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