├── DIRECTORY.md ├── .github ├── CODEOWNERS └── pull_request_template.md ├── .gitignore ├── mojoproject.toml ├── maths ├── ceil.mojo ├── average_mean.mojo ├── abs.mojo └── aliquot_sum.mojo ├── LICENSE ├── README.md ├── CONTRIBUTING.md └── magic.lock /DIRECTORY.md: -------------------------------------------------------------------------------- 1 | # Directory 2 | -------------------------------------------------------------------------------- /.github/CODEOWNERS: -------------------------------------------------------------------------------- 1 | * @SatinWukerORIG -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # for PyCharm 2 | .idea/ 3 | 4 | # for Mac 5 | .DS_Store 6 | 7 | # for magic 8 | .magic -------------------------------------------------------------------------------- /mojoproject.toml: -------------------------------------------------------------------------------- 1 | [project] 2 | authors = ["TheAlgorithms "] 3 | channels = ["conda-forge", "https://conda.modular.com/max"] 4 | description = "All algorithms implemented in Mojo. (The first open-sourced Mojo repository on GitHub)" 5 | name = "Mojo" 6 | platforms = ["osx-arm64", "linux-64"] 7 | version = "0.1.0" 8 | 9 | [tasks] 10 | 11 | [dependencies] 12 | max = ">=24.5.0,<25" 13 | -------------------------------------------------------------------------------- /.github/pull_request_template.md: -------------------------------------------------------------------------------- 1 | 8 | 9 | - [ ] I have performed a self-review of my code 10 | - [ ] My code follows the style guidelines of this project 11 | - [ ] I have added tests that prove my fix is effective or that my feature works 12 | - [ ] New and existing unit tests pass locally with my changes 13 | - [ ] Comments in areas I changed are up to date 14 | - [ ] I have added comments to hard-to-understand areas of my code -------------------------------------------------------------------------------- /maths/ceil.mojo: -------------------------------------------------------------------------------- 1 | ## Ceiling function 2 | ## 3 | ## The ceiling function maps a real number x to the smallest integer greater than or equal to x. 4 | 5 | # https://en.wikipedia.org/wiki/Floor_and_ceiling_functions 6 | 7 | fn ceil(number: Float64) -> Int: 8 | """ 9 | Return the ceiling of number as an integer. 10 | 11 | Parameters: 12 | - number: A floating-point number. 13 | 14 | Returns: 15 | - The smallest integer greater than or equal to number. 16 | 17 | ```mojo 18 | from testing import assert_equal 19 | from ceil import ceil 20 | assert_equal(ceil(1.1), 2) 21 | assert_equal(ceil(1.9), 2) 22 | assert_equal(ceil(1.0), 1) 23 | assert_equal(ceil(0.0), 0) 24 | assert_equal(ceil(-1.0), -1) 25 | assert_equal(ceil(-1.1), -1) 26 | assert_equal(ceil(-1.9), -1) 27 | ``` 28 | """ 29 | var int_number = int(number) 30 | if number - int_number > 0.0: 31 | return int_number + 1 32 | return int_number 33 | 34 | -------------------------------------------------------------------------------- /maths/average_mean.mojo: -------------------------------------------------------------------------------- 1 | ## Average mean 2 | ## Find mean of a list of numbers. 3 | ## Wiki: https://en.wikipedia.org/wiki/Mean. 4 | 5 | fn mean(nums: List[Int]) raises -> Float64: 6 | """ 7 | Parameters: 8 | - nums: List of integers. 9 | 10 | Returns: 11 | - Mean of the list of numbers. 12 | 13 | ```mojo 14 | from testing import assert_almost_equal, assert_raises 15 | from average_mean import mean 16 | DELTA = 1e-6 17 | assert_almost_equal(mean(List(5, 10, 15, 20, 25, 30, 35)), 20.0, atol=DELTA) 18 | assert_almost_equal(mean(List(1, 2, 3, 4, 5, 6, 7, 8)), 4.5, atol=DELTA) 19 | assert_almost_equal(mean(List(3, 6, 9, 12, 15, 18, 21)), 12.0, atol=DELTA) 20 | with assert_raises(): 21 | var empty = List[Int]() 22 | _ = mean(empty) 23 | ``` 24 | """ 25 | if len(nums) == 0: 26 | raise Error("List is empty") 27 | 28 | var list_sum = 0.0 29 | for num in nums: 30 | list_sum += num[] 31 | 32 | return list_sum / len(nums) 33 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2023 The Algorithms 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /maths/abs.mojo: -------------------------------------------------------------------------------- 1 | ## Absolute Value 2 | ## 3 | ## The absolute value of a number is the number without its sign. 4 | 5 | 6 | struct complex: 7 | var real_part: Int 8 | var imaginary_part: Int 9 | 10 | 11 | fn __init__(inout self: Self, real_part: Int, imaginary_part: Int): 12 | self.real_part = real_part 13 | self.imaginary_part = imaginary_part 14 | 15 | struct Math: 16 | @staticmethod 17 | fn absolute(number: Int) -> Int: 18 | ## Returns the absolute value of an integer. 19 | ## >>> Math.absolute(-5) 20 | ## 5 21 | ## >>> Math.absolute(5) 22 | ## 5 23 | return number if number >= 0 else -number 24 | 25 | @staticmethod 26 | fn absolute(number: FloatLiteral) -> FloatLiteral: 27 | ## Returns the absolute value of a float. 28 | ## >>> Math.absolute(-5.5) 29 | ## 5.5 30 | ## >>> Math.absolute(5.5) 31 | ## 5.5 32 | return number if number >= 0 else -number 33 | 34 | 35 | ## For a complex number z = x + yi, 36 | ## we define the absolute value |z| as being the distance from z to 0 in the complex plane C. 37 | ## Reference: https://www2.clarku.edu/faculty/djoyce/complex/abs.html#:~:text=For%20a%20complex%20number%20z,on%20the%20real%20number%20line. 38 | @staticmethod 39 | fn absolute(number: complex) -> FloatLiteral: 40 | ## Returns the absolute value of a complex number. 41 | ## >>> Math.absolute(complex(5, 12)) 42 | ## 13.0 43 | ## >>> Math.absolute(complex(3, 4)) 44 | ## 5.0 45 | return math.sqrt(number.real_part ** 2 + number.imaginary_part ** 2) 46 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 |
3 | 4 | 5 | 6 | 7 |

The Algorithms - Mojo

8 | All Algorithms implemented in Mojo! 9 |
10 |
11 | 12 | 13 | 14 | Contributions Welcome 15 | 16 | 17 | Discord chat 18 | 19 | 20 | Gitter chat 21 | 22 | 23 | [![HitCount](https://hits.dwyl.com/TheAlgorithms/Mojo.svg?style=flat-square)](http://hits.dwyl.com/TheAlgorithms/Mojo) 24 | 25 |
26 | 27 | GitHub Workflow Status 28 | 29 | 30 | pre-commit 31 | 32 | 33 | code style: black 34 | 35 | 36 |

All algorithms implemented in Mojo - for education

37 |
38 | 39 | ## Getting Started 40 | 41 | Read through our [Contribution Guidelines](CONTRIBUTING.md) before you contribute. 42 | 43 | ## Community Channels 44 | 45 | We are on [Discord](https://the-algorithms.com/discord) and [Gitter](https://gitter.im/TheAlgorithms/community)! Community channels are a great way for you to ask questions and get help. Please join us! 46 | 47 | ## List of Algorithms 48 | 49 | See our [directory](DIRECTORY.md) for easier navigation and a better overview of the project. 50 | -------------------------------------------------------------------------------- /maths/aliquot_sum.mojo: -------------------------------------------------------------------------------- 1 | ## Aliquot Sum 2 | ## 3 | ## The aliquot sum of a number n is defined as the sum of all natural numbers less than n that divide n evenly. 4 | ## This implementation provides both a basic O(n) approach and an optimized O(sqrt(n)) version. 5 | ## https://en.wikipedia.org/wiki/Aliquot_sum 6 | 7 | fn aliquot_sum(input_num: Int) raises -> Int: 8 | """ 9 | Finds the aliquot sum of an input integer. 10 | 11 | The aliquot sum is the sum of all proper divisors of a number (all positive divisors less than the number itself). 12 | This is a simple O(n) implementation that directly follows the definition. 13 | 14 | Parameters: 15 | - input_num: A positive integer whose aliquot sum is to be found. 16 | Returns: 17 | - The aliquot sum of input_num. If input_num is 1, returns 0 since there are no natural numbers less than 1. 18 | Raises: 19 | - Error: If input_num is not positive. 20 | 21 | Examples: 22 | - The aliquot sum of 12 is 1 + 2 + 3 + 4 + 6 = 16 23 | - The aliquot sum of 6 is 1 + 2 + 3 = 6 (perfect number) 24 | - The aliquot sum of 15 is 1 + 3 + 5 = 9 25 | - The aliquot sum of 19 is 1 (prime numbers only have 1 as a proper divisor) 26 | - The aliquot sum of 1 is 0 (there are no natural numbers less than 1) 27 | 28 | ```mojo 29 | from testing import assert_equal, assert_raises 30 | from aliquot_sum import aliquot_sum, optimized_aliquot_sum 31 | assert_equal(aliquot_sum(15), 9) 32 | assert_equal(aliquot_sum(6), 6) 33 | assert_equal(aliquot_sum(12), 16) 34 | assert_equal(aliquot_sum(1), 0) 35 | assert_equal(aliquot_sum(19), 1) 36 | with assert_raises(): 37 | _ = aliquot_sum(-1) 38 | with assert_raises(): 39 | _ = aliquot_sum(0) 40 | ``` 41 | """ 42 | if input_num <= 0: 43 | raise Error("Input must be positive") 44 | 45 | var sum = 0 46 | for divisor in range(1, input_num // 2 + 1): 47 | if input_num % divisor == 0: 48 | sum += divisor 49 | 50 | return sum 51 | 52 | fn optimized_aliquot_sum(input_num: Int) raises -> Int: 53 | """ 54 | Optimized implementation of aliquot sum with O(sqrt(n)) time complexity. 55 | 56 | This implementation leverages the mathematical property that divisors come in pairs: 57 | if i is a divisor of n, then n/i is also a divisor. By iterating only up to sqrt(n), 58 | we can find all divisor pairs and significantly improve performance. 59 | 60 | Parameters: 61 | - input_num: A positive integer whose aliquot sum is to be found. 62 | Returns: 63 | - The aliquot sum of input_num. 64 | Raises: 65 | - Error: If input_num is not positive. 66 | """ 67 | if input_num <= 0: 68 | raise Error("Input must be positive") 69 | 70 | var sum = 1 # Start with 1 as it's always a divisor for positive numbers 71 | if input_num == 1: 72 | return 0 # Special case: aliquot sum of 1 is 0 73 | 74 | # Find all divisor pairs up to sqrt(input_num) 75 | var i = 2 76 | while i * i <= input_num: 77 | if input_num % i == 0: 78 | sum += i 79 | # Add the pair if they're not the same (perfect square case) 80 | if i != input_num // i: 81 | sum += input_num // i 82 | i += 1 83 | 84 | return sum -------------------------------------------------------------------------------- /CONTRIBUTING.md: -------------------------------------------------------------------------------- 1 | # Contributing Guidelines 2 | 3 | Welcome to [TheAlgorithms/Mojo](https://github.com/TheAlgorithms/Mojo)! 4 | 5 | Welcome to Mojo! This repository is meant to be referenced and used by learners worldwide, and we aspire to maintain the highest possible quality of the code presented here! If you have any questions or concerns about this guide, please feel free to [state them clearly in an issue](https://github.com/TheAlgorithms/Mojo/issues/new) or ask the community in [Discord](https://the-algorithms.com/discord). 6 | 7 | ## Table Of Contents 8 | 9 | * [What is an Algorithm?](#what-is-an-algorithm) 10 | * [Contributor agreement](#contributor-agreement) 11 | * [Contribution guidelines](#contribution-guidelines) 12 | + [Implementation requirements](#implementation-requirements) 13 | + [Mojo Coding Style](#Mojo-coding-style) 14 | - [Readability and naming conventions](#readability-and-naming-conventions) 15 | - [Compilation](#compilation) 16 | - [Types](#types) 17 | - [Exceptions and side-effects](#exceptions-and-side-effects) 18 | - [Documentation, examples, and tests](#documentation-examples-and-tests) 19 | - [Other](#other) 20 | + [Minimal example](#Minimal-example) 21 | + [Submissions Requirements](#submissions-requirements) 22 | 23 | ## What is an Algorithm? 24 | 25 | An Algorithm is one or more functions that: 26 | 27 | - take one or more inputs, 28 | - perform some internal calculations or data manipulations, 29 | - return one or more outputs, 30 | - have minimal side effects (Examples of side effects: `print`, `read`). 31 | 32 | ## Contributor Agreement 33 | 34 | Being one of our contributors, you agree and confirm that: 35 | 36 | - Your work will be distributed under [MIT License](LICENSE) once your pull request is merged. 37 | - Your work meets the standards of this guideline. 38 | 39 | ## Contribution Guidelines 40 | 41 | We appreciate any contribution, from fixing a grammar mistake in a comment to implementing complex algorithms. Please check the [directory](DIRECTORY.md) and [issues](https://github.com/TheAlgorithms/Mojo/issues/) for an existing (or declined) implementation of your algorithm and relevant discussions. 42 | 43 | **New implementations** are welcome! This includes new solutions for a problem, different representations for a data structure, and algorithm design with different complexity or features. 44 | 45 | **Improving documentation and comments** and **adding tests** is also highly welcome. 46 | 47 | **Identical implementations** are not allowed. 48 | 49 | ### Environment 50 | My current version is `mojo 24.4.0 (64d14e85)` on Ubuntu 20.04.6 LTS. There is no strict requirement on the version because of the fast update on this new language. However, we encourage you to use newer versions. 51 | Installing the SDK is guided by this doc: https://docs.modular.com/mojo/manual/get-started/ 52 | 53 | ### Implementation requirements 54 | 55 | - Although the main goals of this repository are educational, the module form mirrors a real-world scenario and makes it easy to use the code from this repository in other projects. 56 | - The first line must contain the canonical title of the module prefixed by double hashes (`## Title Of The Module`). This title is used in this repository's automation for populating the [Directory](DIRECTORY.md). 57 | - The module should be thoroughly documented with comments. 58 | - The file begins with the module-level documentation with the general description and explanation of the algorithm/data-structure: 59 | * Any restrictions of the implementation and any constraints for the input data. 60 | * An overview of the use cases. 61 | * Recommendations for when to use or avoid using it. 62 | * Comparison with the alternatives. 63 | * Links to source materials and further reading. 64 | - Use intuitive and descriptive names for objects, functions, and variables. 65 | - Return all calculation results instead of printing or plotting them. 66 | - Avoid importing third-party libraries. Only use those for complicated algorithms and only if the alternatives of relying on the standard library or including a short amount of the appropriately-licensed external code are not feasible. 67 | ### Mojo Coding Style 68 | 69 | #### Readability and naming conventions 70 | 71 | We want your work to be readable by others; Although there is no naming conventions or best practices of Mojo, Mojo code style can be considered exactly same as Python 3 code style, [PEP 8](https://peps.python.org/pep-0008/). 72 | 73 | - Help your readers by using **descriptive names** that eliminate the need for redundant comments. 74 | - Avoid single-letter variable names, unless it has a Minimal lifespan. If your variable comes from a mathematical context or no confusion is possible with another variable, you may use single-letter variables. Generally, single-letter variables stop being OK if there are more than just a couple of them in scope. Some examples: 75 | * Prefer `index` or `idx` than `i` for loops. 76 | * Prefer `src` and `dst` than `a` and `b`. 77 | * Prefer `remainder` than `r` and `prefix` than `p`. 78 | - Expand acronyms. Prefer `greatest_common_divisor()` than `gcd()`, as the former is easier to understand than the latter, especially for non-native English speakers. 79 | 80 | ### Simple example 81 | 82 | ```Python 83 | ## Algorithm Name 84 | ## 85 | ## Description + link 86 | 87 | ## Comment 88 | fn algo(arr): 89 | ## Comment 90 | return arr[0] + arr[1] 91 | 92 | ``` 93 | 94 | ### Submissions Requirements 95 | 96 | - Make sure the code compiles before submitting. 97 | - Look up the name of your algorithm in other active repositories of [TheAlgorithms](https://github.com/TheAlgorithms/), like [TheAlgorithms/Python](https://github.com/TheAlgorithms/Python). By reusing the same name, your implementation will be appropriately grouped alongside other implementations on the [project's website](https://the-algorithms.com/). 98 | - Please help us keep our issue list small by adding fixes: Add the number of the issue you solved — even if only partially — to the commit message of your pull request. 99 | - Use *snake_case* (words separated with an underscore `_`) for the filename. 100 | - Try to fit your work into the existing directory structure as much as possible. Please open an issue first if you want to create a new subdirectory. 101 | - Writing documentation, be concise, and check your spelling and grammar. 102 | - Add a corresponding explanation to [Algorithms-Explanation](https://github.com/TheAlgorithms/Algorithms-Explanation) (optional but recommended). 103 | - Most importantly, **be consistent in the use of these guidelines**. 104 | 105 | **Happy coding!** 106 | 107 | --- 108 | 109 | Authors: [@SatinWuker](https://github.com/SatinWuker) 110 | -------------------------------------------------------------------------------- /magic.lock: -------------------------------------------------------------------------------- 1 | version: 5 2 | environments: 3 | default: 4 | channels: 5 | - url: https://conda.anaconda.org/conda-forge/ 6 | - url: https://conda.modular.com/max/ 7 | packages: 8 | linux-64: 9 | - conda: https://conda.anaconda.org/conda-forge/linux-64/_libgcc_mutex-0.1-conda_forge.tar.bz2 10 | - conda: https://conda.anaconda.org/conda-forge/linux-64/_openmp_mutex-4.5-2_gnu.tar.bz2 11 | - 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