Algorithms - 3.3 & 3.4

Overview: what is an ALGORITHM?

  • Sequencing - Selection - Iteration

  • Algorithms are step-by-step procedures or sets of rules used to solve problems or perform tasks
    • Also known as sequencing
      • Step 1, Step 2, Step 3…(in order)
      • Ex: putting on clothes one at a time in the morning, washing dishes, etc.
  • Selection
    • Decision to make based on a given circumstance
      • Ex: is it raining? If so, bring an umbrella outside
  • Iteration
    • Also referred to as repetition
    • After performing steps of a procedure/problem, iteration means checking to see if a task is completed
      • Refers back accordingly
  • Algorithms can be represented using flowcharts, Pseudo Code, or programming languages
  • Conditional statements
    • Conditional statements (if-else statements) allow a program to make decisions based on certain conditions
    • Enable different code branches to be executed depending on whether a condition is true or false
  • Loops
    • Loops (for loops, while loops) enable repetitive execution of code
    • They are used when a set of instructions needs to be repeated multiple times.
  • Strings
    • A string is a data type used to represent text or sequences of characters
    • Strings are commonly used in programming for tasks like input/output and text processing

Pseudo Code vs. a Python Algorithm

Pseudo Code is essentially describing/writing code in a more “human-written” format rather than formally/actually “coded” format.

Below, see examples highlighting the key difference(s) between a coded (Python) algorithm against a College Board Pseudo Code example.

College_Board_Algorithms_Diagram.png

College Board Pseudo Code example

Below is an algorithm to find the largest number in a list of positive numbers.

  1. Set largest number to 0
  2. Get next number in the list
  3. If number is larger than largestNumber then set largestNumber to number
  4. If there are more numbers in list, go back to step 2
  5. Display largest number
largestNumber = 0

numberList = [5, 8, 3, 12, 7, 10]

for number in numberList:
    if number > largestNumber:
        largestNumber = number

print("Largest number:", largestNumber)

Largest number: 12

3.3 - Mathematical Expressions/Operations in Algorithms

Mathematics in algorithms may involve many of the basic actions we all know to be part of the Order of Operations. This includes basic addition (a + b), subtraction (a - b), multiplication (a * b), and division (a / b).

However, there is also a likely unfamiliar action named Modulus (in Python: a % b).

MOD: (a / b -> whatever remains).

NOTE: in PEMDAS, MOD is held at the same level as multiplication and divison.

# arithmetic operations
# (a + b)
num1 = 4
num2 = 7
print(num2 + num1)

# (a - b)
num1 = 3
num2 = 9
print(num2 - num1)

11
6

# order of operations example below with grades
# remember PEMDAS
num1 = 12
num2 = 25
num3 = 14
answer = num1 / 4 * num3 + 9
print(answer)

51.0

Popcorn Hack #1

Create YOUR OWN order of operations problem like the one above using any values and operations in any order (ex: addition, multiplication, MOD).

Hint: remember to define your values, as seen above.

# use this code cell to make your own calculation!
num1 = 134
num2 = 49
num3 = 987
print(num3*num1+num2)

132307

Fibonacci and Factorial

What is a sequence of FIBONACCI?

A Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. It commonly starts with 0 and 1, and the sequence continues infinitely. The first few numbers in the Fibonacci sequence can be seen below.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34,…

Fibonacci function example:

def fibonacci(n):
    if n <= 0:
        return []
    elif n == 1:
        return [0]
    elif n == 2:
        return [0, 1]
    else:
        fib_sequence = [0, 1]
        while len(fib_sequence) < n:
            next_number = fib_sequence[-1] + fib_sequence[-2]
            fib_sequence.append(next_number)
        return fib_sequence

n = 10
result = fibonacci(n)
print(result)

[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

What is FACTORIAL?

In mathematics, the factorial of a non-negative integer, denoted by the symbol “!”, is the product of all positive integers from 1 to that integer. The notation is typically a number with “!” after (ex: n!)

Example of factorial: 5! = 5 x 4 x 3 x 2 x 1 = 120

Factorial function example:

def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n - 1)

n = 5
result = factorial(n)
print(f"{n}! = {result}")

5! = 120

Popcorn Hack #2

Complete the following tasks. Fill in the blank numbers in the segment of a Fibonacci sequence below:

[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]

Write the answer to the following factorials:

  • 4! = 432*1 = 24
  • 6! = 65432*1 = 720

    3.4 - Strings

What is a string?

  • Strings are ordered sequences of characters
    • Ex: characters can be numbers, letters, special characters like underscores, or even spaces
  • Substring: a substring can be described as part of an already existing string
  • String concatenation: joins two or more strings end-to-end to make a new string
  • Note that each programmming language has its own procedures, methods, or functions for strings
    • We will be covering Python

Let’s look at some of the string examples below.

Below is “len(str)”. This command counts the number of characters in a word (str) and returns that number. For example, for the word “happy” (“len(‘happy’)”), the value returned would be 5.

# len example:

string = "Hello, World!"
stringLength = len(string)
print(f"The string length is {stringLength} characters.")

The string length is {stringLength} characters.

Below is “concat(str1, str2)”. This returns a single string consisting of “str1” immediately followed by the characters of the second string (“str2”). For example, “concat(‘AP’, ‘class’)” would return “APclass”.

# concat example:

string1 = "Hel"
string2 = "lo!"

# concatenation seen right below

result = string1 + string2
print(result)

Hello!

Below is a substring “substring(str1, start, length)”. This returns a substring of consecutive characters from “str1”, starting with the character at position “start” and containing “length” characters. For example, “substring(‘APCSPrinciples’, 3, 6)” would return “CSPrin”.

# substring example:

string = "Hello, World!"
substring = string[2:10]
print(substring)

llo, Wor

Palindromes

The most commonly known definition of a palindrome is represented as being a word or phrase that is spelt the same both forward and backward.

For example, the word “racecar” is a palindrome, because the word is the same whether you read it from left to right or vice versa.

# palindrome example

def is_palindrome(s):
    s = s.lower().replace(" ", "").replace(",", "").replace("!", "")
    return s == s[::-1]

word = "racecar"
print(f"{word} {'is' if is_palindrome(word) else 'is not'} a palindrome.")

racecar is a palindrome.

Popcorn Hack #3

Decide if the following code cell is a “len(str)”, a concatenation, or a substring.

# len, concat, or substring?

thing1 = "Del "
thing2 = "Norte"
result = thing1 + thing2
print(result)

# type your answer HERE: -> This is a concatenation

Del Norte

Homework Hacks

Hack #1

  1. Concatenate your first and last name and print it (full name).

  2. Select/write a random sentence of your choice (be creative; it can be whatever you want it to be) and calculate the number of characters in it and display that as the result.

# put your work for Hack #1 in here below:
name = "Matthew " + "Wang"
print(name)
sentence = "The quick brown duck hopped lazyily over the energetic bear cubs"
display(len(sentence))

Matthew Wang



64



64

Hack #2

Similarly to the first Popcorn Hack, create your own order of operations problem (PEMDAS) in a code cell, but this time using modulus/MOD (a % b).

Try to make your answer not have a decimal in it.

# put your work for Hack #2 in here below:
num1 = 64
num2 = 98
num3 = 28
answer = (num1/num3*num2%num1)
print(answer)

32.0