Solve problem 105 in Python way quicker than expected

python/e105.py

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+
+def build_sets(sets, numbers):
+    """ Sets is a list of two tuples. Each field represents the sum of the two
+    sets. For each new number, we can add the number to set one, add the
+    number to set two, or don't add the number to any sets. If there are no
+    more numbers we return the list so that we can check if there are tuples
+    that have the same sum. """
+    if not numbers:
+        return sets
+    current_number, numbers = numbers[0], numbers[1:]
+    new_sets = []
+    for t in sets:
+        new_sets.append(t)
+        new_sets.append((t[0] + current_number, t[1]))
+        new_sets.append((t[0], t[1] + current_number))
+    return build_sets(new_sets, numbers)
+
+
+def is_condition_one_met(s):
+    tuples = build_sets([(0, 0)], s)
+    for a, b in tuples:
+        if a != 0 and b != 0 and a == b:
+            return False
+    return True
+
+
+def is_condition_two_met(s):
+    """ The second condition says that if |B| > |C| then sum(B) > sum(C). Since
+    each line is sorted we take the two smallest integers and compare it to the
+    biggest. Then we take the three smallest integers and compare it to the two
+    biggest, and so on. Comparing the smallest with the biggest integers is the
+    worst case and if there is violation of the condition it will be met for
+    all other subset pairs. """
+    half_len = (len(s) - 1) // 2
+    for i in range(1, half_len + 1):
+        if not sum(s[:i + 1]) > sum(s[-i:]):
+            # print(f"{s[:i + 1]=} < {s[-i:]=}")
+            return False
+    return True
+
+
+def is_special_sum_set(s):
+    """ Check for the two conditions and return True if they are both met. """
+    if not is_condition_two_met(s):
+        return False
+    if not is_condition_one_met(s):
+        return False
+    return True
+
+
+def load_sets():
+    """ Parse sets from file into a list of lists. Each line contains a list of
+    comma separated integers. We sort the integers in each line. """
+    def line_to_set(line):
+        return sorted(map(int, line.strip().split(",")))
+
+    with open("../txt/e105.txt") as f:
+        return list(map(line_to_set, f))
+
+
+def euler_105():
+    xs = load_sets()
+    s = 0
+    for i, x in enumerate(xs):
+        if is_special_sum_set(x):
+            s += sum(x)
+    return s
+
+
+if __name__ == "__main__":
+    solution = euler_105()
+    print("e105.py: " + str(solution))
+    assert(solution == 73702)
+