Vocab

  • Collatz: A conjecture that asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1.
  • Hailstone numbers: A squence of integers generated by the Collatz conjecture.
  • Undecidable problems: one that should give a "yes" or "no" answer, but yet no algorithm exists that can correctly answer on all outputs
  • Unsolvable problems: one for which no algorithm can ever be written to find the solution

Hack 1 

i = int(input("Enter a number"))
print("Number:", i)

def collatz(i):
    while i > 1:
        print(i, end=' ')
        if (i % 2):
            i = 3*i + 1
            list_.append(i)
        else:
            i = i//2
            list_.append(i)
    print(1, end='')

list_ = [i]
l = list(i)
print('Number of iterations:', len(l) - 1)
print('Sequence: ')
collatz(i)
## the number is 10, the number of iterations is 6, and the sequence is 10,5,16,8,4,2,1

Hack 2 

num1 = 10
num2 = 20
num3 = 30
print(num1 + num2 + num3)

60

nums = [10, 20, 30]
print(sum(nums))

60

The second algorithm is more efficient than the first because the second uses less lines of code (it did not individually assigns and adds each number in the list).

Hack 3

Algorithm efficiency: Making an algorithm more efficient by using less lines of code and more resources

Hack 4 

tasks = ["review notes", "do practice problems", "ask teacher questions"]
 
def complete_tasks(tasks):
 for task in tasks:
# code to complete each task goes here
 
   if task == "wake up":
     print("Reviewing Confidence intervals")
   elif task == "do practice problems":
     print("Doing practice problems now!")
   elif task == "ask teacher questions":
       print("Asking questions now!")
 
# and so on for each task in the list
 
# call the function to complete the tasks
complete_tasks(tasks)

Doing practice problems now!
Asking questions now!