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Euler 0014

The Problem:

ThereWe isare 100 50-digit numbers that neededtrying to befind summedthe together.longest TheCollatz attachedsequence fileunder has been added to do this.1000000.

Considerations:

InThe pythoncollatz thissequence problemfollows 2 simple rules:
- if n is irrelevanteven, becausethen wen/2
- canif fitn giantis numbersodd, intothen then*3 integer+ space1

and

5 python-> will16 work-> with8 it.-> 4 -> 2 -> 1  
6 -> 5  -> 4 -> 3 -> 2 -> 1

The Approach:

WeThe readapproach I'll take to this is to set up a dictionary of lengths at key n.  If the file,key sumdoesn't thehave numbers,a convert to string, andvalue then convertit backgenerates intoa numbercollatz aftersequence slicinguntil theit firstreturns 101 digits.or a key that has a length value


The Code:

numbers_filehighest_starting =  open("numbers.txt",1000000
"r")

totallengths_dict = 0{1:1}
max_length = 1
length_key = 1

#the recursive function to generate collatz.
#Base case is satisfied by the lengths_dict above already having 1 initialized.
def update_lengths(number, lengths):
    #print(number)
    if lengths.get(number) == None:
        if number % 2 == 0:
            one_down = number/2
        else:
            one_down = number*3 + 1
        lengths = update_lengths(one_down, lengths)
        lengths[number] = lengths[one_down] + 1

    return lengths

for numberi in numbers_file:
    totalrange(1,highest_starting + 1):
    if lengths_dict.get(i) == int(number)None:
        lengths_dict = update_lengths(i, lengths_dict)
    
    if lengths_dict.get(i) > max_length:
        length_key = i
        max_length = lengths_dict.get(i)

print(str(total)[:10])length_key, max_length)
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