题目
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.
That is, 3+7+4+9=23.
Find the maximum total from top to bottom of the triangle below:
NOTE: As there are only 16384routes, 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)
解答
首先是读一个这个三角形的数据，以一个list of list的形式存储。
def parse_tri(x):
y = x.split("\n")[1:-1]
res = []
for i in range(len(y)):
ln = [int(j) for j in y[i].split(' ')]
res.append(ln)
return res
然后从上往下走，我们可以累加下来，只存最佳路径的加和。那么首先是两行的相加。
def myadd(x, y):
n = len(y)
res = [0] * n
for i in range(n):
if i == 0:
res[i] = x[i] + y[i]
elif i == (n-1):
res[i] = x[i-1] + y[i]
else:
tmp1 = x[i] + y[i]
tmp2 = x[i-1] + y[i]
res[i] = max(tmp1, tmp2)
return(res)
再来就是整个三角形加起来，到最底下一行的最优路径。
def tri_add(tri):
res = tri[0]
for i in range(1, len(tri)):
res = myadd(res, tri[i])
return res
那整体最大值，就是最后这一行加和的最大值了，解这个题的函数就可以简单地写成：
def solution18(x):
y = parse_tri(x)
res = tri_add(y)
return max(res)
那么解题就是：
x = """
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
"""
solution18(x)
