What is the Ordering Dependencies (Topological Sort) pattern?

The Ordering Dependencies (Topological Sort) is a common coding interview pattern in Graphs problems. It provides a structured approach to solving related algorithm challenges efficiently.

When should I use Ordering Dependencies (Topological Sort)?

Use the Ordering Dependencies (Topological Sort) pattern when you encounter problems matching its characteristics. Check the "When to Use" and "Clues" sections in the lesson for specific indicators.

Is Ordering Dependencies (Topological Sort) asked in FAANG interviews?

Yes, Ordering Dependencies (Topological Sort) is an essential pattern commonly tested in FAANG and top tech company technical interviews.

Graphs (Topological Sort)

Medium

Ordering Dependencies (Topological Sort)

Learn how to order tasks with dependencies using Topological Sort and detect cycles.

12 min

Solve on LeetCode

What is Topological Sort?

Given a Directed Acyclic Graph (DAG), a Topological Sort is a linear ordering of vertices such that for every directed edge u -> v, vertex u comes before vertex v.

It is the standard algorithm for resolving dependencies (e.g., compiling code, scheduling tasks, course prerequisites).

The Motivation: Course Schedule

You need to take N courses. Some courses have prerequisites.

Physics II requires Physics I.
Calc III requires Calc II requires Calc I.

Goal: Find a valid order to take ALL courses. If impossible (due to a cycle), tell us.

The Cycle Problem

What if you have a cycle?

Course A requires Course B.
Course B requires Course A.

You can never start! This is a Circular Dependency. A Topological Sort is ONLY possible if the graph has NO Cycles (DAG).

Visualizing a Cycle

Step 1 / 1

Visualization coming soon...

Initializing...

Custom Input

See the Logic in Motion

Stop memorizing code. Unlock the full interactive visualizer to master the logic step-by-step.

Unlock VisualizerPREMIUM FEATURE

When to use Topological Sort?

Pattern Recognition Triggers:

Dependencies: Keywords like "prerequisites", "build order", "depends on".
Linear Ordering: You need to arrange items in a sequence respecting constraints.
Directed Graph: The relationships are one-way.

The Intuition: Find the Start

To start, we must find a node that has NO prerequisites (Indegree = 0).

Pick a node with Indegree == 0. Add it to our sorted list.
"Remove" it from the graph.
When removed, its neighbors' indegrees decrease.
Repeat until all nodes are picked.

This is Kahn's Algorithm.

Interactive Walkthrough (Kahn's Algo)