I coded a Python solution for Problem #14 on the Project Euler website. I was
very surprised to find that it took 107 sec. to run even though it's a pretty
simple program. I also coded an equivalent solution for the problem in the old
MSDOS basic. (That's the 16 bit app of 1980s vintage.) It ran in 56 sec. Is
there a flaw in my coding, or is Python really this slow in this particular
application. MSDOS Basic usually runs at a snails pace compared to Python.
Below is the problem and the code:
The following iterative sequence is defined for the set of positive integers:
n → n/2 (n is even)
n → 3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains
10 terms. Although it has not been proved yet (Collatz Problem), it is thought
that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
NOTE: Once the chain starts the terms are allowed to go above one million.
max=0
m=0
while m<=1000000:
m+=1
count=0
n=m
while n!=1:
count+=1
if n%2==0:
n=n//2
else:
n=3*n+1
if count>max:
max=count
num=m
print(num,max)
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