Data Structures and Algorithms in Python | 3. Euclid's algorithm for gcd by Abraham | Learn Smarter
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3. Euclid's algorithm for gcd

The chapter explores Euclid's algorithm for finding the greatest common divisor (gcd) of two numbers, emphasizing its historical significance and algorithmic efficiency. It begins with basic definitions and progressively simplifies the calculation method, ultimately converging on the remainder approach for optimal performance. Various programming aspects, particularly in Python, are also discussed to illustrate the implementation of these concepts.

Sections

  • 3.1

    Programming, Data Structures And Algorithms In Python

    The section introduces Euclid's algorithm for computing the greatest common divisor (gcd) and explores its implementation in Python.

    Learning Practice

  • 3.1.1.

    Prof. Madhavan Mukund

    This section introduces Euclid's Algorithm for computing the greatest common divisor (gcd), explaining its significance and efficiency in modern algorithms.

    Learning Practice

  • 3.1.2

    Department Of Computer Science And Engineering

    This section introduces Euclid's algorithm for computing the greatest common divisor (gcd) of two numbers, exploring both recursive and iterative implementations in Python.

    Learning Practice

  • 3.1.3

    Chennai Mathematical Institute, Madras

    This section discusses Euclid's Algorithm for finding the greatest common divisor (gcd) and its implementations in Python.

    Learning Practice

  • 3.1.4

    Week - 01

    This section covers Euclid's algorithm for computing the greatest common divisor (gcd) and its efficient implementation in Python.

    Learning Practice

  • 3.1.5

    Lecture - 03

    This section discusses Euclid's Algorithm for finding the greatest common divisor (gcd) between two numbers using both recursive and iterative implementations.

    Learning Practice

  • 3.1.6

    Euclid's Algorithm For Gcd

    This section explores Euclid's Algorithm for calculating the greatest common divisor (gcd) using a method based on remainders, illustrating efficiency improvements over naive approaches.

    Learning Practice

  • 3.2

    Basic Definition Of Gcd

    This section introduces the concept of the greatest common divisor (GCD) through various methods, including the naive method of finding factors and the optimized approach derived from Euclid's algorithm.

    Learning Practice

  • 3.3

    Simplification Observations

    This section focuses on the simplifications relating to calculating the greatest common divisor (gcd) using various methodologies, particularly Euclid’s algorithm.

    Learning Practice

  • 3.4

    First Version Of Euclid's Algorithm

    This section outlines the fundamentals of Euclid's algorithm for finding the greatest common divisor (gcd), detailing its evolution from a factor-based approach to a more efficient method using remainders.

    Learning Practice

  • 3.4.1

    Assuming M > N

    This section introduces Euclid's algorithm for finding the greatest common divisor (gcd) of two numbers, focusing on the method of subtraction and remainders.

    Learning Practice

  • 3.4.2

    Python Implementation

    This section discusses Euclid's algorithm for computing the greatest common divisor (gcd) using a Python implementation.

    Learning Practice

  • 3.4.2.1

    Comments In Python

    This section explores the concept of comments in Python programming, explaining their role in providing explanations within the code.

    Learning Practice

  • 3.4.2.2

    Simultaneous Assignment In Python

    This section explores the concept of simultaneous assignment in Python and its application to Euclid's algorithm for calculating the greatest common divisor (gcd).

    Learning Practice

  • 3.4.2.3

    Using Recursion

    This section explores the application of recursion in computing the greatest common divisor (gcd) using Euclid's algorithm.

    Learning Practice

  • 3.5

    While Loop Version Of Euclid's Algorithm

    This section discusses the implementation of Euclid's algorithm for finding the greatest common divisor (gcd) using a while loop, highlighting both its computational efficiency and its evolution from recursive to iterative approaches.

    Learning Practice

  • 3.5.1

    Comparison To Recursive Version

    This section explores the evolution of Euclid's algorithm for computing the greatest common divisor (gcd), from a straightforward method to a more efficient recursive implementation.

    Learning Practice

  • 3.6

    Improved Algorithm Using Remainder

    This section discusses Euclid's algorithm for finding the greatest common divisor (gcd) using remainders, focusing on its efficiency compared to previous methods.

    Learning Practice

  • 3.6.1

    Reminder Of Euclid's Algorithm

    This section discusses the implementation and simplifications of Euclid's Algorithm for finding the greatest common divisor (gcd) using both recursive and iterative methods.

    Learning Practice

  • 3.6.2

    Comparison Of Efficiency

    This section explores the efficiency of various algorithms for computing the greatest common divisor (gcd), including Euclid's Algorithm.

    Learning Practice

  • 3.7

    Conclusion About Programming, Data Structures, And Algorithms

    The section concludes by emphasizing the interconnectedness of programming, data structures, and algorithms in effectively addressing computational problems.

    Learning Practice

References

CHapter 3.pdf

Class Notes

Memorization

What we have learnt

  • Euclid's algorithm simplifi...
  • Python features such as sim...
  • The efficiency of the remai...

Final Test

Revision Tests