---
id: toposort
title: "Topological Sort"
author: Benjamin Qi
prerequisites: 
 - 
     - Gold - Breadth First Search
---

A [topological sort](https://en.wikipedia.org/wiki/Topological_sorting) of a directed graph is a linear ordering of its vertices such that for every directed edge $u\to v$ from vertex $u$ to vertex $v$, $u$ comes before $v$ in the ordering. 

## Example Problems

 - [CSES Course Schedule](https://cses.fi/problemset/task/1679)
 - [CSES Longest Flight Route](https://cses.fi/problemset/task/1680)
 - [CSES Game Routes](https://cses.fi/problemset/task/1681)

## Tutorial

 - CPH 16.1, 16.2
   - DFS
 - [cp-algorithms](https://cp-algorithms.com/graph/topological-sort.html)
   - DFS
 - [CSAcademy](https://csacademy.com/lesson/topological_sorting)
   - both BFS, DFS

## Problems

 - USACO Gold
   - [Timeline](http://www.usaco.org/index.php?page=viewproblem2&cpid=1017)
   - [Milking Order](http://www.usaco.org/index.php?page=viewproblem2&cpid=838)
 - Other
   - [Minimal Labels](http://codeforces.com/contest/825/problem/E) [](53)
   - [Quantum](https://open.kattis.com/contests/acpc17open/problems/quantumsuperposition) [](84)