Project Euler Problem 18

最新推荐文章于 2018-10-15 14:36:04 发布

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最新推荐文章于 2018-10-15 14:36:04 发布

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本文介绍了一种通过动态规划解决数字三角形中寻找从顶到底的最大路径和的方法。使用Python和NumPy库实现了算法，并给出了具体示例。

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Problem 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:

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, 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)

# 在数字三角形中，从顶到底，各条路径上数字之和最大是多少？

思路：使用动态规划

import numpy as np

data_arr = np.array([
[75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[95,64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[17,47,82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[18,35,87,10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[20, 4,82,47,65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[19, 1,23,75, 3,34, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[88, 2,77,73, 7,63,67, 0, 0, 0, 0, 0, 0, 0, 0],
[99,65, 4,28, 6,16,70,92, 0, 0, 0, 0, 0, 0, 0],
[41,41,26,56,83,40,80,70,33, 0, 0, 0, 0, 0, 0],
[41,48,72,33,47,32,37,16,94,29, 0, 0, 0, 0, 0],
[53,71,44,65,25,43,91,52,97,51,14, 0, 0, 0, 0],
[70,11,33,28,77,73,17,78,39,68,17,57, 0, 0, 0],
[91,71,52,38,17,14,91,43,58,50,27,29,48, 0, 0],
[63,66, 4,68,89,53,67,30,73,16,69,87,40,31, 0],
[ 4,62,98,27,23, 9,70,98,73,93,38,53,60, 4,23]])

for i in range(1,15):
    for j in range(i+1):
        if j == 0:
            data_arr[i][j] += data_arr[i-1][j]
        else:
            data_arr[i][j] += max(data_arr[i-1][j-1],data_arr[i-1][j])
print(max(data_arr[14][:]))

结果：1074