Collatz Conjecture (Python Example)

Collatz_Conjecture_Example.py

#!/usr/bin/python
#
# Collatz Conjecture:
#      x → x/2 (if x is even)
#      x → 3x + 1 (if x is odd)

import sys, time

# Default seed if no arguments given
seed = 27

def collatz_sequence(x):
    seq = [x]
    while seq[-1] > 1:
       if x % 2 == 0:
         seq.append(int(x/2))
       else:
         seq.append(int(3*x+1))
       x = seq[-1]
    return seq

# test for cli arguments
try:
  if len(sys.argv)>1 :
    seed = int(sys.argv[1])
except ValueError:
  print("Not a number.")
  sys.exit(1)


# time the method
start = time.time()

# execute function
list = collatz_sequence(seed)

# stop/record our stopwatch
finish = (time.time() - start)

# print list and total list items
print("\nSeed = " + str(seed) + "\n")
print(list)
print("\nItems = " + str(len(list)))

# time spent
print("\nFunction took {} milliseconds".format(1000 * finish))
#print("Script execution took {} milliseconds\n".format(1000 * (time.time() - start)))

# clean exit
print()
sys.exit(0)

Collatz_Conjecture_Example_2.py

# Collatz Conjecture:
#      x → x/2 (if x is even)
#      x → 3x + 1 (if x is odd)
#
# Calculate max amount of elements in numbers 1-(iterations):

import sys, time, operator

# Range to cover  1 - (iteratons - 1)
iterations = 1000001

def collatz_sequence(x):
    seq = [x]
    while seq[-1] > 1:
       if x % 2 == 0:
         seq.append(int(x/2))
       else:
         seq.append(int(3*x+1))
       x = seq[-1]
    return seq

start = time.time()

# set our dictionary and for loop
Fullcount = {}
for number in range(1, iterations):
  list = collatz_sequence(number)
  Fullcount[number] = len(list)
#  print("Seed = " + str(number) + " , " + "Items = " + str(len(list)))

# stop/record our stopwatch
finish = (time.time() - start)

# alternative way to find max key
#max(Fullcount.keys(), key=(lambda k: Fullcount[k]))

# find max key
maximum = max(Fullcount, key=Fullcount.get)

print()
print("Range to test: 1 - " + str(iterations - 1) + "\n" + "The number " + str(maximum) + " wins.\nIt has " + str(Fullcount[maximum]) + " items.")

# time spent
print("\nFunction took {} milliseconds".format(1000 * finish))

# clean exit
print()
sys.exit(0)

Default is 27 / no line arguments.

Find max in range (Example 2 / second script) then you can show elements by running first script on same number found: