'Sum of Triangles': Codechef How can the code be optimised for speed and large test cases?

Question

I am a Python newbie.

The following was a beginner level problem at codechef.com Link to problem

Problem Text:

Let's consider a triangle of numbers in which a number appears in the first line, two numbers appear in the second line, three in the third line, etc. Develop a program which will compute the largest of the sums of numbers that appear on the paths starting from the top towards the base, so that:

• on each path the next number is located on the row below, more precisely either directly below or below and one place to the right;
• the number of rows is strictly positive, but less than 100
• all numbers are positive integers between O and 99.

Input

In the first line integer n - the number of test cases (equal to about 1000). Then n test cases follow. Each test case starts with the number of lines which is followed by their content.

Output

For each test case write the determined value in a separate line.

The following is my code:

tempij=[]
s=0

def solve(i,j,ll):
    global s
    s=0
    tempij=[]
    if i==len(ll):
        return 0
    elif (i,j) in tempij:
        return s
    else:
        tempij.append((i,j))
        t1=solve(i+1,j,ll)
        t2=solve(i+1,j+1,ll)
        t=max(t1,t2)+ll[i][j]
        s=t
        return t
    
t=int(input())
ll=[]

for k in range(t):
    ll=[]
    n=int(input())
    for i in range(n):
        lst=[]
        text=input().split()
        for j in range(len(text)):
            lst.append(int(text[j]))
        ll.append(lst)
    print(solve(0,0,ll))

Problem with this code:

I have tried to implement Recursion with Memoization in accordance with their editorial on this problem. Link to editorial

Code explained (Relevant part of editorial):

(I am using tempij for caching in the code above. Something similar to SO question: SO question about memoization)

While it works for the test cases given as example, it seems to be exceeding the time limit for other test cases.

My question: How do I improve this code? Or is there a better way?

Answer 1

I realized my mistake. Thanks to JCVanHamme.

The above code was not caching correctly because of reasons mentioned by JCVanHamme. I had been resetting the cache after every call. So I did away with all the global variables which were creating problems (since they would have to be re-set for every test case and that was creating a problem). Modified code looks like:

def solve(i,j,ll,cache):


    if i==len(ll):
        return 0
    elif (i,j) not in cache:
        t1=solve(i+1,j,ll,cache)
        t2=solve(i+1,j+1,ll,cache)
        t=max(t1,t2)+ll[i][j]
        cache[(i, j)] = t
    return cache[(i, j)]

t=int(input())
ll=[]
cache={}

for k in range(t):
    ll=[]
    cache={}
    n=int(input())
    for i in range(n):
        lst=[]
        text=input().split()
        for j in range(len(text)):
            lst.append(int(text[j]))
        ll.append(lst)
    print(solve(0,0,ll,cache))

The original question still holds. Can it be made faster and better using python itself? I checked out run-times of people who used other languages like C/C++ and it is as low as 0:08 while for python 3.x it is 0.57!

Answer 2

I'm not convinced your memoization is working. Every time you call solve, you blow away your cache and you have a local tempij that shadows the global copy. Moreover, you're only storing one calculated value at a time in s, so even if it was working, you probably wouldn't retrieve the correct cached value in most cases. Leaving aside the use of the global variable (shudder), I think you should use something more like

cache = {}

def solve(i,j,ll):
    global cache
    if i==len(ll):
        return 0
    elif (i,j) not in cache:
        t1=solve(i+1,j,ll)
        t2=solve(i+1,j+1,ll)
        t=max(t1,t2)+ll[i][j]
        cache[(i, j)] = t
    return cache[(i, j)]