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#
# Solution to Project Euler problem 105
# Copyright (c) Project Nayuki. All rights reserved.
#
# https://www.nayuki.io/page/project-euler-solutions
# https://github.com/nayuki/Project-Euler-solutions
#
def compute():
ans = sum(sum(s) for s in SETS if is_special_sum_set(s))
return str(ans)
def is_special_sum_set(s):
sumsseen = set()
minsum = [None] * (len(s) + 1)
maxsum = [None] * (len(s) + 1)
def explore_subsets(i, count, sum):
if i == len(s):
sumsseen.add(sum)
if minsum[count] is None or sum < minsum[count]:
minsum[count] = sum
if maxsum[count] is None or sum > maxsum[count]:
maxsum[count] = sum
else:
explore_subsets(i + 1, count, sum)
explore_subsets(i + 1, count + 1, sum + s[i])
explore_subsets(0, 0, 0)
return len(sumsseen) == 2**len(s) and all(maxsum[i] < minsum[i + 1] for i in range(len(s)))
SETS = [
[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],
]
if __name__ == "__main__":
print(compute())