84 lines
2.8 KiB
Python
84 lines
2.8 KiB
Python
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def build_sets(sets, numbers):
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""" Sets is a list of two tuples. Each field represents the sum of the two
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sets. For each new number, we can add the number to set one, add the
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number to set two, or don't add the number to any sets. If there are no
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more numbers we return the list so that we can check if there are tuples
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that have the same sum. """
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if not numbers:
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return sets
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current_number, numbers = numbers[0], numbers[1:]
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new_sets = []
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for t in sets:
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new_sets.append(t)
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new_sets.append((t[0] + current_number, t[1]))
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new_sets.append((t[0], t[1] + current_number))
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return build_sets(new_sets, numbers)
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def is_condition_one_met(s):
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tuples = build_sets([(0, 0)], s)
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for a, b in tuples:
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if a != 0 and b != 0 and a == b:
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return False
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return True
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def is_condition_two_met(s):
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""" The second condition says that if |B| > |C| then sum(B) > sum(C). Since
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each line is sorted we take the two smallest integers and compare it to the
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biggest. Then we take the three smallest integers and compare it to the two
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biggest, and so on. Comparing the smallest with the biggest integers is the
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worst case and if there is no violation of the condition it will be met for
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all other subset pairs. """
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half_len = (len(s) - 1) // 2
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for i in range(1, half_len + 1):
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if not sum(s[:i + 1]) > sum(s[-i:]):
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# print(f"{s[:i + 1]=} < {s[-i:]=}")
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return False
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return True
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def is_special_sum_set(s):
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""" Check for the two conditions and return True if they are both met. """
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if not is_condition_two_met(s):
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return False
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if not is_condition_one_met(s):
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return False
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return True
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def next_set_heuristic(xs):
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""" Calculate the estimated next optimum based on the formul given in the
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question. """
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b = xs[(len(xs) - 1) // 2]
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next_set = [b]
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for a in xs:
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next_set.append(a + b)
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return next_set
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def euler_103():
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e_max = 50
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min_set = None
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for a in range(1, e_max):
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for b in range(a + 1, e_max):
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for c in range(b + 1, e_max):
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for d in range(c + 1, e_max):
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for e in range(d + 1, e_max):
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for f in range(e + 1, e_max):
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for g in range(e + 1, e_max):
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s = [a, b, c, d, e, f, g,]
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if is_special_sum_set(s):
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s_sum = sum(s)
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if min_set is None or s_sum < sum(min_set):
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min_set = s
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return int("".join(map(str, min_set)))
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if __name__ == "__main__":
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solution = euler_103()
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print("e103.py: " + str(solution))
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assert(solution == 20313839404245)
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