Solve problem 105 in Python way quicker than expected

python/e105.py

@@ -0,0 +1,74 @@
+
+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)
+

txt/e105.txt

@@ -0,0 +1,100 @@
+81,88,75,42,87,84,86,65
+157,150,164,119,79,159,161,139,158
+673,465,569,603,629,592,584,300,601,599,600
+90,85,83,84,65,87,76,46
+165,168,169,190,162,85,176,167,127
+224,275,278,249,277,279,289,295,139
+354,370,362,384,359,324,360,180,350,270
+599,595,557,298,448,596,577,667,597,588,602
+175,199,137,88,187,173,168,171,174
+93,187,196,144,185,178,186,202,182
+157,155,81,158,119,176,152,167,159
+184,165,159,166,163,167,174,124,83
+1211,1212,1287,605,1208,1189,1060,1216,1243,1200,908,1210
+339,299,153,305,282,304,313,306,302,228
+94,104,63,112,80,84,93,96
+41,88,82,85,61,74,83,81
+90,67,84,83,82,97,86,41
+299,303,151,301,291,302,307,377,333,280
+55,40,48,44,25,42,41
+1038,1188,1255,1184,594,890,1173,1151,1186,1203,1187,1195
+76,132,133,144,135,99,128,154
+77,46,108,81,85,84,93,83
+624,596,391,605,529,610,607,568,604,603,453
+83,167,166,189,163,174,160,165,133
+308,281,389,292,346,303,302,304,300,173
+593,1151,1187,1184,890,1040,1173,1186,1195,1255,1188,1203
+68,46,64,33,60,58,65
+65,43,88,87,86,99,93,90
+83,78,107,48,84,87,96,85
+1188,1173,1256,1038,1187,1151,890,1186,1184,1203,594,1195
+302,324,280,296,294,160,367,298,264,299
+521,760,682,687,646,664,342,698,692,686,672
+56,95,86,97,96,89,108,120
+344,356,262,343,340,382,337,175,361,330
+47,44,42,27,41,40,37
+139,155,161,158,118,166,154,156,78
+118,157,164,158,161,79,139,150,159
+299,292,371,150,300,301,281,303,306,262
+85,77,86,84,44,88,91,67
+88,85,84,44,65,91,76,86
+138,141,127,96,136,154,135,76
+292,308,302,346,300,324,304,305,238,166
+354,342,341,257,348,343,345,321,170,301
+84,178,168,167,131,170,193,166,162
+686,701,706,673,694,687,652,343,683,606,518
+295,293,301,367,296,279,297,263,323,159
+1038,1184,593,890,1188,1173,1187,1186,1195,1150,1203,1255
+343,364,388,402,191,383,382,385,288,374
+1187,1036,1183,591,1184,1175,888,1197,1182,1219,1115,1167
+151,291,307,303,345,238,299,323,301,302
+140,151,143,138,99,69,131,137
+29,44,42,59,41,36,40
+348,329,343,344,338,315,169,359,375,271
+48,39,34,37,50,40,41
+593,445,595,558,662,602,591,297,610,580,594
+686,651,681,342,541,687,691,707,604,675,699
+180,99,189,166,194,188,144,187,199
+321,349,335,343,377,176,265,356,344,332
+1151,1255,1195,1173,1184,1186,1188,1187,1203,593,1038,891
+90,88,100,83,62,113,80,89
+308,303,238,300,151,304,324,293,346,302
+59,38,50,41,42,35,40
+352,366,174,355,344,265,343,310,338,331
+91,89,93,90,117,85,60,106
+146,186,166,175,202,92,184,183,189
+82,67,96,44,80,79,88,76
+54,50,58,66,31,61,64
+343,266,344,172,308,336,364,350,359,333
+88,49,87,82,90,98,86,115
+20,47,49,51,54,48,40
+159,79,177,158,157,152,155,167,118
+1219,1183,1182,1115,1035,1186,591,1197,1167,887,1184,1175
+611,518,693,343,704,667,686,682,677,687,725
+607,599,634,305,677,604,603,580,452,605,591
+682,686,635,675,692,730,687,342,517,658,695
+662,296,573,598,592,584,553,593,595,443,591
+180,185,186,199,187,210,93,177,149
+197,136,179,185,156,182,180,178,99
+271,298,218,279,285,282,280,238,140
+1187,1151,890,593,1194,1188,1184,1173,1038,1186,1255,1203
+169,161,177,192,130,165,84,167,168
+50,42,43,41,66,39,36
+590,669,604,579,448,599,560,299,601,597,598
+174,191,206,179,184,142,177,180,90
+298,299,297,306,164,285,374,269,329,295
+181,172,162,138,170,195,86,169,168
+1184,1197,591,1182,1186,889,1167,1219,1183,1033,1115,1175
+644,695,691,679,667,687,340,681,770,686,517
+606,524,592,576,628,593,591,584,296,444,595
+94,127,154,138,135,74,136,141
+179,168,172,178,177,89,198,186,137
+302,299,291,300,298,149,260,305,280,370
+678,517,670,686,682,768,687,648,342,692,702
+302,290,304,376,333,303,306,298,279,153
+95,102,109,54,96,75,85,97
+150,154,146,78,152,151,162,173,119
+150,143,157,152,184,112,154,151,132
+36,41,54,40,25,44,42
+37,48,34,59,39,41,40
+681,603,638,611,584,303,454,607,606,605,596