"""
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
"""
from itertools import takewhile
from common import elapsed
from seq import fib
limit = 4000000
total = sum(
takewhile(lambda x: x <= limit, filter(lambda x: x % 2 == 0, fib())))
print("Sum of even fibonnaci numbers up to {}: {}".format(limit, total))
elapsed()
def solve_by_pairing(target_size=target_set_size):
# This algorithm will populate prime_pairs with each prime (key) pointing to a set of all
# smaller primes that form a valid prime pair with it.
# Each of these is then checked by get_connected_set to see if there are enough pairwise
# connections to complete the problem.
# NOTE: prime index starts from 3 to avoid primes 2 and 5, which cannot be part of any prime pair.
# 3 is chained into the inner loop, but not the outer loop because no valid primes are less than 3.
log_step = 1000
next_step = 0
for p in primes(step=10000, start_index=3):
for q in chain(reversed(sieve_primes(max_prime=p)[3:-1]), [3]):
populate_prime_pairs(p, q)
if p > next_step:
split_timer()
print(f"Reached p > {next_step} -- {p}: {prime_pairs.get(p)}")
next_step += log_step
if p in prime_pairs:
p_set = get_connected_set(prime_pairs[p], target_size - 1)
if p_set:
p_set.add(p)
return sorted(p_set)[:target_size]
print(solve_by_pairing(5))
elapsed() # Around 20 minutes!
