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usaco-guide/content/4_Silver/DFS.md
2020-06-16 13:09:59 -04:00

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---
id: dfs
title: Depth First Search
author: Siyong Huang
prerequisites:
-
- Bronze - Introduction to Graphs
---
- Depth First Search (DFS)
- Flood Fill
- Graph Two-Coloring
<!-- END DESCRIPTION -->
## Depth First Search (DFS)
*Depth First Search*, more commonly DFS, is a fundamental graph algorithm that traverses an entire connected component. The rest of this document describes various applications of DFS. Of course, it is one possible way to implement flood fill. *Breadth first search* (BFS) is **not** required for silver.
- [CSES Building Roads](https://cses.fi/problemset/task/1666)
### Tutorial
- Recommended:
- CPH 12.1
- [CSAcademy DFS](https://csacademy.com/lesson/depth_first_search/)
- Additional:
- [CPC.7](https://github.com/SuprDewd/T-414-AFLV/tree/master/07_graphs_1)
- [cp-algo DFS](https://cp-algorithms.com/graph/depth-first-search.html)
- hard to parse if this is your first time learning about DFS
- [Topcoder Graphs Pt 2](https://www.topcoder.com/community/data-science/data-science-tutorials/introduction-to-graphs-and-their-data-structures-section-2/)
### Problems
- CF
- [PolandBall & Forest](http://codeforces.com/problemset/problem/755/C) [](56)
- [Bear & Friendship](http://codeforces.com/problemset/problem/771/A)
- [Journey](http://codeforces.com/contest/839/problem/C) [](54)
- DFS on Tree
- [Wizard's Tour](http://codeforces.com/contest/860/problem/D) [](59)
- USACO
- [Mootube, Silver (Easy)](http://usaco.org/index.php?page=viewproblem2&cpid=788)
- [Closing the Barn, Silver (Easy)](http://usaco.org/index.php?page=viewproblem2&cpid=644)
- [Moocast, Silver (Easy)](http://usaco.org/index.php?page=viewproblem2&cpid=668)
- [Pails (Normal)](http://usaco.org/index.php?page=viewproblem2&cpid=620)
- [Milk Visits (Normal)](http://www.usaco.org/index.php?page=viewproblem2&cpid=968)
- [Count Cross](http://usaco.org/index.php?page=viewproblem2&cpid=716)
- [Wormhole Sort (Normal)](http://www.usaco.org/index.php?page=viewproblem2&cpid=992)
- also binary search on the answer
- [Fence Planning](http://usaco.org/index.php?page=viewproblem2&cpid=944)
- [Moo Particle](http://www.usaco.org/index.php?page=viewproblem2&cpid=1040)
- Other
- [POI Hotels](https://szkopul.edu.pl/problemset/problem/gDw3iFkeVm7ZA3j_16-XR7jI/site/?key=statement) [](61)
- [Kattis Birthday Party (Easy)](https://open.kattis.com/problems/birthday)
- DFS with each edge removed
## Flood Fill
[Flood Fill](https://en.wikipedia.org/wiki/Flood_fill) refers to finding the number of connected components in a graph, usually when the graph is a grid.
- [CSES Counting Rooms](https://cses.fi/problemset/task/1192)
- [CSES Labyrinth](https://cses.fi/problemset/task/1193)
### Tutorial
- Recommended:
- Ch 10 of https://www.overleaf.com/project/5e73f65cde1d010001224d8a
### Problems
- [Ice Perimeter (Easy)](http://usaco.org/index.php?page=viewproblem2&cpid=895)
- [Switching on the Lights (Normal)](http://www.usaco.org/index.php?page=viewproblem2&cpid=570)
- [Build Gates (Normal)](http://www.usaco.org/index.php?page=viewproblem2&cpid=596)
- [Milk Pails (Normal)](http://usaco.org/index.php?page=viewproblem2&cpid=620)
- [Where's Bessie?](http://usaco.org/index.php?page=viewproblem2&cpid=740)
- [Why Did the Cow Cross the Road III, Silver (Normal)](http://usaco.org/index.php?page=viewproblem2&cpid=716)
- [Multiplayer Moo (Hard)](http://usaco.org/index.php?page=viewproblem2&cpid=836)
- [Snow Boots (Hard)](http://usaco.org/index.php?page=viewproblem2&cpid=811)
- [Mooyo Mooyo](http://usaco.org/index.php?page=viewproblem2&cpid=860)
## Graph Two-Coloring
*Graph two-coloring* refers to assigning a boolean value to each node of the graph, dictated by the edge configuration
The most common example of a two-colored graph is a *bipartite graph*, in which each edge connects two nodes of opposite colors.
- [CSES Building Teams](https://cses.fi/problemset/task/1668)
### Tutorial
The idea is that we can arbitrarily label a node and then run DFS. Every time we visit a new (unvisited) node, we set its color based on the edge rule. When we visit a previously visited node, check to see whether its color matches the edge rule. For example, an implementation of coloring a bipartite graph is shown below.
```cpp
//UNTESTED
bool is_bipartite = true;
void dfs(int node)
{
visited[node] = true;
for(int u:adj_list[node])
if(visited[u])
{
if(color[u] == color[node])
is_bipartite = false;
}
else
{
color[u] = !color[node];
dfs(u);
}
}
```
- Additional:
- [Bipartite Graphs: cp-alg bipartite check](https://cp-algorithms.com/graph/bipartite-check.html)
- Note: CP-Algorithms uses BFS, but DFS accomplishes the same task
### Problems
- [CF Bipartiteness](http://codeforces.com/contest/862/problem/B) [](49)
- [The Great Revegetation (Normal)](http://usaco.org/index.php?page=viewproblem2&cpid=920)