Developing Algorithms

What is an Algorithm

An algorithm is a set of instructions for solving a specific problem or performing a particular task.

Purpose of developing Algorithms

  • Automate and simplify repetitive code
  • More efficient functions
## Example of algorithm
import random
# Define min and max values
min_num = 1
max_num = 10
# Generate Random Number
random_number = random.randint(min_num, max_num)
# Output
print(f"Random number: {random_number}")

Random number: 9

image.png

Same goal, different Process

The examples show different processes to see if you got an A, passed, or failed on a test. However, these two algorithms yield different results. The first algorithm uses three different “if” statements which will check each condition independently so two messages can be displayed. The second algorithm uses an elif statement to ensure that only one of the three conditions will be displayed.

display("What did you get on your test?")
testScore = int(input())
if testScore > 90:
    display("You got an A!")
if testScore > 70:
    display("Congragulations. You didn't fail.")
if testScore < 70:
    display("You failed.")

'What did you get on your test?'



'You failed.'

display("What did you get on your test?")
testScore = int(input())
if testScore > 90:
    display("You got an A!")
elif testScore > 70:
    display("Congratulations. You didn't fail.")
else:
    display("You failed.")

'What did you get on your test?'



'You failed.'

Algorithms in statistic/mathematical calculation

Algorithms in statistical and mathematical calculations refer to systematic step-by-step procedures or methods for solving specific problems, performing computations, or making decisions. These algorithms are designed to ensure in various mathematical and statistical tasks.

# Mean
numberlist = [3, 6, 9, 12, 15]
mean = sum(numberlist) / len(numberlist)
print("Mean:", mean)

Mean: 9.0

# Median
numberlist = [3, 6, 9, 12, 15]
n = len(numberlist)
if n % 2 == 0:
    median = (numberlist[n // 2 - 1] + numberlist[n // 2]) / 2
else:
    median = numberlist[n // 2]
print("Median:", median)

Median: 9

# Mode
from collections import Counter

def find_mode(numbers):
    count = Counter(numbers)
    max_count = max(count.values())
    modes = [num for num, freq in count.items() if freq == max_count]
    
    return modes 
numbers = [3, 9, 9, 12, 15]
modes = find_mode(numbers)

if len(modes) == 1:
    print(f"The mode is {modes[0]}")
else:
    print("There are multiple modes:", modes)

The mode is 9

Popcorn Hack #1

Create your own algorithm using numbers to calculate a value.

## Insert your popcorn hack here:
print("enter two numbers to be added together.")
group = (1,2,3,4,5,34,98,200,300)
firstinp = int(input())
secondinp = int(input())
total = firstinp + secondinp
mean = (sum(group) + total)/ (len(group) + 1)
print("the number you made is:" + total)
print("mean when give 1,2,3,4,5,34,98,200,300 plus the number you made is: " + str(mean))

enter two numbers to be added together.
66
mean when give 1,2,3,4,5,34,98,200,300 plus the number you made is: 71.3

Using algorithms to organize lists

There are two different ways in which data can be sorted.

  • SELECTION SORT: Splits list into sorted & unsorted, takes the greatest or smallest value and puts it into sorted section, repeat
  • INSERTION SORT: Splits list into sorted & unsorted, takes any value from list, inserts into correct position on sorted section, repeat
### Selection sort example
list = [5, 2, 9, 3, 6]

for i in range(len(list)):
    min_index = i
    for j in range(i + 1, len(list)):
        if list[j] < list[min_index]:
            min_index = j
    list[i], list[min_index] = list[min_index], list[i]

print("Smallest to Biggest: ", list)

Smallest to Biggest:  [2, 3, 5, 6, 9]
  • i represents the position of the value in the list that is being evaluated and is the starting value that it chosen as the smallest
  • j represents the position of a value outside the sorted position of the list
  • If j is smaller than the original minimum index, the new minimum index will be the value of j
  • Process of sortining most minimum number into index is continued until all numbers are in order from least to greatest
### Insertion sort example
def insertion_sort(list):
    for i in range(1, len(list)):
        key = list[i]
        j = i - 1
        while j >= 0 and key < list[j]:
            list[j + 1] = list[j]
            j -= 1
        list[j + 1] = key

list = [64, 25, 12, 22, 11]
insertion_sort(list)
print("Smallest to Biggest:", list)

Smallest to Biggest: [11, 12, 22, 25, 64]
  • i is starting point of unsorted section
  • key=list[i] is the current variable that is inserted into the sorted section, list[i] is the element at i index position
  • j+1 portion places the key in the proper location of the sorted section

Popcorn Hack #2

Use one of the two sorting methods to organize the following list from BIGGEST to SMALLEST:

[1,5,34,2,6,7,65,90,42]

### Insert your popcorn hack here:
list = [1, 5, 34, 2, 6, 7, 65, 90, 42]

for i in range(len(list)):
    min_index = i
    for j in range(i + 1, len(list)):
        if list[j] < list[min_index]:
            min_index = j
    list[i], list[min_index] = list[min_index], list[i]

print("Smallest to Biggest: ", list)

Smallest to Biggest:  [1, 2, 5, 6, 7, 34, 42, 65, 90]

Homework Hacks

Homework Hack 1

Create your own algorithm using a loop until you reach a desired value. Be creative!

# Example algorithm of loop

# Initialize a counter to keep track of the count of odd numbers
count = 0
# Loop through numbers from 1 to 10
for number in range(1, 11):  
 # Check if the number is odd
 if number % 2 != 0: 
        # Increment the count if the number is odd
        count += 1  

print("Count of odd numbers from 1 to 10:", count)

Count of odd numbers from 1 to 10: 5

## Insert your code here:
import random

def creative_number_quest(desired_number):
    current_number = 1
    count = 0

    while current_number < desired_number:
        # Generate a random action to progress towards the goal
        action = random.choice(["add", "double", "subtract", "square", "add_42"])
        
        if action == "add":
            current_number += random.randint(1, 10)
        elif action == "double":
            current_number *= 2
        elif action == "subtract":
            current_number -= random.randint(1, 5)
        elif action == "square":
            current_number = current_number ** 2
        elif action == "add_42":
            current_number += 42

        count += 1

    return count

desired_number = 100  # Set your desired number here
steps_taken = creative_number_quest(desired_number)

print(f"Hooray! You creatively reached your desired number {desired_number} in {steps_taken} imaginative steps.")


Hooray! You creatively reached your desired number 100 in 5 imaginative steps.

Homework Hack 2

Write two different algorithms of your own choosing that reach the same end output. Refer to the examples in the lesson above for support.

## Insert your code here:
## algorithm 1
def sum_even_numbers_with_loop(n):
    even_sum = 0
    for i in range(1, n + 1):
        if i % 2 == 0:
            even_sum += i
    return even_sum

# Example usage
n = 10
result1 = sum_even_numbers_with_loop(n)
print(f"The sum of even numbers from 1 to {n} is {result1}.")

##algorithm 2
def sum_even_numbers_with_formula(n):
    # Sum of even numbers formula: n * (n + 1)
    even_sum = (n // 2) * ((n // 2) + 1)
    return even_sum

# Example usage
n = 10
result2 = sum_even_numbers_with_formula(n)
print(f"The sum of even numbers from 1 to {n} is {result2}.")


The sum of even numbers from 1 to 10 is 30.
The sum of even numbers from 1 to 10 is 30.

Reflection:
Developing Algorithms:

  • Problem Solving: I learned that algorithms are step-by-step solutions to problems. They are like recipes for computers to follow.

  • Efficiency Matters: Developing efficient algorithms is crucial because it can make a significant difference in how quickly a program runs.

  • Logical Thinking: Algorithm development improved my logical thinking. I had to break problems down into smaller, manageable steps.

  • Algorithm Design Techniques: I explored various algorithm design techniques, such as divide and conquer, greedy algorithms, and dynamic programming. These techniques help solve different types of problems.

  • Data Structures: Understanding data structures like arrays, linked lists, and trees is essential for developing efficient algorithms. Picking the right data structure is key.

  • Complexity Analysis: I learned to analyze algorithm complexity using Big O notation. This helps predict how an algorithm will perform as the input size grows.

  • Iteration and Recursion: I worked with both iterative and recursive algorithms. Iteration involves loops, while recursion uses functions that call themselves.

  • Problem Decomposition: Breaking complex problems into smaller sub-problems simplifies algorithm development. It’s like solving a puzzle one piece at a time.

  • Testing and Debugging: I practiced testing and debugging algorithms to ensure they work correctly. Debugging helps find and fix errors in code.

  • Real-World Applications: I realized that algorithms are used in various real-world applications, from sorting data to route planning and machine learning.

  • In summary, learning to develop algorithms in computer science taught me problem-solving skills, logical thinking, and the importance of efficiency. These skills are essential for writing code that performs well and solves real-world problems effectively.