usaco-guide/content/3_Gold/4_Gold_TopoSort.md

---
slug: /gold/topological-sort
title: "Topological Sort"
author: Benjamin Qi
order: 4
---

Assumes familiarity with "Silver - Depth 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. 

<!-- END DESCRIPTION -->

## 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
 - [cp-algorithms](https://cp-algorithms.com/graph/topological-sort.html)
 - 

## 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)
add frontmatter to all modules 2020-06-04 01:42:57 +00:00			`---`
			`slug: /gold/topological-sort`
update frontmatter for all modules 2020-06-04 05:39:49 +00:00			`title: "Topological Sort"`
+ Plat 2020-06-04 03:26:53 +00:00			`author: Benjamin Qi`
update frontmatter for all modules 2020-06-04 05:39:49 +00:00			`order: 4`
add frontmatter to all modules 2020-06-04 01:42:57 +00:00			`---`

+ descriptions 2020-06-04 21:42:30 +00:00			`Assumes familiarity with "Silver - Depth First Search."`

+ some descriptions 2020-06-04 14:28:47 +00:00			`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.`
update frontmatter for all modules 2020-06-04 05:39:49 +00:00
+ some descriptions 2020-06-04 14:28:47 +00:00			`<!-- END DESCRIPTION -->`
+ plat stuff 2020-06-04 13:54:18 +00:00
+ some descriptions 2020-06-04 14:28:47 +00:00			`## Example Problems`
Gold_Graphs 2020-06-03 20:56:04 +00:00
+ graph probs 2020-06-03 21:08:42 +00:00			`- [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)`

+ plat stuff 2020-06-04 13:54:18 +00:00			`## Tutorial`
Gold_Graphs 2020-06-03 20:56:04 +00:00
			`- CPH 16.1, 16.2`
			`- [cp-algorithms](https://cp-algorithms.com/graph/topological-sort.html)`
+ some descriptions 2020-06-04 14:28:47 +00:00			`-`
Gold_Graphs 2020-06-03 20:56:04 +00:00
+ plat stuff 2020-06-04 13:54:18 +00:00			`## Problems`
Gold_Graphs 2020-06-03 20:56:04 +00:00
+ plat stuff 2020-06-04 13:54:18 +00:00			`- 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)`