#ProjectEuler/Python/Problem29.py
#Matthew Ellison
# Created: 10-10-19
#Modified: 10-10-19
#How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100?
#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


#Setup the variables
__BOTTOM_A = 2	#The lowest possible value for A
__TOP_A = 100	#The highest possible value for A
__BOTTOM_B = 2	#The lowest possible value for B
__TOP_B = 100	#The highest possible value for B


def Problem29():
	unique = []	#This will hold all of the unique answers

	#Start with the first A and move towards the top
	for currentA in range(__BOTTOM_A, __TOP_A + 1):
		#Start with the first B and move towards the top
		for currentB in range(__BOTTOM_B, __TOP_B + 1):
			#Get the new number
			currentNum = currentA ** currentB
			#If the new number isn't in the list add it
			if currentNum not in unique:
				unique.append(currentNum)

	#Print the results
	print("The number of unique values generated by a^b for " + str(__BOTTOM_A) + " <= a < = " + str(__TOP_A) + " and " + str(__BOTTOM_B) + " <= b <= " + str(__TOP_B) + " is " + str(len(unique)))

#This calls the appropriate functions if the script is called stand alone
if __name__ == "__main__":
	timer = Stopwatch()
	timer.start()
	Problem29()
	timer.stop()
	print("It took " + timer.getString() + " to run this algorithm")

""" Results:
The number of unique values generated by a^b for 2 <= a < = 100 and 2 <= b <= 100 is 9183
It took 304.630 milliseconds to run this algorithm
"""