Project Euler Problem 018
http://projecteuler.net/index.php?section=problems&id=18
By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom of the triangle below: NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)
グラフの問題。
ダイクストラ法かなと思ったけど、各ノードの繋がり方は固定なので経路探索する必要もない。
元のリストを破壊してしまうのが問題。嫌ならコピーを作る。
import datetime def find_max(s): def walking(t): for i in xrange(1, len(t)): for j in xrange(len(t[i])): t[i][j] += max(t[i-1][max(0, j-1):j+1]) return max(t[-1]) T = [ [ int(i) for i in line.strip().split(' ') ] for line in s.split('\n') if line ] return walking(T) s = """ 75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 34 88 02 77 73 07 63 67 99 65 04 28 06 16 70 92 41 41 26 56 83 40 80 70 33 41 48 72 33 47 32 37 16 94 29 53 71 44 65 25 43 91 52 97 51 14 70 11 33 28 77 73 17 78 39 68 17 57 91 71 52 38 17 14 91 43 58 50 27 29 48 63 66 04 68 89 53 67 30 73 16 69 87 40 31 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 """ begin = datetime.datetime.now() print find_max(s) end = datetime.datetime.now() print end - begin
答え: 1074
実行時間: 0.000747秒くらい