欧拉计划(python) problem 67

Maximum path sum II

Problem 67

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 in triangle.txt (right click and ‘Save Link/Target As...‘), a 15K text
file containing a triangle with one-hundred rows.

NOTE: This is a much more difficult version of Problem 18. It is not
possible to try every route to solve this problem, as there are 2⁹⁹ altogether! If you could check one trillion (10¹²) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve
it. ;o)

Go to the thread for problem 67 in the forum.

解题思路：动态规划

python code :

import math

sqrt=math.sqrt

a=[]

f = open("data.txt")

line = f.readline()

while line:

row=line.split(‘ ‘)

for i in range(0,len(row)):

a.append(int(row[i]))

line = f.readline()

f.close()

k=len(a)

def getsun(x):

redult=[];

k=int((sqrt(1+8*x)-1)/2)+1

return [x+k,x+k+1]

def getrowstart(x):

return int(x*(x-1)/2)

for i in range(99,0,-1):

start=getrowstart(i)

for j in range(0,i):

sun=getsun(start+j)

a[start+j]+=max(a[sun[0]],a[sun[1]])

print(a[0])

time: <1s