Problem 18

Problem 18

31 May 2002

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 5
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:

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

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, , is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

从(i, j)开始的最大值为(i+1,j)与(i+1,j+1)中的大者加上(i, j)自身，

我们从最下面一行开始计算

def fun18():
    fp = open("68.txt", "r")
    lines = fp.readlines()
    lines.reverse()

    line = map(int, lines[0].split())
    for i in lines[1:]:
        result = map(int, i.split())
        for i in range(len(result)):
            result[i] += max(line[i], line[i+1])
        line = result
    return result

answer is 1074

该方法同样可以计算Problem 68

answer is 7273

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