# nayuki/Project-Euler-solutions

Switch branches/tags
Nothing to show
Fetching contributors…
Cannot retrieve contributors at this time
141 lines (130 sloc) 4.84 KB
 # # 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())