#ProjectEuler/Python/Problem25.py
#Matthew Ellison
# Created: 03-25-19
#Modified: 03-28-19
#What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
#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


__numDigits = 1000	#The number of digits to calculate up to


def Problem25():
	#Setup the variables
	number = 0	#The current Fibonacci number
	index = 2	#The index of the just calculated Fibonacci number

	#Move through all Fibonacci numbers until you reach the one with at least __numDigits digits
	while(len(str(number)) < __numDigits):
		index += 1	#Increase the index number. Doing this at the beginning keeps the index correct at the end of the loop
		number = Algorithms.getFib(index)	#Calculate the number

	#Print the results
	print("The first Fibonacci number with " + str(__numDigits) + " digits is " + str(number))
	print("Its index is " + str(index))


#This runs the appropriate functions if the script is called by itself
if __name__ == "__main__":
	timer = Stopwatch()
	timer.start()
	Problem25()
	timer.stop()
	print("It took " + timer.getString() + " to run this algorithm")

""" Results:
The first Fibonacci number with 1000 digits is 1070066266382758936764980584457396885083683896632151665013235203375314520604694040621889147582489792657804694888177591957484336466672569959512996030461262748092482186144069433051234774442750273781753087579391666192149259186759553966422837148943113074699503439547001985432609723067290192870526447243726117715821825548491120525013201478612965931381792235559657452039506137551467837543229119602129934048260706175397706847068202895486902666185435124521900369480641357447470911707619766945691070098024393439617474103736912503231365532164773697023167755051595173518460579954919410967778373229665796581646513903488154256310184224190259846088000110186255550245493937113651657039447629584714548523425950428582425306083544435428212611008992863795048006894330309773217834864543113205765659868456288616808718693835297350643986297640660000723562917905207051164077614812491885830945940566688339109350944456576357666151619317753792891661581327159616877487983821820492520348473874384736771934512787029218636250627816
Its index is 4782
It took 4.216 seconds to run this algorithm
"""