Big O Notation

Big O Notation classifies algorithms by their speed.

What is Big O Notation? ⏱️

Big O Notation classifies types of algorithms by there speed. Big O Notation is used to determine how long an algorithm will take to complete.

Seconds or Years?⏲️

The point of Big O Notation is to give the user an idea of how fast or slow an algorithm will take to complete.

• Seconds? ⏲️
• Minutes? ⏳ ⌛
• Hours? 🕓
• Days? 🌞🌚
• Years? 🥳 🎂
• Centuries? 👶 ⚰️
• Millennia? 🗿
• Eons? ♾️

Math without the Math 🤔

Big O Notation works by approximating the total amount of steps an algorithm will take. lets create a list of the numbers 1 through 100 and classify different algorithms by their speed.

Array = [1,2,3..99,100]

• O(1)🚀

  • Fastest completion time possible

  • Fixed amount of steps

  • Example: 1 + 100

    • 2 steps

• O(log(N)) 🏎️

  • Fast Completion Time

  • The steps are a small fraction(log) of the size of the data

  • Example: 0 + 75 + 88 + 94 + 97 + 99

    • 6 steps

• O(N) 🏇

  • Completion time is okay

  • Steps are the size of the data

  • Example: 1+2+3+4+5...100

    • 100 steps

• O(N^2) 🐌

  • Completion time is slow

  • Steps are size of the data squared

  • Example: [1+2+3..100] + [2+3+4..100] + [3+4+5..100]...

    • 5050 steps

♾️Important to note as the size of the data grows, run times can approach infinity ♾️