https://github.com/sufftea/link-cut-treeez

Link-cut trees visualisation on Qt C++
https://github.com/sufftea/link-cut-treeez

algorithms cpp qt visualization

Last synced: 7 months ago
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Link-cut trees visualisation on Qt C++

• Host: GitHub
• URL: https://github.com/sufftea/link-cut-treeez
• Owner: sufftea
• Created: 2020-11-09T16:44:16.000Z (over 5 years ago)
• Default Branch: main
• Last Pushed: 2021-03-20T16:25:34.000Z (about 5 years ago)
• Last Synced: 2023-07-19T22:29:58.882Z (over 2 years ago)
• Topics: algorithms, cpp, qt, visualization
• Language: C++
• Homepage:
• Size: 63.5 MB
• Stars: 3
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
# Link-Cut-Treeez

Link cut trees visualization.

# Abstract/represented tree

![](pics/abstract_tree.gif)

# Concrete/auxiliary tree

![](pics/concrete_tree.gif)

# A brief explanation of what it is

Link cut tree is able to perform the following operations in O(log(n)) amortized time:

- path-aggregate operations (on the path form node v to its root)

  - sum(v)

  - min(v)

  - max(v)

- find_root(v)

- LCA(v, u);

- add_const(v) (not implemented) - add a constant to each node on the path from v to its root

### Abstract or represented tree

Abstract tree is not stored in the memory; it's the way we imagine a link-cut tree when working with it, thus the name.

Each node can have an unlimited number of children and one prefered child (has red edge on the visualisation).

A chain of preferred children forms a preferred path. 

expose(v) seelects all the edges on the path from v to its root to make the path prefered.

The path-aggregate operations described above are performed on prefered paths.

### Concrete or auxiliary tree

The way link-cut tree is actually stored in the memory.

It's a forest of splay trees where each splay tree represents a phrefered path in the Abstract tree.

The root of each splay tree contains a path-parent pointer to the path's predecessor in the abstract tree.

## I waas adding those while developing the program:

## Update1:

![](pics/progress_so_far.gif?raw=true "Title")

## Update2:

![](pics/update2.gif?raw=true "Title")

## Update3

![](pics/update3.gif?raw=true "Title")

## Update4

![](pics/Update4.gif?raw=true "Title")

## Update5

![](pics/Update5.gif?raw=true "Title")

## Update6

![](pics/Update6.gif?raw=true "Title")