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Classic algorithms including Fizz Buzz, Bubble Sort, the Fibonacci Sequence, a Sudoku solver, and more.

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# Algorithms

Classic algorithms including Fizz Buzz, Bubble Sort, the Fibonacci Sequence, a Sudoku solver, and more.

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</div>

## Algorithm Complexity

> Time and Space Complexity (Big O Notation)

All algorithms have a complexity known as `Big O Notation`, the more complex an algorithm, the less efficient it gets as more data is introduced. Listed below are the `Big-O` complexities listed from best to worst:

* O(1)
* O(log n)
* O(n)
* O(n * log n)
* O(n^2)
* O(2^n)
* O(n!)

## Available Algorithms

### Recursion

[**Invert Binary Tree - O(n)**](algorithms/recursion/invert_binary_tree.py)

[**Sudoku Solver - O(n)**](algorithms/recursion/sudoku.py)

```text
Original:
[3, 0, 6, 5, 0, 8, 4, 0, 0]
[5, 2, 0, 0, 0, 0, 0, 0, 0]
[0, 8, 7, 0, 0, 0, 0, 3, 1]
[0, 0, 3, 0, 1, 0, 0, 8, 0]
[9, 0, 0, 8, 6, 3, 0, 0, 5]
[0, 5, 0, 0, 9, 0, 6, 0, 0]
[1, 3, 0, 0, 0, 0, 2, 5, 0]
[0, 0, 0, 0, 0, 0, 0, 7, 4]
[0, 0, 5, 2, 0, 6, 3, 0, 0]

Solved:
[3, 1, 6, 5, 7, 8, 4, 9, 2]
[5, 2, 9, 1, 3, 4, 7, 6, 8]
[4, 8, 7, 6, 2, 9, 5, 3, 1]
[2, 6, 3, 4, 1, 5, 9, 8, 7]
[9, 7, 4, 8, 6, 3, 1, 2, 5]
[8, 5, 1, 7, 9, 2, 6, 4, 3]
[1, 3, 8, 9, 4, 7, 2, 5, 6]
[6, 9, 2, 3, 5, 1, 8, 7, 4]
[7, 4, 5, 2, 8, 6, 3, 1, 9]
Numbers put into the Sudoku puzzle: 769
Numbers that had to be backtracked due to a dead-end: 720
```

### Search

This graph is for both Breadth and Depth First Search ^

[**Breadth First Search - O(V + E)**](algorithms/search/breadth_first_search.py)

The purpose of this algorithm is to search all neighbors before traversing further down the graph. A real world use-case of this is GPS navigation to find the shortest route to your destination.

```text
[5, 3, 7, 2, 4, 8]
```

[**Depth First Search - O(V + E)**](algorithms/search/depth_first_search.py)

The purpose of this algorithm is to traverse an entire branch before backtracking to traverse a neighbor higher up the graph. A real world use-case of this is solving a puzzle with only one solution (eg: Sudoku solver)

```text
[5, 3, 2, 4, 8, 7]
```

### Sequences

[**Fibonnaci Sequence - O(2^n)**](algorithms/sequences/fibonnaci_sequence.py)

```text
The Fibonacci Sequence to 20 iterations:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181
```

[**Fizz Buzz - O(n)**](algorithms/sequences/fizzbuzz.py)

```text
Fizz Buzz to 15 iterations:
1
2
Fizz
4
Buzz
Fizz
7
8
Fizz
Buzz
11
Fizz
13
14
FizzBuzz
```

### Sorting

[**Bubble Sort - O(1)**](algorithms/sorting/bubble_sort.py)

```text
Original: [3, 1, 5, 9, 7, 6, 2, 8, 4]
[1, 3, 5, 9, 7, 6, 2, 8, 4] => Swapped 3 and 1
[1, 3, 5, 7, 9, 6, 2, 8, 4] => Swapped 9 and 7
[1, 3, 5, 7, 6, 9, 2, 8, 4] => Swapped 9 and 6
[1, 3, 5, 7, 6, 2, 9, 8, 4] => Swapped 9 and 2
[1, 3, 5, 7, 6, 2, 8, 9, 4] => Swapped 9 and 8
[1, 3, 5, 7, 6, 2, 8, 4, 9] => Swapped 9 and 4
[1, 3, 5, 6, 7, 2, 8, 4, 9] => Swapped 7 and 6
[1, 3, 5, 6, 2, 7, 8, 4, 9] => Swapped 7 and 2
[1, 3, 5, 6, 2, 7, 4, 8, 9] => Swapped 8 and 4
[1, 3, 5, 2, 6, 7, 4, 8, 9] => Swapped 6 and 2
[1, 3, 5, 2, 6, 4, 7, 8, 9] => Swapped 7 and 4
[1, 3, 2, 5, 6, 4, 7, 8, 9] => Swapped 5 and 2
[1, 3, 2, 5, 4, 6, 7, 8, 9] => Swapped 6 and 4
[1, 2, 3, 5, 4, 6, 7, 8, 9] => Swapped 3 and 2
[1, 2, 3, 4, 5, 6, 7, 8, 9] => Swapped 5 and 4
List sorted successfully in 0:00:00.000080 with Bubble Sort Algorithm!
```

[**Wordle Solver - O(n^2)**](algorithms/sorting/wordle_solver.py)

```text
Total number of Wordles: 12947
Most common starting letter: [('s', 365), ('c', 198), ('b', 173), ('t', 149), ('p', 141), ('a', 140), ('f', 135), ('g', 115), ('d', 111), ('m', 107), ('r', 105), ('l', 87), ('w', 82), ('e', 72), ('h', 69), ('v', 43), ('o', 41), ('n', 37), ('i', 34), ('u', 33), ('q', 23), ('k', 20), ('j', 20), ('y', 6), ('z', 3)]
Most common letters: [('e', 31980), ('a', 25350), ('r', 23322), ('o', 19578), ('t', 18954), ('l', 18616), ('i', 17420), ('s', 17368), ('n', 14898), ('c', 12350), ('u', 12116), ('y', 11024), ('d', 10218), ('h', 10062), ('p', 9490), ('m', 8216), ('g', 8060), ('b', 7280), ('f', 5954), ('k', 5460), ('w', 5044), ('v', 3952), ('z', 1040), ('x', 962), ('q', 754), ('j', 702)]
Possible words: 2251
Top 5 Best Guesses:
('steer', 117)
('stare', 116)
('store', 114)
('sleet', 114)
('steel', 114)
```

Watch a video about the creation of this solver: <https://www.youtube.com/watch?v=KiOiV8rpC7c>

## Install

```bash
just install
```

## Usage

See each script for additional descriptions, usage, features, and lessons learned.

```bash
venv/bin/python algorithms/category/script.py
```

## Development

```bash
# Get a comprehensive list of development tools
just --list
```

## Contributing

I will not be accepting pull requests to this repo for new algorithms as this project is more of a playground for my own learning and exploration of algorithms and not an exhaustive collection for reference. I will consider improvement PRs for existing algorithms however.

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