Automatic commit performed through alias...

problems/005_problem/005_problem.py

@@ -0,0 +1,150 @@
+#!/usr/bin/env python
+
+#  Problem 5:
+#
+#  2520 is the smallest number that can 
+#  be divided by each of the numbers 
+#  from 1 to 10 without any remainder.
+# 
+#  What is the smallest positive number 
+#  that is evenly divisible by all of the 
+#  numbers from 1 to 20?
+#
+
+
+#	Standard Imports:
+#	-------------------
+
+import time  # Typically imported for sleep function, to slow down execution in terminal.
+import typing
+import sys
+import pprint
+
+#	Imports from Virtual Environment for this Project:
+#	---------------------------------------------------
+
+sys.path.append('/home/shaun/code/github/euler_project/py_euler_project/venv')
+import numpy
+
+#	Imports from Modules Built for this Project:
+#	-----------------------------------------------
+
+sys.path.append('/home/shaun/code/github/euler_project/py_euler_project/problems')
+import decorators
+
+
+# Create function that finds the next
+# prime number when supplied with an
+# intitial integer.
+
+def primes_gen(start_n: int,max_n: int):
+	"""
+	Returns a generator object, containing the 
+	primes inside a specified range.
+		primes_gen(start_n,max_n)
+			param 'start_n': Previous prime.
+			param 'max_n': Maximum 
+	"""
+	start_n += 1
+	for candidate in range(start_n,max_n):
+		notPrime = False
+		
+		if candidate in [0,1,2,3]:
+			yield candidate
+		for dividend in range(2,candidate):
+			
+			if candidate%dividend == 0:
+				notPrime = True
+		
+		if not notPrime:
+			yield candidate
+
+
+def find_prime_factors(n: int):
+	"""
+	Return a list object containing all 
+	prime factors of the provided integer, n.
+
+		find_prime_factors(n)
+
+			param 'n': The integer to be analyzed.
+
+	"""
+
+	returned_prime = list(primes_gen(0,n))
+	pprint.pprint(returned_prime)
+
+	return returned_prime
+
+	
+def evenly_divisible(candidate: int,factors: list):
+	"""
+	Determines if the supplied integer candidate is 
+	evenly divisble by the supplied list of factors.
+	
+		evenly_divisible(candidate: int, factors: list)
+
+			param 'candidate': Integer to be tested.
+			param 'factors': List of factors for the modulus operator.
+			
+	"""
+	
+	modulus_sum = 0
+
+	for n in factors:
+		modulus_sum += candidate%n
+	
+	if modulus_sum == 0: 
+		return True
+	else:
+		return False
+
+
+@decorators.function_timer
+def main():
+	# Receive problem inputs...
+	smallest_factor = 1
+	largest_factor = 5
+
+	# Compute intermediate inputs
+	factor_list = [int(i) for i in range(smallest_factor,largest_factor+1)]
+	maximum_solution_bound = 1
+	for f in factor_list:
+		maximum_solution_bound *= f
+	common = []
+	product = 1
+#
+# 	Brute force method below breaks down
+#	and doesn't scale well ...
+# 	
+#	# Initialize loop parameters
+#	n = 1
+#	test_passed = False
+#
+#	while n<maximum_solution_bound and not test_passed:
+#		test_passed = evenly_divisible(n,factor_list)
+#		if not test_passed:
+#			n += 1
+
+#	Mathematically, the trick is to recognize
+# 	that this a LCM (Least Common Multiple)
+#	problem. The solution is list all
+# 	the prime factors of each number in
+#	the factor list, then compute their
+# 	collective product.
+
+	pprint.pprint(common)
+
+	for j in common:
+		for k in j:
+			product *= k
+
+	print(product)
+
+	print(numpy.array(common))
+
+
+#	print("The largest palindrome number which is a product of two numbers of length {} is {} ... ".format("foo_list","foo"))
+
+main()
+