Красно черное дерево реализация питон

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Red-Black-Tree using Python

BazNick/Red-Black-Tree

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README.md

Red-Black-Tree realisation using Python. Includes followings methods:

1. Create tree;
2. Delete nodes from the tree;
3. Find node in the tree;
4. Display all nodes;
5. Display height of the tree;
6. Display number of black nodes;
7. Rotation methods (right rotation, left rotation, left-right rotation, right-left rotation);

Also you may want to see a small wiki about this realisation: https://github.com/BazNick/Red-Black-Tree/wiki

Реализация Красно-Черного Дерева на Python. Включает следующие методы:

1. Create tree (Создание дерева, то есть его узлов);
2. Delete nodes from the tree (Удаление узлов из дерева);
3. Find node in the tree (Нахождение элемента в дереве);
4. Display all nodes (Выводит все элементы, которые есть в дереве);
5. Display height of the tree (Выводит высоту дерева);
6. Display number of black nodes (Выводит количество черных узлов);
7. Rotation methods (right rotation, left rotation, left-right rotation, right-left rotation) (Методы вращения: левое, правое, лево-правое и право-левое);

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Building a Red-Black Binary Tree in Python

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A red-black tree is a kind of self-balancing binary search tree. Each node stores an extra bit, which we will call the color, red or black. The color ensures that the tree remains approximately balanced during insertions and deletions. When the tree is modified, the new tree is rearranged and repainted to restore the coloring properties that constrain how unbalanced the tree can become in the worst case.

The purpose of a red-black tree is to stay balanced which ensures that its common operations, like lookup and delete, never degrade to worse than O(n*log(n)) .

🔗 What is a balanced binary tree?

Since the reason colors are added to a binary tree is to ensure that it remains balanced, we need to understand how and why a binary tree is balanced. To put it simply, a balanced tree’s branches differ in height by no more than 1.

The following tree is balanced because between its two branches one has a height of 2, and the other 3, meaning they differ by no more than 1.

The next tree is unbalanced because it’s branches differ in height by more than 1. C ’s right side has a height of 2 while its left side has a height of 4).

🔗 Why do we want balanced trees?

Balanced binary search trees ensure speed. The speed of an operation in a binary tree depends on the height of the tree. If the tree is balanced, then the height is only the log of the number of nodes, which means the tree will work as fast as possible. However, if the tree is unbalanced, for example with one really long branch, then the height because the total number of nodes rather than the log.

🔗 Properties of a red-black tree

In addition to all the properties of a Binary Search Tree, a red-black tree must have the following:

1. Each node is either red or black
2. 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.
3. All nil leaf nodes are black.
4. If a node is red, then both its children are black.
5. All paths from a single node go through the same number of black nodes to reach any of its descendant nil nodes.

🔗 Implementing a Red-Black Tree in Python

🔗 Step 1 – RBNode Class

Our implementation will use a Tree class and a Node class. The Node will be fairly simple, it’s just a constructor.

Next let’s create a tree class with a constructor.

    The insert method will look a lot like a traditional binary tree insert method. The biggest difference is that after doing an insert, we’ll call a special fix_insert method. For now just call it, we’ll implement it in just a moment.

🔗 Step 4 — Rotate left

We’ll need some rotation methods in our “fix” step that’s coming up. Let’s code those now.

The real bread and butter is in this step, it’s what makes a red-black tree balanced.

   Full Example of Red-Black Tree in Code 

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Python implementation of reb black tree

ersul4ik/rbt

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README.md

Реализация алгоритма написана на Python 3.

Девушка: Нарисуй дерево. Программист: (рисует бинарное дерево) Девушка: Нет, другое. Программист: Я и красно-черное дерево могу нарисовать.

КЧД наследует все свойства от обычного бинарного дерева + :

• Каждый узел окрашен либо в красный, либо в черный цвет (в структуре данных узла появляется дополнительное поле – бит цвета).
• Корень окрашен в черный цвет.
• Листья(так называемые NULL-узлы) окрашены в черный цвет.
• Каждый красный узел должен иметь два черных дочерних узла. Нужно отметить, что у черного узла могут быть черные дочерние узлы. Красные узлы в качестве дочерних могут иметь только черные.
• Пути от узла к его листьям должны содержать одинаковое количество черных узлов(это черная высота).

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Python implementation of reb black tree

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