
        if (!current.right) {
          current.right = node;
          break;
        }
        current = current.right;
      } else if (value < current.value) {
        if (!current.left) {
          current.left = node;
          break;
        }
        current = current.left;
      } else {
        break;
      }
    }
  }
}

module.exports = {
  List,
  HashTable,
  Stack,
  Queue,
  Graph,
  LinkedList,
  Tree,
  BinarySearchTree,
};

Data Structures By Example?

Essentially, they are different methods of storing and organizing data tha serve a number of different needs.
Data can always be represented in many different ways. However, depending on
what that data is and what you need to do with it, one representation will
be a better choice than the others.
To understand why let's first talk a bit about algorithms.

ALGORITHMS

Algorithm is a fancy name for step-by-step sets of operations to be performed

Data structures are implemented with algorithms, and algorithms are
implemented with data structures. It's data structures and algorithms all the way down until you reach the microscopic people with punch cards that control the computer. (That's how computers work right?)
Any given task can be implemented in an infinite number of ways. So for common tasks there are often many different algorithms that people have come up with.
For example, there are an absurd number of algorithms for sorting a set of unordered items:
Insertion Sort, Selection Sort, Merge Sort, Bubble Sort, Heap Sort,
Quick Sort, Shell Sort, Timsort, Bucket Sort, Radix Sort, ...
Some of these are significantly faster than others. Some use less memory.
Some are easy to implement. Some are based on assumptions about the dataset.
Every single one of them will be better for something. So you'll need to
make a decision based on what your needs are and for that, you'll need a way
of comparing them, a way to measure them.
When we compare the performance of algorithms we use a rough measurement of
their average and worst-case performance using something called "Big-O".

BIG-O NOTATION

Big-O Notation is a way of roughly measuring the performance of algorithms

in order to compare one against another when discussing them.
Big-O is a mathematical notation that we borrowed in computer science to
classify algorithms by how they respond to the number (N) of items that you
give them.
There are two primary things that you measure with Big-O:
Time complexity refers to the total count of operations an algorithm
will perform given a set of items.
Space complexity refers to the total memory an algorithm will take up
while running given a set of items.
We measure these independently from one another because while an algorithm
may perform fewer operations than another, it may also take up way more
memory. Depending on what your requirements are, one may be a better choice
than the other.
These are some common Big-O's: | Name | Notation | How you feel when they show up at your party | |--------------|------------|----------------------------------------------| | Constant | O(1) | AWESOME!! | | Logarithmic | O(log N) | GREAT! | | Linear | O(N) | OKAY. | | Linearithmic | O(N log N) | UGH... | | Polynomial | O(N ^ 2) | SHITTY | | Exponential | O(2 ^ N) | HORRIBLE | | Factorial | O(N!) | WTF |
To give you an idea of how many operations we're talking about. Let's look
at what these would equal given the (N) number of items. | N=5 | 10 | 20 | 30 | | ---------- | --------- | --------- | -------------- | | O(1) | 1 | 1 | 1 | 1 | | O(log N) | 2.3219... | 3.3219... | 4.3219... | 4.9068... | | O(N) | 5 | 10 | 20 | 30 | | O(N log N) | 11.609... | 33.219... | 84.638... | 147.204... | | O(N ^ 2) | 25 | 100 | 400 | 900 | | O(2 ^ N) | 32 | 1024 | 1,048,576 | 1,073,741,824 | | O(N!) | 120 | 3,628,800 | 2,432,902,0... | 265,252,859,812,191,058,636,308,480,000,000 |
As you can see, even for relatively small sets of data you could do
a lot of extra work.
With data structures, you can perform 4 primary types of actions:
Accessing, Searching, Inserting, and Deleting.
It is important to note that data structures may be good at one action but
bad at another.

Comparison

Accessing	Searching	Inserting	Deleting
Array	O(1)	O(N)	O(N)	O(N)
L-List	O(N)	O(N)	O(1)	O(1)
BST	O(log N)	O(log N)	O(log N)	O(log N)

Or rather...
Accessing Searching Inserting Deleting

Array AWESOME!! OKAY OKAY OKAY

Linked List OKAY OKAY AWESOME!! AWESOME!!
Binary Search Tree GREAT! GREAT! GREAT! GREAT!
Even further, some actions will have a different "average" performance and a
"worst case scenario" performance.
There is no perfect data structure, and you choose one over another based on
the data that you are working with and the things you are going to do with
it. This is why it is important to know a number of different common data
structures so that you can choose from them.

MEMORY

A computer's memory is pretty boring, it's just a bunch of ordered slots

where you can store information. You hold onto memory addresses in order to
find information.
Let's imagine a chunk of memory like this:
Values: |1001|0110|1000|0100|0101|1010|0010|0001|1101|1011...
Addresses: 0 1 2 3 4 5 6 7 8 9 ...
If you've ever wondered why things are zero-indexed in programming languages
before, it is because of the way that memory works. If you want to read the
first chunk of memory you read from 0 to 1, the second you read from 1 to 2.
So the address that you hold onto for each of those is 0 and 1 respectively.
Your computer has much much more memory than this, and it is all just a
continuation of the pattern above.
Memory is a bit like the wild west, every program running on your machine is
stored within this same physical data structure. Without layers of
abstraction over it, it would be extremely difficult to use.
But these abstractions serve two additional purposes:
Storing data in memory in a way that is more efficient and/or faster to
work with.
Storing data in memory in a way that makes it easier to use.

LISTS

To demonstrate the raw interaction between memory and a data structure we're

going to first implement a list.
A list is a representation of an ordered sequence of values where the same
value may appear many times.

class List {

We start with an empty block of memory which we are going to represent
with a normal JavaScript array and we'll store the length of the list.
-
Note that we want to store the length separately because in real life the
"memory" doesn't have a length you can read from.

 constructor() {
    this.memory = [];
    this.length = 0;
  }

First we need a way to retrieve data from our list.
With a plain list, you have very fast memory access because you keep track
of the address directly.
List access is constant O(1) * "AWESOME!!"

 get(address) {
    return this.memory[address];
  }

Because lists have an order you can insert stuff at the start, middle,
or end of them.
For our implementation, we're going to focus on adding and removing values
at the start or end of our list with these four methods:
Push * Add value to the end
Pop * Remove a value from the end
Unshift * Add value to the start
Shift * Remove a value from the start

Starting with "push" we need a way to add items to the end of the list.

It is as simple as adding a value in the address after the end of our
list. Because we store the length this is easy to calculate. We just add
the value and increment our length.
Pushing an item to the end of a list is constant O(1) * "AWESOME!!"

 push(value) {
    this.memory[this.length] = value;
    this.length++;
  }

Next we need a way to "pop" items off of the end of our list.
Similar to push all we need to do is remove the value at the address at
the end of our list. Then just decrement length.
Popping an item from the end of a list is constant O(1) * "AWESOME!!"

 pop() {

Don't do anything if we don't have any items.

if (this.length === 0) return;

Get the last value, stop storing it, and return it.

let lastAddress = this.length * 1;
let value = this.memory[lastAddress];
delete this.memory[lastAddress];
this.length--;

Also return the value so it can be used.

    return value;
  }

"push" and "pop" both operate on the end of a list, and overall are pretty
simple operations because they don't need to be concerned with the rest of
the list.
Let's see what happens when we operate at the beginning of the list with
"unshift" and "shift".

In order to add a new item at the beginning of our list, we need to make

room for our value at the start by sliding all of the values over by one.

  * [a, b, c, d, e]
  *  0  1  2  3  4
  *   ⬊  ⬊  ⬊  ⬊  ⬊
  *  1  2  3  4  5
  * [x, a, b, c, d, e]

In order to slide all of the items over we need to iterate over each one
moving the prev value over.
Because we have to iterate over every single item in the list:
Unshifting an item to the start of a list is linear O(N) * "OKAY."

 unshift(value) {

Store the value we are going to add to the start.

let previous = value;

Iterate through each item...

   for (let address = 0; address < this.length; address++) {

replacing the "current" value with the "previous" value and storing the

"current" value for the next iteration.

   let current = this.memory[address];
   this.memory[address] = previous;
   previous = current;
    }

Add the last item in a new position at the end of the list.

   this.memory[this.length] = previous;
   this.length++;
 }

// Finally, we need to write a shift function to move in the opposite
direction.
We delete the first value and then slide through every single item in the
list to move it down one address.
[x, a, b, c, d, e]
1 2 3 4 5
⬋ ⬋ ⬋ ⬋ ⬋
0 1 2 3 4
[a, b, c, d, e]
Shifting an item from the start of a list is linear O(N) * "OKAY."

 shift() {

Don't do anything if we don't have any items.

if (this.length === 0) return;
let value = this.memory[0];

Iterate through each item...

    for (let address = 0; address < this.length * 1; address++) {

and replace them with the next item in the list.

  this.memory[address] = this.memory[address + 1];
   }

Delete the last item since it is now in the previous address.

   delete this.memory[this.length * 1];
   this.length--;
   return value;
 }
}

Lists are great for fast access and dealing with items at the end. However

as we've seen it isn't great at dealing with items not at the end of the
list and we have to manually hold onto memory addresses.
So let's take a look at a different data structure and how it deals with
adding, accessing, and removing values without needing to know memory
addresses.

HASH TABLES

A hash table is a data structure that's unordered. Instead we have "keys" and "values" where we
computed an address in memory using the key.
The basic idea is that we have keys that are "hashable" (which we'll get to
in a second) and can be used to add, access, and remove from memory very
efficiently.
var hashTable = new HashTable();
hashTable.set('myKey', 'myValue');
hashTable.get('myKey');

'myValue'

class HashTable {

Again we're going to use a plain JavaScript array to represent our memory.

 constructor() {
    this.memory = [];
  }

In order to store key-value pairs in memory from our hash table we need a
way to take the key and turn it into an address. We do this through an
operation known as "hashing".
Basically it takes a key and serializes it into a unique number for that
key.
hashKey("abc") => 96354
hashKey("xyz") => 119193
You have to be careful though, if you had a really big key you don't want
to match it to a memory address that does not exist.
So the hashing algorithm needs to limit the size, which means that there
are a limited number of addresses for an unlimited number of values.
The result is that you can end up with collisions. Places where two keys
get turned into the same address.
Any real-world hash table implementation would have to deal with this,
however, we are just going to glaze over it and pretend that doesn't happen.

Let's set up our "hashKey" function

Don't worry about understanding the logic of this function, just know that
it accepts a string and outputs a (mostly) unique address that we will use
in all of our other functions.

 hashKey(key) {
    let hash = 0;
    for (let index = 0; index < key.length; index++) {

//Oh look*magic.

   let code = key.charCodeAt(index);
hash = ((hash << 5)* hash) + code | 0;
    }
    return hash;
  }

Next, let's define our "get" function so we have a way of accessing values
by their key.
HashTable access is constant O(1) * "AWESOME!!"

 get(key) {

We start by turning our key into an address

let address = this.hashKey(key);
// then we simply return whatever is at that address.
return this.memory[address];

}

We also need a way of adding data before we access it, so we will create
a "set" function that inserts values.
HashTable setting is constant O(1) * "AWESOME!!"

 set(key, value) {

Again we start by turning the key into an address.

    let address = this.hashKey(key);



 // then just set the value at that address.
    this.memory[address] = value;
  }


* // Finally we just need a way to remove items from our hash table.

HashTable deletion is constant O(1) * "AWESOME!!"

 remove(key) {

As always, we hash the key to get an address.

    let address = this.hashKey(key);

 // then, if it exists, we `delete` it.
    if (this.memory[address]) {
   delete this.memory[address];
    }
  }
}

From this point going forward we are going to stop interacting directly with

memory as the rest of these data structures start to be implemented with
other data structures.
These data structures focus on doing two things:
Organizing data based on how it is used
Abstracting away implementation details
These data structures focus on creating an organization that makes sense for
various types of programs. They insert a language that allows you to discuss
more complicated logic. All of this while abstracting away implementation
details so that their implementation can change to be made faster.

STACKS

Stacks are similar to lists in that they have an order, but they limit you

to only pushing and popping values at the end of the list, which as we saw
before are very fast operations when mapping directly to memory.
However, Stacks can also be implemented with other data structures in order
to add functionality to them.
The most common usage of the stacks is in the places where you have one process adding
items to the stack and another process removing them from the end-
prioritizing items added most recently.

class Stack {

We're going to again be backed by a JavaScript array, but this time it
represents a list like we implemented before rather than memory.

 constructor() {
    this.list = [];
    this.length = 0;
  }

We're going to implement two of the functions from list's "push" and "pop"
which are going to be identical in terms of functionality.

####  Push to add items to the top of the stack.

---
```js
 push(value) {
    this.length++;
    this.list.push(value);
  }

And pop to remove items from the top of the stack.

 pop() {

Don't do anything if we don't have any items. if (this.length === 0) return;

 Pop the last item off the end of the list and return the value.
    this.length--;
    return this.list.pop();
  }

We're also going to add a function in order to view the item at the top of
the stack without removing it from the stack.

 peek() {

Return the last item in "items" without removing it.

    return this.list[this.length * 1];
  }
}

QUEUES

Next, we're going to build a queue which is complementary to stacks. The

difference is that this time you remove items from the start of the queue
rather than the end. Removing the oldest items rather than the most recent.
Again, because this limits the amount of functionality, there are many
different ways of implementing it. A good way might be to use a linked list
which we will see later.

class Queue {

Again, our queue is using a JavaScript array as a list rather than memory.

 constructor() {
    this.list = [];
    this.length = 0;
  }

Similar to stacks we're going to define two functions for adding and
removing items from the queue. The first is "enqueue".
This will push values to the end of the list.

 enqueue(value) {
    this.length++;
    this.list.push(value);
  }

Next is "dequeue", instead of removing the item from the end of the list,
we're going to remove it from the start.

 dequeue() {

Don't do anything if we don't have any items. if (this.length === 0) return;

 Shift the first item off the start of the list and return the value.
    this.length--;
    return this.list.shift();
  }

Same as stacks we're going to define a "peek" function for getting the next
value without removing it from the queue.

 peek() {
    return this.list[0];
  }
}

The important thing to note here is that because we used a list to back our

queue it inherits the performance of "shift" which is linear O(N) "OKAY."
Later we'll see linked lists that will allow us to implement a much faster
Queue.

From this point forward we're going to start dealing with data structures

where the values of the data structure reference one another.
Data Structure

| Item A

Item B

| Value: 1 | | Value: 2 |
| Reference to: (Item B) | Reference to: (Item A) |

The values inside the data structure become their own mini data structures
in that they contain a value along with additional information including
references to other items within the overall data structure.
You'll see what I mean by this in a second.

GRAPHS

Contrary to the ascii art above, a graph is not a visual chart of some sort

Instead imagine it like this:
A -→ B ←---* C → D ↔ E
↑ ↕ ↙ ↑ ↘
F -→ G → H ← I----→ J
↓ ↘ ↑
K L
We have a bunch of "nodes" (A, B, C, D, ...) that are connected with lines.
These nodes are going to look like this:
Node {
value: ...,
lines: [(Node), (Node), ...]
}
The entire graph will look like this:
Graph {
nodes: [
Node {...},
Node {...},
...
]
}

class Graph {

We'll hold onto all of our nodes in a regular JavaScript array. Not
because there is any particular order to the nodes but because we need a
way to store references to everything.

 constructor() {
    this.nodes = [];
  }

We can start to add values to our graph by creating nodes without any
lines.

 addNode(value) {
    return this.nodes.push({
   value,
   lines: []
    });
  }

Next we need to be able to lookup nodes in the graph. Most of the time
you'd have another data structure on top of a graph in order to make
searching faster.
But for our case, we're simply going to search through all of the nodes to find
the one with the matching value. This is a slower option, but it works for
now.

 find(value) {
    return this.nodes.find(node => {
   return node.value === value;
    });
  }

Next we can connect two nodes by making a "line" from one to the other.

 addLine(startValue, endValue) {

Find the nodes for each value.

    let startNode = this.find(startValue);
    let endNode = this.find(endValue);

```js
 Freak out if we didn't find one or the other.
    if (!startNode || !endNode) {
   throw new Error('Both nodes need to exist');
    }

And add a reference to the endNode from the startNode.

    startNode.lines.push(endNode);
  }
}

// Finally you can use a graph like this

var graph = new Graph();
graph.addNode(1);
graph.addNode(2);
graph.addLine(1, 2);
var two = graph.find(1).lines[0];
This might seem like a lot of work to do very little, but it's actually a
quite powerful pattern, especially for finding sanity in complex programs.
They do this by optimizing for the connections between data rather than
operating on the data itself. Once you have one node in the graph, it's
extremely simple to find all the related items in the graph.
Tons of things can be represented this way, users with friends, the 800
transitive dependencies in a node_modules folder, the internet itself is a
graph of webpages connected together by links.

LINKED LISTS

Next we're going to see how a graph-like structure can help optimize ordered

lists of data.
Linked lists are a very common data structure that is often used to
implement other data structures because of its ability to efficiently add
items to the start, middle, and end.
The basic idea of a linked list is similar to a graph. You have nodes that
point to other nodes. They look sorta like this:
1 -> 2 -> 3 -> 4 -> 5
Visualizing them as a JSON-like structure looks like this:
{
value: 1,
next: {
value: 2,
next: {
value: 3,
next: {...}
}
}
}

class LinkedList {

Unlike a graph, a linked list has a single node that starts off the entire
chain. This is known as the "head" of the linked list.
We're also going to track the length.

 constructor() {
    this.head = null;
    this.length = 0;
  }

First we need a way to retrieve a value in a given position.
This works differently than normal lists as we can't just jump to the
correct position. Instead, we need to move through the individual nodes.

 get(position) {

Throw an error if position is greater than the length of the LinkedList

if (position >= this.length) {
  throw new Error("Position outside of list range");
}

Start with the head of the list.

let current = this.head;

Slide through all of the items using node.next until we reach the specified position.

for (let index = 0; index < position; index++) {
  current = current.next;
}

Return the node we found.

    return current;
  }

Next we need a way to add nodes to the specified position.
We're going for a generic add method that accepts a value and a position.

 add(value, position) {

// First create a node to hold our value.

let node = {
  value,
  next: null,
};

We need to have a special case for nodes being inserted at the head

We'll set the "next" field to the current head and then replace it with

 our new node.
    if (position === 0) {
   node.next = this.head;
   this.head = node;

If we're adding a node in any other position we need to splice it in between the current node and the previous node. } else { First, find the previous node and the current node.

let prev = this.get(position * 1);
let current = prev.next;

// then insert the new node in between them by setting its "next" field

to the current node and updating the previous node's "next" field to

 // the new one.
   node.next = current;
   prev.next = node;
    }
 // Finally just increment the length.
    this.length++;
  }

The last method we need is a remove method. We're just going to look up a
node by its position and splice it out of the chain.

 remove(position) {

We should not be able to remove from an empty list

if (!this.head) {
  throw new Error("Removing from empty list");
}

If we're removing the first node we simply need to set the head to the

 next node in the chain
    if (position === 0) {
   this.head = this.head.next;

For any other position, we need to look up the previous node and set it

to the node after the current position.

   } else {
  let prev = this.get(position * 1);
  prev.next = prev.next.next;
   }
// then we just decrement the length.
   this.length--;
 }
}

The remaining two data structures we are going to cover are both in the

"tree" family.
Much like real life, there are many different types of tree data structures.
Binary Trees:
AA Tree, AVL Tree, Binary Search Tree, Binary Tree, Cartesian Tree,
left child/right sibling tree, order statistic tree, Pagoda, ...
B Trees:
B Tree, B+ Tree, B* Tree, B Sharp Tree, Dancing Tree, 2-3 Tree, ...
Heaps:
Heap, Binary Heap, Weak Heap, Binomial Heap, Fibonacci Heap, Leonardo
Heap, 2-3 Heap, Soft Heap, Pairing Heap, Leftist Heap, Treap, ...
Trees:
Trie, Radix Tree, Suffix Tree, Suffix Array, FM-index, B-trie, ...
Multi-way Trees:
Ternary Tree, K-ary tree, And-or tree, (a,b)-tree, Link/Cut Tree, ...
Space Partitioning Trees:
Segment Tree, Interval Tree, Range Tree, Bin, Kd Tree, Quadtree,
Octree, Z-Order, UB-Tree, R-Tree, X-Tree, Metric Tree, Cover Tree, ...
Application-Specific Trees:
Abstract Syntax Tree, Parse Tree, Decision Tree, Minimax Tree, ...
Little did you know you'd be studying dendrology today... and that's not even
all of them. But don't let any of this scare you, most of those don't matter
at all. There were just a lot of Computer Science PhDs who had something to
prove.
Trees are much like graphs or linked lists except they are "unidirectional".
All this means is that they can't have loops of references.
Tree: | Not a Tree:
A | A
↙ ↘ | ↗ ↘
B C | B ←---* C
If you can draw a loop between connected nodes in a tree... well, you don't
have a tree.
Trees have many different uses, they can be used to optimize searching or
sorting. They can organize programs better. They can give you a
representation that is easier to work with.

TREES

We'll start off with an extremely simple tree structure. It doesn't have any

special rules to it and looks something like this:
Tree {
root: {
value: 1,
children: [{
value: 2,
children: [...]
}, {
value: 3,
children: [...]
}]
}
}

class Tree {

The tree has to start with a single parent, the "root" of the tree.

 constructor() {
    this.root = null;
  }

We need a way to traverse our tree and call a function on each node in the
tree.

 traverse(callback) {

We'll define a walk function that we can call recursively on every node

 in the tree.
    function walk(node) {

```js
 First call the callback on the node.
   callback(node);

```js
 // then recursively call the walk function on all of its children.
   node.children.forEach(walk);
    }

Now kick the traversal process off.

   walk(this.root);
 }

Next we need a way to add nodes to our tree.

 add(value, parentValue) {
    let newNode = {
   value,
   children: []
    };

If there is no root, just set it to the new node.

if (this.root === null) {
  this.root = newNode;
  return;
}

 Otherwise traverse the entire tree and find a node with a matching value


 and add the new node to its children.
    this.traverse(node => {
   if (node.value === parentValue) {
     node.children.push(newNode);
   }
    });
  }
}

This is one of the most basic trees you could have and is probably only

useful if the data you are representing actually resembles a tree.
But with some extra rules, a tree can serve a lot of different purposes.

BINARY SEARCH TREES

Binary search trees are a fairly common form of tree for their ability to

efficiently access, search, insert, and delete values all while keeping them
in a sorted order.
Imagine taking a sequence of numbers:
1 2 3 4 5 6 7
And turning it into a tree starting from the center.
4
/ \
2 6
/ \ / \
1 3 5 7
-^--^--^--^--^--^--^-
1 2 3 4 5 6 7
This is how a binary tree works. Each node can have two children:
- Left: Less than parent node's value.
- Right: Greater than parent node's value.
Note: In order to make this work all values must be unique in the tree.
This makes the traversal to find a value very efficient. Say we're trying to
find the number 5 in our tree:
(4) <

5 > 4, so move right.

/ \
2 (6) <

5 < 6, so move left.

/ \ / \
1 3 (5) 7 <

We've reached 5!

Notice how we only had to do 3 checks to reach the number 5. If we were to
expand this tree to 1000 items. We'd go:
500 -> 250 -> 125 -> 62 -> 31 -> 15 -> 7 -> 3 -> 4 -> 5
Only 10 checks for 1000 items!
The other important thing about binary search trees is that they are similar
to linked lists in the sense that you only need to update the immediately
surrounding items when adding or removing a value.

class BinarySearchTree {

Same as the previous Tree, we need to have a "root" of the binary search
tree.

 constructor() {
    this.root = null;
  }

In order to test if the value exists in the tree, we first need to search
through the tree.

 contains(value) {

We start at the root

let current = this.root;

We're going to keep running as long as we have another node to visit

If we reach a left or right that is null then this loop ends. while (current) {
If the value is greater than the current.value we move to the right

   if (value > current.value) {
     current = current.right;

If the value is less than the current.value we move to the left.

   } else if (value < current.value) {
     current = current.left;

Otherwise we must be equal values and we return true.

  } else {
    return true;
  }
   }

If we haven't matched anything then we return false.

    return false;
  }

In order to add items to this tree we are going to do the same traversal
as before, bouncing between left and right nodes depending on them being
less than or greater than the value we're adding.
However, this time when we reach a left or right that is null we're
going to add a new node in that position.

 add(value) {

First let's setup our node.

let node = {
  value: value,
  left: null,
  right: null,
};

Special case for when there isn't any root node and we just need to add one.

if (this.root === null) {
  this.root = node;
  return;
}

We start at the root node

let current = this.root;

We're going to loop until we've either added our item or discovered it

already exists in the tree. while (true) {

If the value is greater than the current.value we move to the right. if (value > current.value) {
If right does not exist, set it to our node, and stop traversing.

     if (!current.right) {
   current.right = node;
   break;
     }

Otherwise just move on to the right node. current = current.right;

If the value is less than the current.value we move to the left. } else if (value < current.value) {
If left does not exist, set it to our node, and stop traversing.

     if (!current.left) {
   current.left = node;
   break;
     }

Otherwise just move on to the left node. current = current.left;

If the number isn't less than or greater, then it must be the same and

We don't do anything.

   } else {
     break;
   }
    }
  }
}

YOU REACHED THE END

Just exporting everything for the tests...

module.exports = {
  List,
  HashTable,
  Stack,
  Queue,
  Graph,
  LinkedList,
  Tree,
  BinarySearchTree,
};