# Algorithms

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

## 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)

Sudoku Solver – O(n)

``````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
``````

### Sequences

Fibonnaci Sequence – O(2^n)

``````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)

``````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)

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!”>

``````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!
``````

## Install

`make install`

## Usage

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

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

## Development

```# Get a comprehensive list of development tools
make help```

View Github