APCSP_Algorithms_Lesson.md

Introduction to Algorithms in JavaScript

AP Computer Science Principles (AP CSP)

Key Vocabulary

• Algorithm: A step-by-step procedure to solve a problem
• Pseudocode: Notational system for algorithms using plain language
• Efficiency: A measure of time/space resources required by an algorithm
• Iteration: Repeating steps in an algorithm
• Selection: Conditional decision-making in algorithms (if-else)
• Abstraction: Simplifying complex systems by focusing on key ideas

---

What is an Algorithm?

An algorithm is a set of clear, step-by-step instructions to perform a task or solve a problem.

In computer science, algorithms can be expressed in pseudocode or a programming language like JavaScript.

---

Why Are Algorithms Important?

Algorithms allow computers to automate tasks, solve problems, and perform complex calculations efficiently.

Understanding algorithms is critical to success in computer science.

---

Components of an Algorithm

• Sequencing: The order in which instructions are executed
• Selection: Decision-making based on conditions (e.g., if statements)
• Iteration: Repeating instructions using loops (for, while)

---

Example 1: Max of Two Numbers

Pseudocode:

1. Input number1 and number2
2. If number1 > number2:
    Return number1
3. Else:
    Return number2

JavaScript:

function findMax(num1, num2) {
  if (num1 > num2) {
    return num1;
  } else {
    return num2;
  }
}

---

Example 2: Even or Odd

Pseudocode:

1. Input number
2. If number % 2 == 0:
    Output 'Even'
3. Else:
    Output 'Odd'

JavaScript:

function checkEvenOdd(number) {
  if (number % 2 === 0) {
    console.log("Even");
  } else {
    console.log("Odd");
  }
}

---

Example 3: Sum of Numbers to n (Iteration)

Pseudocode:

1. Input n
2. Set sum = 0
3. For i = 1 to n:
    sum = sum + i
4. Output sum

JavaScript:

function sumToN(n) {
  let sum = 0;
  for (let i = 1; i <= n; i++) {
    sum += i;
  }
  return sum;
}

---

Efficiency and Complexity

• Time Complexity: How long an algorithm takes to run relative to input size (e.g., O(n), O(log n))
• Space Complexity: The amount of memory the algorithm uses

---

Practice Problem: Factorial of n

Pseudocode:

JavaScript:

---