Solve problem 110.
parent
dd89390a04
commit
303eae42c9
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@ -1,4 +1,6 @@
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from fractions import Fraction
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from lib_misc import proper_divisors
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from math import ceil
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def get_distinct_solutions(n):
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@ -16,11 +18,16 @@ def get_distinct_solutions(n):
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return n_distinct
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def get_distinct_solutions2(n):
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ds = proper_divisors(n * n)
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return ceil((len(ds) + 1) / 2)
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def euler_108():
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d_max, n_prev = 0, 0
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# I arrived at the starting values empirically by observing the deltas.
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for n in range(1260, 1000000, 420):
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d = get_distinct_solutions(n)
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d = get_distinct_solutions2(n)
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if d > d_max:
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# print("n={} d={} delta={}".format(n, d, n - n_prev))
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n_prev = n
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@ -0,0 +1,75 @@
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from lib_misc import get_item_counts
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from lib_prime import primes
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def divisors(counts):
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r = 1
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for c in counts:
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r *= (c + 1)
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return r
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def tau(factors):
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orig_factors = factors
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factors = factors + factors
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counts = get_item_counts(factors)
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r = divisors(counts.values())
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p = 1
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for f in orig_factors:
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p *= f
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return r, p
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def counters(digits, max_digit):
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def incrementing_counters(curr, left, max_digit, result):
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if left == 0:
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result.append(curr)
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return
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start = 1 if not curr else curr[-1]
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for i in range(start, max_digit + 1):
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incrementing_counters(curr + [i], left - 1, max_digit, result)
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result = []
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incrementing_counters([], digits, max_digit, result)
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return result
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def euler_110():
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target = 1000
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target = 4 * 10**6
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threshold = (target * 2) - 1
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psupper = primes(1000)
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lowest_distinct = 0
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lowest_number = 0
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# find upper bound
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for i in range(len(psupper)):
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distinct, number = tau(psupper[:i])
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if distinct > threshold:
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# print(lowest_distinct, number)
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lowest_distinct = distinct
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lowest_number = number
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psupper = psupper[:i]
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for j in range(1, len(psupper)):
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ps = psupper[:-j]
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for prime_counts in counters(len(ps), 5):
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prime_counts.reverse()
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nps = []
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i = 0
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for i in range(len(prime_counts)):
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nps += [ps[i]] * prime_counts[i]
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nps += ps[i + 1:]
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distinct, number = tau(nps)
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if distinct > threshold and distinct < lowest_distinct:
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lowest_distinct = distinct
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lowest_number = number
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# print(lowest_distinct, lowest_number)
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return lowest_number
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if __name__ == "__main__":
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solution = euler_110()
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print("e110.py: " + str(solution))
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assert(solution == 9350130049860600)
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