3.14

  • Documentation: Text that explains the what, how, or why of your code
def gradeAverage(num):
    sumNums = 0
    for t in num:
        sumNums = sumNums + t

    average = sumNums / len(num)
    return average
print("The average grade is", gradeAverage([65, 70, 72, 75, 80, 73, 61, 84, 81, 83]))
  • Documentation for the example above: The procedure gradeAverage takes a list of integer values representing the percentages in a certain class, and returns the average of those integers.
  • Libraries: A collection of pre-written code or procedures that coders can use to maximize their efficiency
import math
math.sqrt(64)
  • Application Programming Interface: A type of software through several computers are able to communicate information amongst each other

    3.15

  • Randomization: generates a value between two numbers
import random
answer1 = random.randint(0,3)
print(answer1)

3.16

  • Simulations: an imitation of a situation or process
import random
status = "in"
while status != "out":
    chooseCorner = input("What corner do you choose?")
    corner = random.randint(1,4)
    if int(chooseCorner) == corner:
        status = "out"
        print("You chose corner number " + chooseCorner + " and you're OUT")
    else:
        print("You chose corner number " + chooseCorner + " and are still in!")
  • Experiment: procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact

    3.17

  • Algorithm Efficiency: aspect of algorithmic programming that measures the number of steps needed to solve a problem
    • Inefficient:
      def inefficientWay(numbers):
      for i in range(len(numbers)):
      min_index = i
      for j in range(i+1, len(numbers)):
          if numbers[j] < numbers[min_index]:
          min_index = j
      numbers[i], numbers[min_index] = numbers[min_index], numbers[i]
      return numbers
  print(inefficientWay([2, 4, 5, 1, 3]))
    • Efficient:
      def efficient_sort(numbers):
      for i in range(len(numbers)):
      min_index = i
      for j in range(i+1, len(numbers)):
          if numbers[j] < numbers[min_index]:
          min_index = j
      numbers[i], numbers[min_index] = numbers[min_index], numbers[i]
      return numbers
  print(efficient_sort([2, 4, 5, 1, 3]))
  • Heuristic Approach: taking the shortest or easiest possibilities to the result

    3.18

  • Collatz Conjecture: asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1
def collatz(i):
    while i != 1:
        if i % 2 > 0:
             i =((3 * i) + 1)
             list_.append(i)
        else:
            i = (i / 2)
            list_.append(i)
    return list_
  • Hailstone numbers: sequence of integers generated by Collatz conjecture
  • Undecidable problems: should give a “yes” or “no” answer, but yet no algorithm exists that can answer correctly on all inputs
  • Unsolvable problems: no algorithm can ever be written to find the solution