Python Math: Implement Euclidean Algorithm to compute the greatest common divisor
Python Math: Exercise-76 with Solution
Write a Python program to implement the Euclidean Algorithm to compute the greatest common divisor (GCD).
Note: In mathematics, the Euclidean algorithm[a], or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two numbers, the largest number that divides both of them without leaving a remainder.
The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (252 = 21 × 12 and 105 = 21 × 5), and the same number 21 is also the GCD of 105 and 147 = 252 − 105.
from math import * def euclid_algo(x, y, verbose=True): if x < y: # We want x >= y return euclid_algo(y, x, verbose) print() while y != 0: if verbose: print('%s = %s * %s + %s' % (x, floor(x/y), y, x % y)) (x, y) = (y, x % y) if verbose: print('gcd is %s' % x) return x euclid_algo(150, 304) euclid_algo(1000, 10) euclid_algo(150, 9)
304 = 2 * 150 + 4 150 = 37 * 4 + 2 4 = 2 * 2 + 0 gcd is 2 1000 = 100 * 10 + 0 gcd is 10 150 = 16 * 9 + 6 9 = 1 * 6 + 3 6 = 2 * 3 + 0 gcd is 3
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Python: Tips of the Day
Combining Lists Using Zip:
- Takes multiple collections and returns a new collection.
- The new collection contains items where each item contains one element from each input collection.
- It allows us to transverse multiple collections at the same time.
name = 'abcdef' suffix = [1,2,3,4,5,6] zip(name, suffix) --> returns (a,1),(b,2),(c,3),(d,4),(e,5),(f,6)
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