📅 Day 1: Introduction to Algorithms & Big O Notation

🧠 Concept

An algorithm is a step-by-step method to solve a problem — just like a cooking recipe. Computers follow these “recipes” to process data and make decisions.

Big O Notation is how we talk about how fast (or slow) an algorithm is. It tells us how the time or memory usage of your code grows with the input size n.

Big O	Name	Example
O(1)	Constant Time	Access array element
O(n)	Linear Time	Loop through an array
O(n²)	Quadratic Time	Nested loops
O(log n)	Logarithmic Time	Binary Search

Think of O(n) as a chore that takes longer the more things you have — like checking every item in a list.

👨‍💻 Example

function findMax(arr: number[]): number {
  let max = arr[0]; // O(1) - constant time
  for (let i = 1; i < arr.length; i++) { // O(n) - linear time
    if (arr[i] > max) {
      max = arr[i];
    }
  }
  return max;
}

Time Complexity: O(n)
We look at every element once.

📊 ASCII Trace

Input: [3, 8, 2, 9]

Start: max = 3
→ 8 > 3 → max = 8
→ 2 > 8 → ❌
→ 9 > 8 → max = 9
Return 9

🏁 Homework

✍️ Problem: Return the smallest element in an array.

function findMin(arr: number[]): number {
  // your code here
}

Example:

Input: [4, 2, 7, 1, 9]
Output: 1

🔜 Up Next:

Day 2: Big O Notation – O(1), O(n), O(n²)