* [Red-Black Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/red-black-tree)

A red–black tree is a kind of self-balancing binary search

tree in computer science. Each node of the binary tree has

an extra bit, and that bit is often interpreted as the

color (red or black) of the node. These color bits are used

to ensure the tree remains approximately balanced during

insertions and deletions.

Balance is preserved by painting each node of the tree with

one of two colors in a way that satisfies certain properties,

which collectively constrain how unbalanced the tree can

become in the worst case. When the tree is modified, the

new tree is subsequently rearranged and repainted to

restore the coloring properties. The properties are

designed in such a way that this rearranging and recoloring

can be performed efficiently.

The balancing of the tree is not perfect, but it is good

enough to allow it to guarantee searching in `O(log n)` time,

where `n` is the total number of elements in the tree.

The insertion and deletion operations, along with the tree

rearrangement and recoloring, are also performed

in `O(log n)` time.

An example of a red–black tree:


In addition to the requirements imposed on a binary search

tree the following must be satisfied by a red–black tree:

- Each node is either red or black.

- The root is black. This rule is sometimes omitted.

Since the root can always be changed from red to black,

but not necessarily vice versa, this rule has little

effect on analysis.

- All leaves (NIL) are black.

- If a node is red, then both its children are black.

- Every path from a given node to any of its descendant

NIL nodes contains the same number of black nodes.

Some definitions: the number of black nodes from the root

to a node is the node's **black depth**; the uniform

number of black nodes in all paths from root to the leaves

is called the **black-height** of the red–black tree.

These constraints enforce a critical property of red–black

trees: _the path from the root to the farthest leaf is no more than twice as long as the path from the root to the nearest leaf_.

The result is that the tree is roughly height-balanced.

Since operations such as inserting, deleting, and finding

values require worst-case time proportional to the height

of the tree, this theoretical upper bound on the height

allows red–black trees to be efficient in the worst case,

unlike ordinary binary search trees.


- Left Left Case (`p` is left child of `g` and `x` is left child of `p`)

- Left Right Case (`p` is left child of `g` and `x` is right child of `p`)

- Right Right Case (`p` is right child of `g` and `x` is right child of `p`)

- Right Left Case (`p` is right child of `g` and `x` is left child of `p`)





- [Wikipedia](https://en.wikipedia.org/wiki/Red%E2%80%93black_tree)

- [Red Black Tree Insertion by Tushar Roy (YouTube)](https://www.youtube.com/watch?v=UaLIHuR1t8Q&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=63)

- [Red Black Tree Deletion by Tushar Roy (YouTube)](https://www.youtube.com/watch?v=CTvfzU_uNKE&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=64)

- [Red Black Tree Insertion on GeeksForGeeks](https://www.geeksforgeeks.org/red-black-tree-set-2-insert/)

- [Red Black Tree Interactive Visualisations](https://www.cs.usfca.edu/~galles/visualization/RedBlack.html)