I've written a Python solution for Euler Project problem 27. It works, but is geologically slow (1765 seconds to find the correct result of -59,231). To speed things up, I would like to replace the mammoth 2D list "box" with a 1D list? My question is, how do I do that? Here's the problem: And here's my code: import time from sympy import isprime start_time = time.time() a_lower_limit = -999 a_upper_limit = 1000 b_lower_limit = 0 b_upper_limit = 1001 a1 = abs(a_lower_limit) a2 = a_upper_limit - a_lower_limit b2 = b_upper_limit - b_lower_limit # 2d list of primes for permutations of a, b box = [[] for j in range(a2 * b2)] # 2d list of a*b for each a, b permutation box_ab = [[] for j in range(a2 * b2)] for a in range(a_lower_limit, a_upper_limit): for b in range(b_lower_limit, b_upper_limit): a_prime = a + a1 for n in range(0, b_upper_limit): num = n**2 + a*n + b if isprime(num): box[(a_prime * b2) + b].append(num) box_ab[(a_prime * b2) + b].append(a*b) # Define a function that finds the longest sub-list in "box" def max_length_list(box): max_length = max(len(x) for x in box) max_list = max(box, key=len) return (max_list) # Find index of max_length_list in box x = box.index(max_length_list(box)) # Product of coefficients a and b that produce the longest sub-list in "box" print((box_ab[x])[0]) print(f"Run time: {(time.time() - start_time):.2f} seconds") For each permutation of a and b, the code finds the number of primes generated for consecutive values of n, starting with n = 0. These are then stored in different sub-lists in the 2D list “box”. I would like to replace this 2D “box” with a list: box = [] and a variable max_number_primes, initially set to zero. For each permutation of a and b, the generated primes need to be stored in the list “box”. After each permutation, I would then like to compare len(box) with max_number_primes. If len(box) > max_number_primes, then max_number_primes = len(box). Eventually, I will get the largest possible max_number_primes. I can then try to find the corresponding a*b. This (and variations on this) is what I've tried. But I can't get it to work. a_lower_limit = -999 a_upper_limit = 1000 b_lower_limit = 0 # for now, always set to zero b_upper_limit = 1001 a1 = abs(a_lower_limit) b1 = abs(b_lower_limit) # don't need this if b_lower_limit set to zero a2 = a_upper_limit - a_lower_limit b2 = b_upper_limit - b_lower_limit box = [] # list of primes max_number_primes = 0 for a in range(a_lower_limit, a_upper_limit): for b in range(b_lower_limit, b_upper_limit): if a_lower_limit < 0: a_prime = a + a1 else: a_prime = a - a_lower_limit for n in range(0, b_upper_limit): num = n**2 + a*n + b if isprime(num): box.append(num) if len(box) > max_number_primes: max_number_primes = len(box) box.clear Continue reading...
