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extended_euclidean_gcd.py: Add Extended Euclidean GCD Algorithm
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This adds Extended Euclidean Algorithm with Python implementation of the same.
This implementation uses iterative method of the algorithm, takes two
values and gives out the gcd along with the polynomial equation to get
inverse directly if the gcd is 1. Code uses generic notations and
naming standard used in documentation along with that found in Wikipedia.

Closes NITSkmOS#3 NITSkmOS#159
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@thekaleidoscope
thekaleidoscope committed Oct 2, 2018
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55 changes: 27 additions & 28 deletions README.md
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# Welcome to the NITSkmOS/Algorithms

[![Gitter](https://badges.gitter.im/NITSkmOS/algo.svg)](https://gitter.im/NITSkmOS/algo?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge)
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This repository contains examples of various algorithms written on different programming languages...

## Implemented Algorithms

| Algorithm | C | CPP | Java | Python |
|:----------------------------------------------------------------------------------------------- |:-------------------------------------:|:-------------------------------------:|:-------------------------------------:|:-------------------------------------:|
| [Euclidean GCD](https://en.wikipedia.org/wiki/Euclidean_algorithm) | [:octocat:](euclidean_gcd/C) | | | [:octocat:](euclidean_gcd/Python) |
| [QuickSort](https://en.wikipedia.org/wiki/Quicksort) | | | | [:octocat:](quicksort/Python) |
| [Merge Sort](https://en.wikipedia.org/wiki/Merge_sort) | | | | [:octocat:](merge_sort/Python) |
| [Insertion Sort](https://en.wikipedia.org/wiki/Insertion_sort) | [:octocat:](insertion_sort/C) | [:octocat:](insertion_sort/Cpp) | | [:octocat:](insertion_sort/Python) |
| [Counting Sort](https://en.wikipedia.org/wiki/Counting_sort) | | | | [:octocat:](counting_sort/Python) |
| [Radix Sort](https://en.wikipedia.org/wiki/Radix_sort) | | | | [:octocat:](radix_sort/Python) |
| [Binary Search](https://en.wikipedia.org/wiki/Binary_search_algorithm) | | [:octocat:](binary_search/Cpp) | | [:octocat:](binary_search/Python) |
| [Bubble Sort](https://en.wikipedia.org/wiki/Bubble_sort) | [:octocat:](bubble_sort/C) | [:octocat:](bubble_sort/Cpp) | | |
| [Shell Sort](https://en.wikipedia.org/wiki/Shellsort) | | | | [:octocat:](shell_sort/Python) |

| Algorithm | C | CPP | Java | Python |
| :------------------------------------------------------------------------------------ | :---------------------------: | :-----------------------------: | :--: | :----------------------------------------: |
| [Euclidean GCD](https://en.wikipedia.org/wiki/Euclidean_algorithm) | [:octocat:](euclidean_gcd/C) | | | [:octocat:](euclidean_gcd/Python) |
| [Extended Euclidean GCD](https://en.wikipedia.org/wiki/Extended_Euclidean_algorithmm) | | | | [:octocat:](extended_euclidean_gcd/Python) |
| [QuickSort](https://en.wikipedia.org/wiki/Quicksort) | | | | [:octocat:](quicksort/Python) |
| [Merge Sort](https://en.wikipedia.org/wiki/Merge_sort) | | | | [:octocat:](merge_sort/Python) |
| [Insertion Sort](https://en.wikipedia.org/wiki/Insertion_sort) | [:octocat:](insertion_sort/C) | [:octocat:](insertion_sort/Cpp) | | [:octocat:](insertion_sort/Python) |
| [Counting Sort](https://en.wikipedia.org/wiki/Counting_sort) | | | | [:octocat:](counting_sort/Python) |
| [Radix Sort](https://en.wikipedia.org/wiki/Radix_sort) | | | | [:octocat:](radix_sort/Python) |
| [Binary Search](https://en.wikipedia.org/wiki/Binary_search_algorithm) | | [:octocat:](binary_search/Cpp) | | [:octocat:](binary_search/Python) |
| [Bubble Sort](https://en.wikipedia.org/wiki/Bubble_sort) | [:octocat:](bubble_sort/C) | [:octocat:](bubble_sort/Cpp) | | |
| [Shell Sort](https://en.wikipedia.org/wiki/Shellsort) | | | | [:octocat:](shell_sort/Python) |

## Implemented Data Structures

| Data Structure | C | CPP | Java | Python |
|:----------------------------------------------------------------------------------------------- |:-------------------------------------:|:-------------------------------------:|:-------------------------------------:|:-------------------------------------:|
| [Queue](https://en.wikipedia.org/wiki/Queue_(abstract_data_type)) | | [:octocat:](queue/Cpp) | | |
| [Stack](https://en.wikipedia.org/wiki/Stack_(abstract_data_type)) | | | [:octocat:](stack/Java) | [:octocat:](stack/Python) |
| [Linear Linked List](https://en.wikipedia.org/wiki/Linked_list) | [:octocat:](linked_list/C) | | | |
| [AVL Tree](https://en.wikipedia.org/wiki/AVL_tree) | [:octocat:](avl_tree/C) | | [:octocat:](avl_tree/Java) | |

| Data Structure | C | CPP | Java | Python |
| :------------------------------------------------------------------ | :------------------------: | :--------------------: | :------------------------: | :-----------------------: |
| [Queue](<https://en.wikipedia.org/wiki/Queue_(abstract_data_type)>) | | [:octocat:](queue/Cpp) | | |
| [Stack](<https://en.wikipedia.org/wiki/Stack_(abstract_data_type)>) | | | [:octocat:](stack/Java) | [:octocat:](stack/Python) |
| [Linear Linked List](https://en.wikipedia.org/wiki/Linked_list) | [:octocat:](linked_list/C) | | | |
| [AVL Tree](https://en.wikipedia.org/wiki/AVL_tree) | [:octocat:](avl_tree/C) | | [:octocat:](avl_tree/Java) | |

## Sample Run

| Language | Steps |
| --------------- | ---------------------------------------------------------------------- |
| JavaScript | <pre>node [filename.js]</pre> |
| Python | <pre>python [filename.py]</pre> |
| C | <pre>gcc [filename.c]<br>./a.out # unix<br>a.exe # windows</pre> |
| CPP | <pre>g++ [filename.cpp]<br>./a.out # unix<br>a.exe # windows</pre> |
| Java | <pre>javac [filename.java]<br>java [filename]</pre> |

| Language | Steps |
| ---------- | ------------------------------------------------------------------ |
| JavaScript | <pre>node [filename.js]</pre> |
| Python | <pre>python [filename.py]</pre> |
| C | <pre>gcc [filename.c]<br>./a.out # unix<br>a.exe # windows</pre> |
| CPP | <pre>g++ [filename.cpp]<br>./a.out # unix<br>a.exe # windows</pre> |
| Java | <pre>javac [filename.java]<br>java [filename]</pre> |

## Contributing

Expand All @@ -51,6 +49,7 @@ This repository contains examples of various algorithms written on different pro
4. Commit your changes: `git commit -am 'Add some feature'`.

Go through [Commit Messages guidelines](CONTRIBUTING.md#write-good-commit-messages)

5. Push to the branch: `git push origin my-new-feature`
6. Submit a pull request :smile:

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29 changes: 29 additions & 0 deletions extended_euclidean_gcd/Python/extended_euclidean_gcd.py
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# Element style: gcd(a,b)-> a*x + b*y = r = gcd(a,b)

# Inverse of elements if gcd(a,b)==1:
# * a^-1 mod (b) = x mod(b)
# * b^-1 mod (a) = y mod(a)

# Naming is according to Bézout's identity matching to that on Wikipedia


def extended_euclidean_gcd(a, b):
x, y, u, v = 0, 1, 1, 0
while a != 0:
q, r = b//a, b % a
m, n = x-u*q, y-v*q
b, a, x, y, u, v = a, r, u, v, m, n

gcd = b
return gcd, x, y


def main():
a, b = 26, 15
gcd, x, y = extended_euclidean_gcd(a, b)
print("GCD of {} and {} is {}".format(a, b, gcd))
print("The Equation : {}*{} + {}*{} = {}".format(a, x, b, y, gcd))


if __name__ == '__main__':
main()

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