Overview

Algorithms are the recipes of the digital world. They are step-by-step instructions for solving a problem. From Google Search to your GPS, algorithms run modern life.

Core Idea

The core idea is Efficiency. How do we solve a problem using the least amount of time and memory?

Formal Definition

A finite sequence of well-defined, computer-implementable instructions, typically to solve a class of problems or to perform a computation.

Intuition

  • The Recipe: To bake a cake, you follow steps: Mix flour, add eggs, bake at 350. That’s an algorithm.
  • Sorting Cards: How do you sort a deck of cards?
    • Bubble Sort: Compare two, swap if wrong. Repeat forever. (Slow).
    • Merge Sort: Split deck in half, sort halves, merge. (Fast).

Examples

  • PageRank: The algorithm that made Google. It ranks web pages by how many other pages link to them.
  • Dijkstra’s Algorithm: Finding the shortest path on a map (GPS).
  • RSA: The algorithm that secures the internet (Cryptography).

Common Misconceptions

  • Misconception: Algorithms are unbiased.
    • Correction: Algorithms are written by humans and trained on human data. They can inherit and amplify Bias (e.g., facial recognition working poorly on minorities).
  • Misconception: It’s “magic.”
    • Correction: It’s just math. Input -> Logic -> Output.

Applications

  • Finance: High-frequency trading.
  • Biology: DNA sequencing.
  • Social Media: The “Feed” algorithm that decides what you see.

Criticism and Limitations

  • Black Box: Deep Learning algorithms are often uninterpretable. We know that they work, but not how.

Further Reading

  • Introduction to Algorithms by CLRS
  • Algorithms to Live By by Brian Christian