Algorithms can be written in different ways and still accomplish the same tasks. Algorithms that look similar often yield differnet outputs. To solve the same problem, many different algorithms can be used.

Therefore, algorithms are very important for programmers, and today we're going to explore how to determine the outcome of algorithms, how to deteremine the output of similar algorithms, how to edit existing algorithms, and how to develop our own algorithms.

Notes:

An algorithm is like a series of very specific instructions that a computer can follow to execute a certain task
many algorithms are math and computationally involved
an algorithm can be modeled with pseudoode
all algorithms involve some sort of problems, and there are usually many algorithms with accomplist the same tasks
Debugging is used if the algorithm doesn't work as planned

Determine the outcome of algorithms

Consider the following algorithm.

def mystery(num, num2):
    if (num % num2 == 0):
        print("True")
    else:
        print("False")

mystery(20, 4)

True

What does the algorithm do? Please explain in words. The above algorithm shows a function which takes in 2 numbers. If the remainder of the first number divided by the second number is 0, or in other words, if the first number is divisible by the second, True is printed. If not, False is printed
What if I put in 30 as num and 4 as num2. What would be the output? False, as 30 isn't divisible by 4

Determine the outcome of similar algorithms

What is the output of this algorithm? it is too hot outside

temp = 95
if (temp >= 90):
    print("it is too hot outside")
else:
    if (temp >= 65):
        print("I will go outside")
    else:
        print("it is too cold outside")

it is too hot outside

What is the output of this algorithm? it looks similar but the output is different!

it is too hot outside
i will go outside

temp = 95
if (temp >= 90):
    print("it is too hot outside")
else:
    if (temp >= 65):
        print("i will go outside")
    if (temp < 65):
        print("it is too cold outside")

it is too hot outside

Editing Algorithms

Task: Please edit the algorithm above to have it yield the same results as the previous algorithm! (no matter what temp you put in)

Developing Algorithms

To develop algorithms, we first need to understand what the question is asking. Then, think about how you would approach it as a human and then try to find what pattern you went through to arrive at the answer. Apply this to code, and there you have it! An algorithm!

Let's say you wanted to sum up the first five integers. How would you do this in real life? Your thought process would probably be:

The sum of the first integer is 1.
Then, increase that integer by 1. I now add 2 to my existing sum (1). My new sum is 3.
Repeat until I add 5 to my sum. The resulting sum is 15.

Now let's translate this into code.

sum = 0 # start with a sum of 0
for i in range (1, 6): # you will repeat the process five times for integers 1-5
    sum = sum + i # add the number to your sum
print(sum) # print the result

15

Task: Write an algorithm in python that sums up the first 5 odd integers. You can use the following code as a starter.

sum = 0
counter = 1
for i in range (0, 5):
    sum = sum + counter
    counter = counter + 2
print(sum)

25

Homework

Create an algorithm that will start with any positive integer n and display the full sequence of numbers that result from the Collatz Conjecture. The COllatz Conjecture is as follows:

start with any positive integer
if the number is even, divide by 2
if the number is odd, multiply by 3 and add 1
repeat steps 2 and 3 until you reach 1

Example: if the starting number was 6, the output would be 6, 3, 10, 5, 16, 8, 4, 2, 1

def collatz(N):
    print(N)
    while N != 1:
        if N//2 == N/2:
            N //= 2
        else:
            N *= 3
            N += 1
        print(N)
collatz(6)

6
3
10
5
16
8
4
2
1