# How to make my Collatz Conjecture code run a lot faster? (and even better, how do I implement it into multiple computers?) Python

I have been writing this piece of code for a while now, and I was wondering, is it possible to run this code multiple times on my pc? For example could I make the code solve all the numbers from 1 to 1000 and all from 1001 to 2000 at the same time? And, if this is possible, could I use multiple computers to solve it in this way (just with bigger numbers)?

Heres the Code:

#(n*3)+1 = if odd
#else n/2 = if even
import time
import sys

def progress(count, total, status=''):
bar_len = 60
filled_len = int(round(bar_len * count / float(total)))

percents = round(100.0 * count / float(total), 1)
bar = '█' * filled_len + '-' * (bar_len - filled_len)

sys.stdout.write('[%s] %s%s ...%s\r' % (bar, percents, '%', status))
sys.stdout.flush()

one = "nothing"
while one != "n":
if one == "n":
break
else:
total = input("what is the limit number?:")
total = int(total)
total = total+1
highest_step = 0
highest_num = 0

for x in range(0,total):
n = x
steps = 0
print(end="\r")
progress(n, total, status='Doing very long job, current Num:'+str(n))# emulating long-playing job

#print("----IMPOSSIBLE MATH SOLUTION------")
#print()
#print ("staring number is:(",n,")")
#print()

while n != 0:
if n != 1:
if (n%2) == 0:
#print(
eval("n/2")
n = eval("n/2")
steps = steps+1
else:
#print (
eval("(n*3)+1")
n = eval("(n*3)+1")
steps = steps+1

else:
#print ("amount of steps it took to solve:",steps)
if (highest_step <= steps):
highest_step = steps
highest_num = x
break
else:
break

print()
print()
print ("the number with most steps",highest_num)
print ("amount of steps:",highest_step)
one = input("congrats!, do it again? (y/n)")



This would be a great help, thanks

(Also, I am still a beginner coder in python3.)

• Your existing code is fine to review, but this site isn't really well suited to tell you how to rewrite this from scratch in a distributed manner. Oct 27, 2021 at 23:20
• 1 to 1000 [/] 1001 to 2000 Given the relation between argument and run time, that division of labour may need to be refined. There is Python concurrency with modules/packages like concurrent, threading, multiprocessing Oct 28, 2021 at 3:19
• I'm not sure that distributing the calculation on multiple computers would be faster than running the code with memoization of the previous results. Especially checking for powers of 2 should speed up the calculation. As is you're redoing at least the 8 - 4 - 2 -1 sequence for every number >4. Ideally you'd run it on multiple processes with a shared dictionnary [num] -> steps. Oct 28, 2021 at 10:11

Not exactly sure what your goal is. If your primary goal is just getting the highest_step and highest_num a lot faster than your current code does, then you could achieve the goal without any of that. As an example, when I run the following code (basically your code that calculates to 99,999 without taking input or displaying the progress bar) on my machine,

from time import perf_counter_ns as ns

start = ns()
limit = 100_000
highest_step = 0
highest_num = 0

for x in range(limit):
n = x
steps = 0

while n != 0:
if n != 1:
if (n%2) == 0:
n = eval("n/2")
steps = steps+1
else:
n = eval("(n*3)+1")
steps = steps+1
else:
if (highest_step <= steps):
highest_step = steps
highest_num = x
break
else:
break
print("the number with most steps",highest_num)
print("amount of steps:",highest_step)
print(f'it took {(ns() - start)/1e6:,.0f}ms')


it prints this.

the number with most steps 77031
amount of steps: 350
it took 28,098ms


However, the same code without the useless eval() prints this (18x speed).

the number with most steps 77031
amount of steps: 350
it took 1,562ms


If I run the that code with pypy 3.8 instead of python 3.10, then this (49x speed).

the number with most steps 77031
amount of steps: 350
it took 569ms


And when I run the following code on the same machine with pypy3.8,

from time import perf_counter_ns as ns

start = ns()
limit  = 100_000
memo = {i: 0 for i in range(limit)}
for i in range(3):
memo[i] = i
for i in range(3, limit):
counter = 0
cur = i
while i > 1:
if i < cur:
memo[cur] = memo[i] + counter
break
if not i % 2:
i /= 2
counter += 1
else:
i *= 3
i += 1
counter += 1
print(f'the number with most steps: {max(memo, key=memo.get)}')
print(f'amount of steps: {max(memo.values()) - 1}')
print(f'it took {(ns() - start)/1e6:,.0f}ms')


it prints this (375x speed), even though this is probably not the most efficient way to do it, and Python usually take a considerably longer time to compute the same task, compare to many other languages like C++.

the number with most steps: 77031
amount of steps: 350
it took 75ms


EDIT: Added some more benchmark results (limit is now 1 million, instead of 100k shown above)

1. only removed two input()s from your original code (all four eval()s intact):

• python3.10: 771,214ms
2. the 28 seconds code above (two eval()s remaining, progress bar removed):

• python3.10: 344,444ms (2.2x speed)
3. without eval():

• python3.10: 19,238ms (40x speed)
• pypy3.8: 6,937ms (111x speed)
4. using dict memo:

• python3.10: 1,078ms (715x speed)
• pypy3.8: 732ms (1,054x speed)
5. using list memo (shown below):

• python3.10: 805ms (950x speed)
• pypy3.8: 50ms (15,424x speed)
from time import perf_counter_ns as ns

start = ns()
limit  = 1_000_000
memo = [0] * limit
memo[1], memo[2] = 1, 2
for i in range(3, limit):
counter = 0
cur = i
while i > 1:
if i < cur:
memo[cur] = memo[i] + counter
break
if not i % 2:
i //= 2
counter += 1
else:
i *= 3
i += 1
counter += 1
print(f'the number with most steps: {memo.index((m := max(memo)))}')
print(f'amount of steps: {m - 1}')
print(f'it took {(ns() - start)/1e6:,.0f}ms')

1. list variant above vs C++ vector variant (1.96x over pypy, 30,231x speed overall)
pypy: 0.08s user 0.02s system 94% cpu 0.102 total (when it prints 51ms)
g++:  0.05s user 0.00s system 98% cpu 0.052 total