From d28d596d99d4626956f72d800962e162289cf4c4 Mon Sep 17 00:00:00 2001 From: DETCHART Jonathan <jonathan.detchart@isae.fr> Date: Fri, 13 Jun 2025 14:08:39 +0000 Subject: [PATCH] uv migration (mae-ac/trees!6) --- .gitignore | 1 + Makefile | 16 -- README.md | 358 +---------------------- assets/delete.mp4 | Bin 1457352 -> 0 bytes assets/find.mp4 | Bin 1258560 -> 0 bytes assets/insert.mp4 | Bin 3164392 -> 0 bytes assets/maze-tree.jpg | Bin 162925 -> 0 bytes assets/maze.jpg | Bin 87219 -> 0 bytes assets/rotate.mp4 | Bin 686189 -> 0 bytes assets/traverse.mp4 | Bin 5228276 -> 0 bytes assets/trees.png | Bin 893798 -> 0 bytes avl.md | 186 ------------ bst.md | 119 -------- dev-requirements.txt | 1 - huffman.md | 665 ------------------------------------------- maze.md | 123 -------- pyproject.toml | 12 + qtree.md | 179 ------------ requirements.txt | 2 - 19 files changed, 16 insertions(+), 1646 deletions(-) delete mode 100644 Makefile delete mode 100644 assets/delete.mp4 delete mode 100644 assets/find.mp4 delete mode 100644 assets/insert.mp4 delete mode 100644 assets/maze-tree.jpg delete mode 100644 assets/maze.jpg delete mode 100644 assets/rotate.mp4 delete mode 100644 assets/traverse.mp4 delete mode 100644 assets/trees.png delete mode 100644 avl.md delete mode 100644 bst.md delete mode 100644 dev-requirements.txt delete mode 100644 huffman.md delete mode 100644 maze.md create mode 100644 pyproject.toml delete mode 100644 qtree.md delete mode 100644 requirements.txt diff --git a/.gitignore b/.gitignore index 09b31bb..bae9d53 100644 --- a/.gitignore +++ b/.gitignore @@ -1,2 +1,3 @@ __pycache__/ media/ +uv.lock \ No newline at end of file diff --git a/Makefile b/Makefile deleted file mode 100644 index ba9a306..0000000 --- a/Makefile +++ /dev/null @@ -1,16 +0,0 @@ -.PHONY: test-search test-tree test-bst test - -test-search: - pytest tests/test_binary_search.py - -test-tree: - pytest tests/test_binary_tree.py - -test-bst: - pytest tests/test_binary_search_tree.py - -test-avl: - pytest tests/test_balanced_tree.py - -test: - pytest diff --git a/README.md b/README.md index 1f1e7ca..12fdebc 100644 --- a/README.md +++ b/README.md @@ -1,359 +1,7 @@ # Trees -In this class, you will learn about a very common algorithmic tool: trees. -The data structure itself will be motivated by a simple search example and then -implemented and studied from scratch. +This project is part of the 1MAE002 course. Please refer to the [website](https://gitlab-pages.isae-supaero.fr/mae-ac/website/projects/trees/introduction.html) for more information. -Finally, a few examples of trees will be showcased: -- _perfect_ maze generation -- loss-less text compression -- neighborhood optimization in $n$-body systems +# Contact -# Table of content -- [_Upload your work to the LMS_](#upload-your-work-to-the-lms-toc) -- [_Binary search_](#binary-search-toc) - - [_Question 1._](#question-1-toc) - - [_Question 2._](#question-2-toc) -- [_Binary search trees_](#binary-search-trees-toc) - - [_The tree data structure_](#the-tree-data-structure-toc) - - [_Question 3._](#question-3-toc) - - [_Question 4._](#question-4-toc) - - [_Question 5._](#question-5-toc) - - [_Question 6._](#question-6-toc) - - [_Tree traversal_](#tree-traversal-toc) - - [_Question 7._](#question-7-toc) - - [_Implementing the BST_](bst.md#implementing-the-bst-toc) - - [_Question 8._](bst.md#question-8-toc) - - [_Insertion_](bst.md#insertion-toc) - - [_Question 9._](bst.md#question-9-toc) - - [_Search_](bst.md#search-toc) - - [_Question 10._](bst.md#question-10-toc) - - [_Deletion_](bst.md#deletion-toc) - - [_Question 11._](bst.md#question-11-toc) -- [_Huffman encoding_](huffman.md#huffman-encoding-toc) - - [_Introduction_](huffman.md#introduction-toc) - - [_Question 12._](huffman.md#question-12-toc) - - [_Question 13._](huffman.md#question-13-toc) - - [_Huffman trees_](huffman.md#huffman-trees-toc) - - [_Question 14._](huffman.md#question-14-toc) - - [_Coding books_](huffman.md#coding-books-toc) - - [_Question 15._](huffman.md#question-15-toc) - - [_Text compression_](huffman.md#text-compression-toc) - - [_Question 16._](huffman.md#question-16-toc) - - [_Text decompression_](huffman.md#text-decompression-toc) - - [_Question 17._](huffman.md#question-17-toc) - - [_Question 18._](huffman.md#question-18-toc) - - [_Writing a CLI compression tool_](huffman.md#writing-a-cli-compression-tool-toc) - - [_The compression format_](huffman.md#the-compression-format-toc) - - [_Writing to and reading from the disk_](huffman.md#writing-to-and-reading-from-the-disk-toc) - - [_Question 19._](huffman.md#question-19-toc) - - [_Question 20._](huffman.md#question-20-toc) - - [_Wrapping up in a CLI application_](huffman.md#wrapping-up-in-a-cli-application-toc) - - [_Question 21._](huffman.md#question-21-toc) -- [_Unbalanced trees_ (_optional_)](avl.md#unbalanced-trees-toc-optional) - - [_Question 22._](avl.md#question-22-toc) -- [_Height-balanced BSTs_ (_optional_)](avl.md#height-balanced-bsts-toc-optional) - - [_Question 23._](avl.md#question-23-toc) - - [_Question 24._](avl.md#question-24-toc) - - [_Question 25._](avl.md#question-25-toc) - - [_Tree rotations_](avl.md#tree-rotations-toc) - - [_Question 26._](avl.md#question-26-toc) - - [_Question 27._](avl.md#question-27-toc) - - [_Balancing our BSTs_](avl.md#balancing-our-bsts-toc) - - [_Question 28._](avl.md#question-28-toc) -- [_Maze generation and solving_ (_optional_)](maze.md#maze-generation-and-solving-toc-optional) - - [_Generating perfect mazes_](maze.md#generating-perfect-mazes-toc) - - [_Question 29._](maze.md#question-29-toc) - - [_Question 30._](maze.md#question-30-toc) - - [_Question 31._](maze.md#question-31-toc) - - [_solving perfect mazes_](maze.md#solving-perfect-mazes-toc) - - [_Question 32._](maze.md#question-32-toc) - - [_Question 33._](maze.md#question-33-toc) -- [_Quad trees_ (_optional_)](qtree.md#quad-trees-toc-optional) - - [_$n$-body collision simulation_](qtree.md#n-body-collision-simulation-toc) - - [_Question 34._](qtree.md#question-34-toc) - - [_Question 35._](qtree.md#question-35-toc) - - [_Question 36._](qtree.md#question-36-toc) - - [_Let's speed things up_](qtree.md#lets-speed-things-up-toc) - - [_Question 37._](qtree.md#question-37-toc) - - [_Question 38._](qtree.md#question-38-toc) - - [_Question 39._](qtree.md#question-39-toc) - - [_Question 40._](qtree.md#question-40-toc) - - [_Question 41._](qtree.md#question-41-toc) - - [_Question 42._](qtree.md#question-42-toc) - - [_Question 43._](qtree.md#question-43-toc) - - [_Question 44._](qtree.md#question-44-toc) - - [_Question 45._](qtree.md#question-45-toc) - - - ---- - -## Upload your work to the LMS [[toc](#table-of-content)] -- open a terminal -- go into the folder containing your project -- use the `zip` command to compress your project -```shell -zip -r project.zip . -x "venv/**" ".git/**" -``` -- upload the ZIP archive to the [LMS](https://lms.isae.fr/mod/assign/view.php?id=116610&action=editsubmission) - ---- - -## Binary search [[toc](#table-of-content)] -Let's start this class with a quite simple problem: given a list $l$ of $n$ -integers and an integer $i$, how can you tell whether or not $i$ is in $l$? - -:gear: You can run `pytest`. You should have 14 failing tests, that's -normal you will complete your code base and make sure the tests pass during the -class. - -### Question 1. [[toc](#table-of-content)] -:file_folder: Create a new file `search.py`. - -:pencil: let's create a big list, and suppose it is not sorted. Using the module `time`, measure the time to find if the element `199_999_999` is in the list (you can use the keyword `in`). -```python -l = list(range(200_000_000)) -``` - -:question: What is the complexity of your algorithm? - -From now on, we will assume that the elements in $l$ are sorted in ascending -order. -This will greatly help us improve our search algorithm. - -The idea of _binary search_ is the following: because the elements are sorted in -ascending order, if we look at any element $j$ in the middle of a list, if -$i \lt j$ we know that, if $i$ is in $l$, then it must be on the left of $j$! -Now that one half of $l$ has been completely discarded, we can repeat the search -on one of the halfs of $l$. - -The algorithm repeats recursively until either -- $i = j$: $i$ is in $l$ -- we find the empty list: $i$ is not in $l$ - -### Question 2. [[toc](#table-of-content)] -:pencil: Implement binary search and measure the time needed to call it. -You should write a function `binary_search` in `search.py`: -- arguments: - - `l`: a sorted list of integers - - `i`: an integer -- return: a boolean which tells whether `i` is inside `l` or not - -:question: What is the complexity of this new algorithm? - -:gear: Run `pytest tests/test_binary_search.py`. If it's all green, good job :clap: :clap: - -That's much better! However, we have made a quite huge assumption about the -input data... it should be sorted!! - -In the real world, we won't have perfectly sorted data in general and it is -quite expensive to sort lists (remember, comparison-based sorting algorithms are -$O(n \log n)$ at best) or to insert an element (around $O(n)$). - -## Binary search trees [[toc](#table-of-content)] - -This is where trees, and especially _**B**inary **S**earch **T**ree**s**_ (BSTs), -come into play! - -But before getting to BSTs, which will definitely solve our key problem above, -we need to talk about trees. - -### The tree data structure [[toc](#table-of-content)] - -Trees are a very common algorithmic data structure. A tree is a recursive -structure that can either -- be _empty_ -- hold a _value_ and _references_ to other trees - -Some naming conventions: -- the _references_ to other trees are called _subtrees_ or _children_ and if there - are only two such _subtrees_, they are often called _left_ and _right_ -- the entry point of the tree is called the _root_ -- a tree that has no _subtrees_ is called a leaf -- if $a$ is a tree that has $b$ as a _child_, then $a$ is called the _parent_ of - $b$ - -The properties that a tree must satisfy: -- :exclamation: a tree must NOT contain any cycle, i.e. every _node_ in the tree - should have a unique _parent_ - -Below are some examples of trees and non-trees: -- the _empty_ tree (yeah, there is nothing to show with that one) -- a single _leaf_ -```mermaid -flowchart TD - 0((0)) -``` -- a tree where all nodes have at most 2 children -```mermaid -flowchart TD - 0((0)); 1((1)); 2((2)); 3((3)); 4((4)) - 0 --> 1 - 0 --> 2 - 1 --> 3 - 1 --> 4 -``` -- a tree with more than 2 children per node -```mermaid -flowchart TD - 0((0)); 1((1)); 2((2)); 3((3)); 4((4)); 5((5)); 6((6)); 7((7)) - 0 --> 1 - 0 --> 2 - 0 --> 3 - 0 --> 4 - 3 --> 5 - 3 --> 6 - 3 --> 7 -``` -- the following _thing_ is NOT a tree -```mermaid -flowchart TD - 0((0)); 1((1)); 2((2)); 3((3)); 4((4)) - 0 --> 1 - 0 --> 2 - 1 --> 3 - 1 --> 4 - 2 --> 4 -``` - -#### Question 3. [[toc](#table-of-content)] -:file_folder: Create a new file `tree.py`. - -:pencil: In `tree.py`, create a new class called `BinaryTree`. It should have -the following attributes which should all default to `None`: -- `value`: an integer -- `left`: another `BinaryTree`, the left child -- `right`: another `BinaryTree`, the right child - -:gear: Run `pytest tests/test_binary_tree.py`. You should have 6 failing tests, that's normal. - -:pencil: In order to help you debug the code and _see_ the binary trees, please -copy-paste the following method into your `BinaryTree` class. Now, you will be -able to call `print(binary_tree)` and see it in your terminal: -```python - def __repr__(self) -> str: - def aux(t, before: str, is_right: bool, has_right_brother: bool): - if t is None: - return '' - - if before is None: - curr = f"{t.value}\n" - else: - marker = '`' if is_right else '|' - curr = before + f"{marker}---- {t.value}\n" - - next = '' if before is None else ( - before + "| " if has_right_brother else before + " " - ) - right = t.right is not None - if t.left is not None: - left = aux( - t.left, next, is_right=not right, has_right_brother=right - ) - else: - left = '' - if t.right is not None: - right = aux( - t.right, next, is_right=True, has_right_brother=False - ) - else: - right = '' - return curr + left + right - - return aux(self, None, is_right=False, has_right_brother=False).strip() -``` - -First, we will implement some general methods on binary trees and then we'll -move on to BSTs. - -#### Question 4. [[toc](#table-of-content)] -:pencil: Add a method `is_empty` to your `BinaryTree` class. It should return a -`bool`, `True` if the tree is empty and `False` otherwise. - -:gear: Run `pytest tests/test_binary_tree.py`. If the "empty" test is green, good job :clap: -:clap: - -#### Question 5. [[toc](#table-of-content)] -:pencil: Add a method `is_leaf` to your `BinaryTree` class. It should return a -`bool`, `True` if the tree is a leaf and `False` otherwise. - -> :bulb: **Note** -> -> remember the naming conventions from [_The tree data structure_](#the-tree-data-structure-) - -:gear: Run `pytest tests/test_binary_tree.py`. If the "leaf" test is green, good job :clap: :clap: - -#### Question 6. [[toc](#table-of-content)] -:pencil: At the end of `tree.py`, in a _main_ block, define a variable that -represents the following tree: -```mermaid -flowchart TD - 0((0)); 1((1)); 2((2)); 3((3)); 4((4)) - 0 --> 1 - 0 --> 2 - 1 --> 3 - 1 --> 4 -``` - -:question: Can you print the tree to your terminal using `print`? - -:question: By using `BinaryTree.is_empty` and `BinaryTree.is_leaf`, is your tree -variable empty? Is it a leaf? - -:question: What about the right child of the left child? - -### Tree traversal [[toc](#table-of-content)] -In this section, you will learn about the simplest _real_ operation on trees: -_traversal_. - -_Traversing_ a tree means going through every node of the tree and performing -an operation on each one of the nodes. - -There are four main _traversal_ techniques on binary trees: -- **D**epth **F**irst **S**earch (DFS): the tree is explored as deep as possible - first - - prefix: a node is treated before its children - - infix: a node is treated in between its children - - postfix: a node is treated after its children -- **B**readth **F**irst **S**earch (BFS): the tree is explored level of depth - after level of depth - -Below is an animation for each one of these _traversal_ techniques: - - - -#### Question 7. [[toc](#table-of-content)] -:pencil: Implement the four _traversal_ techniques in your `BinaryTree` class. -At the end of this question, you should have four new methods: -- `BinaryTree.dfs_prefix` -- `BinaryTree.dfs_infix` -- `BinaryTree.dfs_postfix` -- `BinaryTree.bfs` - -These methods take as argument a function that will be applied to each node of the tree. - -:pencil: Call the `dfs_prefix` on the previous tree by providing the `print` method as the argument. You should get the following list: `0 1 3 4 2`. - - -:question: With the tree below, compare the order of _traversal_ for each technique. -```mermaid -flowchart TD - 0((0)); 1((1)); 2((2)); 3((3)); 4((4)); 5((5)); 6((6)) - 0 --> 1 - 0 --> 2 - 1 --> 3 - 1 --> 4 - 2 --> 5 - 2 --> 6 -``` - -:question: If you look back at the `BinaryTree.__repr__` method that was given -to you, what is the _traversal_ technique used to achieve the pretty output? - -:gear: Use `pytest tests/test_binary_tree.py` to make sure your traversal implementations are -correct :wink: - ---- ---- -> [go to next](bst.md) +jonathan.detchart@isae-supaero.fr diff --git a/assets/delete.mp4 b/assets/delete.mp4 deleted file mode 100644 index 17e4761f13253b8fdbb27c8a4ba46495e975017a..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1457352 zcmZQzU{FXasVvAW&d+6FU}6B#nZ@}=iDk)#xdkSM3=9k$X+^2245I%Ea#IpZ7#Nt= zv$6jFzxs~r%e~KTdTgJjb3@^#^1JsHMrI}ox(dnpMX3sgX2uFd#s+2v3Z^MZW{HVr 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