Euler project #18 approach

Question

I am looking into an Euler project. Specifically #18.
To sum up, the idea is to find the max path from a triangle:

   3
  7 4
 2 4 6  
8 5 9 3
<         


        

Answer 1

Since the rows are small in number you can use also recursion to compute the greatest sum :

import sys
def max_sum(i,j):
    if i==14:
        return a[i][j]
    return a[i][j]+max(max_sum(i+1,j),max_sum(i+1,j+1))
a=[]
for i in range(15):
    b=list(map(int,sys.stdin.readline().split()))
    a.append(b)
print(max_sum(0,0))

for question 67 -(Maximum path sum II) you can use memoisation:

import sys
d={}
def max_sum(i,j):
    if (i,j) in d:
        return d[(i,j)]
    if i==99:
        return a[i][j]
    d[(i,j)]=a[i][j]+max(max_sum(i+1,j),max_sum(i+1,j+1))
    return d[(i,j)]
a=[]
for i in range(100):
    b=list(map(int,sys.stdin.readline().split()))
    a.append(b)
print(max_sum(0,0))