diff --git a/python/e105.py b/python/e105.py new file mode 100644 index 0000000..1bac4fe --- /dev/null +++ b/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) + diff --git a/txt/e105.txt b/txt/e105.txt new file mode 100644 index 0000000..2a9035a --- /dev/null +++ b/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