Topological Sort — The “What Comes First” Guide

Shreyas Naphad
Jul 10
1 min read

Let’s say you’re baking a cake 🎂. You must mix ingredients before baking, and you can’t bake before heating the oven. You need a clear order of tasks.

That’s where Topological Sort shines. It helps you find the correct order to do things when certain tasks depend on others.

🧠 What It Solves

Topological sort is for Directed Acyclic Graphs (DAGs) — graphs with one-way edges and no loops.

It gives you a linear order of nodes, respecting dependencies.

🛠️ How It Works

Two common methods:

1. DFS-Based

Run DFS
When a node is finished, push it to a stack
Reverse the stack → That’s the order

2. Kahn’s Algorithm (BFS)

Track nodes with no incoming edges
Keep removing them and updating the graph
Each removed node gets added to the final order

🧁 Real-Life Analogy

Baking cake, doing laundry, coding a feature

Some tasks can’t start until others finish.Topological sort helps you build a timeline that respects all rules.

📍 Where It’s Used

Task scheduling
Course prerequisite planning
Resolving package dependencies

✅ Final Thought

Topological Sort is like your personal assistant 🧾 — organizing your day in the only valid way things can happen without breaking anything.