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Problem21.py

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+#ProjectEuler/Python/Problem21.py
+#Matthew Ellison
+# Created: 03-18-19
+#Modified: 03-28-19
+#Evaluate the sum of all the amicable numbers under 10000
+#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
+"""
+	Copyright (C) 2019  Matthew Ellison
+
+	This program is free software: you can redistribute it and/or modify
+	it under the terms of the GNU Lesser General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	This program is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU Lesser General Public License for more details.
+
+	You should have received a copy of the GNU Lesser General Public License
+	along with this program.  If not, see <https://www.gnu.org/licenses/>.
+"""
+
+
+from Stopwatch import Stopwatch
+import Algorithms
+
+__limit = 10000	#The top number that will be evaluated
+
+
+def Problem21():
+	#Setup the variables
+	divisorSum = []	#Holds the sum of the divisors of the subscript number
+	divisorSum.append(0)	#Start with a 0 in the [0] location
+
+	#Generate the divisors of all the numbers < 10000, get their sum, and add it to the list
+	for cnt in range(1, __limit):
+		divisors = Algorithms.getDivisors(cnt)	#Get all the divisors of a number
+		if(len(divisors) > 1):
+			divisors.pop()	#Remove the last entry because it will be the number itself
+		divisorSum.append(int(sum(divisors)))
+	#Check every sum of divisors in the list for a matching sum
+	amicable = []
+	for cnt in range(1, len(divisorSum)):
+		currentSum = divisorSum[cnt]
+		#If the sum is greater than the number of divisors then it is impossible to be amicable. Skip the number and continue
+		if(currentSum >= len(divisorSum)):
+			continue
+		#We know that divisorSum[cnt] == currentSum, so if divisorSum[currentSum] == cnt we found an amicable number
+		if(divisorSum[currentSum] == cnt):
+			#A number can't be amicable with itself
+			if(currentSum == cnt):
+				continue
+			#Add the number to the amicable vector
+			amicable.append(cnt)
+
+	#Print the results
+	print("All amicable numbers less than 10000 are")
+	for num in amicable:
+		print(str(num))
+	print("The sum of all of these amicable numbers is " + str(sum(amicable)))
+
+#Run the correct function if this script is called stand along
+if __name__ == "__main__":
+	timer = Stopwatch()
+	timer.start()
+	Problem21()
+	timer.stop()
+	print("It took " + timer.getString() + " to run this algorithm")
+
+""" Results:
+All amicable numbers less than 10000 are
+220
+284
+1184
+1210
+2620
+2924
+5020
+5564
+6232
+6368
+The sum of all of these amicable numbers is 31626
+It took 59.496 milliseconds to run this algorithm
+"""