How to apply Python generators to finding min and max values?

I’m solving yet another problem in HackerRank (https://www.hackerrank.com/challenges/determining-dna-health/problem). In short: you are given 2 arrays (genes and health), one of which have a ‘gene’ name, and the other – ‘gene’ weight (aka health). You then given a bunch of strings, each containing values m and n, which denote the start and end of the slice to be applied to the genes and health arrays, and the ‘gene’-string, for which we need to determine healthiness. Then we need to return health-values for the most and the least healthy strings.

My solution is below, and it works, but it’s not scalable, i.e. it fails testcases with a lot of values.

import re
if __name__ == '__main__':
    n = int(input())

    genes = input().rstrip().split()

    health = list(map(int, input().rstrip().split()))

    s = int(input())
    weights = ()
    for s_itr in range(s):
        m,n,gn = input().split()
        weight = 0
        for i in range(int(m),int(n)+1):
            if genes(i) in gn:
                compilt = "r'(?=("+genes(i)+"))'"
                matches = len(re.findall(eval(compilt), gn))
                weight += health(i)*matches
        weights.append(weight)
    print(min(weights), max(weights))

Can you advise on how to apply generators here? I suspect that the solution fails because of the very big list that’s being assembled. Is there a way to get min and max values here without collecting them all?

Example values:

genes = ('a', 'b', 'c', 'aa', 'd', 'b')
health = (1, 2, 3, 4, 5, 6)
gene1 = "1 5 caaab" (result = 19 = max)
gene2 = "0 4 xyz" (result = 0 = min)
gene3 = "2 4 bcdybc" (result = 11)

This case returns 0 19

nt.number theory – Calculate generators from $ Gamma_0 (N) $

I found the group in a newspaper $ Gamma_0 (18) $ can be generated by the following list of matrices:

  • $ displaystyle left ( begin {array} {rr} 7 & -1 \ 36 & 5 end {array} right) $

  • $ displaystyle left ( begin {array} {rr} 13 & -8 \ 18 & -11 end {array} right) $

  • $ displaystyle left ( begin {array} {rr} 71 & -15 \ 90 & -9 end {array} right) $

  • $ displaystyle left ( begin {array} {rr} 55 & -13 \ 72 & -17 end {array} right) $
  • $ displaystyle left ( begin {array} {rr} 7 & -2 \ 18 & -5 end {array} right) $
  • $ displaystyle left ( begin {array} {rr} 31 & -25 \ 36 & -29 end {array} right) $
  • $ displaystyle left ( begin {array} {rr} 1 & 1 \ 0 & 1 end {array} right) $
  • $ displaystyle left ( begin {array} {rr} -1 & 0 \ 0 & -1 end {array} right) $

E.g. $ 31 times (-29) – 36 times (-25) = -899 + 900 = $ 1 Actually, $ 36, 18, 19 equiv 0 pmod {18} $.

These generators look anything. There is a list of generators from $ Gamma_0 (N) $ to the $ N <100 $ ?

Is there a computer program or algorithm for finding generators of congruence groups, for example using a linear algebra package such as e.g. sage ?

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rational points – Two additional generators are required for an elliptical Z / 6 curve

We are looking for rank 8 elliptic curves with the torsion subgroup Z / 6 using newly discovered families that are similar to Kihara (Kihara family is described in https://arxiv.org/pdf/1503.03667.pdf).

Today we came across a curve

$ (0.8169768624655967629114128598.0, -451787550647310420612086468536366715869054405951830599.0) $

Both Magma Calculator (http://magma.maths.usyd.edu.au/calc/) and mwrank with $ -b12 $ Return 6 generators for this curve.
Magma V2.20-10 (STUDENT) no longer has enough memory to run the following code:

SetClassGroupBounds("GRH");
E := EllipticCurve((0,8169768624655967629114128598,0,-451787550647310420612086468536366715869054405951830599,0));
MordellWeilShaInformation(E);

Sagemath returns $ 8 $ for the upper limit of the analytical rank, also for max_Delta =$ 3.3 $ (We are still testing for a higher max_Delta):

E = EllipticCurve((0,8169768624655967629114128598,0,-451787550647310420612086468536366715869054405951830599,0))  
E.analytic_rank_upper_bound(max_Delta=3.3,root_number="compute")

Is there a way to find two more generators?

A similar question for that $ 6 $ <= Rank (E) <= $ 7 $ The situation has been successfully resolved by Jeremy Rouse (another elliptical Z / 6 curve generator required), but our software throttles when we try to follow his instructions.

We are ready to award a bounty from a $ 100 $ (How do I transfer my current call?) For both generators. Your name (together with ours) will also be published at the end of the page here: https://web.math.pmf.unizg.hr/~duje/tors/z6.html

Max