""" Project Euler Problem 104 : https://projecteuler.net/problem=104 The Fibonacci sequence is defined by the recurrence relation: Fn = Fn-1 + Fn-2, where F1 = 1 and F2 = 1. It turns out that F541, which contains 113 digits, is the first Fibonacci number for which the last nine digits are 1-9 pandigital (contain all the digits 1 to 9, but not necessarily in order). And F2749, which contains 575 digits, is the first Fibonacci number for which the first nine digits are 1-9 pandigital. Given that Fk is the first Fibonacci number for which the first nine digits AND the last nine digits are 1-9 pandigital, find k. """ import sys sys.set_int_max_str_digits(0) def check(number: int) -> bool: """ Takes a number and checks if it is pandigital both from start and end >>> check(123456789987654321) True >>> check(120000987654321) False >>> check(1234567895765677987654321) True """ check_last = [0] * 11 check_front = [0] * 11 # mark last 9 numbers for _ in range(9): check_last[int(number % 10)] = 1 number = number // 10 # flag f = True # check last 9 numbers for pandigitality for x in range(9): if not check_last[x + 1]: f = False if not f: return f # mark first 9 numbers number = int(str(number)[:9]) for _ in range(9): check_front[int(number % 10)] = 1 number = number // 10 # check first 9 numbers for pandigitality for x in range(9): if not check_front[x + 1]: f = False return f def check1(number: int) -> bool: """ Takes a number and checks if it is pandigital from END >>> check1(123456789987654321) True >>> check1(120000987654321) True >>> check1(12345678957656779870004321) False """ check_last = [0] * 11 # mark last 9 numbers for _ in range(9): check_last[int(number % 10)] = 1 number = number // 10 # flag f = True # check last 9 numbers for pandigitality for x in range(9): if not check_last[x + 1]: f = False return f def solution() -> int: """ Outputs the answer is the least Fibonacci number pandigital from both sides. >>> solution() 329468 """ a = 1 b = 1 c = 2 # temporary Fibonacci numbers a1 = 1 b1 = 1 c1 = 2 # temporary Fibonacci numbers mod 1e9 # mod m=1e9, done for fast optimisation tocheck = [0] * 1000000 m = 1000000000 for x in range(1000000): c1 = (a1 + b1) % m a1 = b1 % m b1 = c1 % m if check1(b1): tocheck[x + 3] = 1 for x in range(1000000): c = a + b a = b b = c # perform check only if in tocheck if tocheck[x + 3] and check(b): return x + 3 # first 2 already done return -1 if __name__ == "__main__": print(f"{solution() = }")