---
id: dfs
title: Depth First Search (DFS)
author: Siyong Huang
prerequisites:
- intro-graphs
description: "A way to recursively traverse through a graph."
frequency: 4
---
import { Problem } from "../models";
export const metadata = {
problems: {
sample: [
new Problem("CSES", "Building Roads", "1666", "Intro|Very Easy", false, ["DFS"]),
],
general: [
new Problem("CF", "Bear & Friendship", "problemset/problem/771/A", "Easy", false, ["DFS"]),
new Problem("Silver", "Closing the Farm", "644", "Easy", false, ["DFS"]),
new Problem("Silver", "Moocast", "668", "Easy", false, ["DFS"]),
new Problem("Silver", "Fence Planning", "944", "Easy", false, ["DFS"]),
new Problem("Kattis", "Birthday Party", "birthday", "Easy", false, ["DFS"], "DFS with each edge removed"),
new Problem("Silver", "Mootube", "788", "Easy", false, ["Tree", "DFS"]),
new Problem("CF", "PolandBall & Forest", "problemset/problem/755/C", "Easy", false, ["Tree", "DFS"]),
new Problem("Silver", "Milk Visits", "968", "Normal", false, ["DFS"]),
new Problem("Silver", "Milk Pails", "620", "Normal", false, ["DFS"]),
new Problem("Silver", "Wormhole Sort", "992", "Normal", false, ["DFS", "Binary Search"]),
new Problem("Silver", "Moo Particle", "1040", "Normal", false, ["Sorting"]),
],
tree: [
new Problem("CSES", "Subordinates", "1674", "Very Easy", false, ["Tree", "DFS"]),
new Problem("CF", "Journey", "contest/839/problem/C", "Easy", false, ["Tree", "DFS"]),
new Problem("CSES", "Tree Diameter", "1131", "Normal", false, ["Tree", "DFS"]),
new Problem("CSES", "Tree Distances I", "1132", "Normal", false, ["Tree", "DFS"]),
new Problem("CSES", "Tree Distances II", "1133", "Normal", false, ["Tree", "DFS"]),
new Problem("CF", "Wizard's Tour", "contest/860/problem/D", "Normal", false, ["Tree", "DFS"]),
new Problem("POI", "Hotels", "https://szkopul.edu.pl/problemset/problem/gDw3iFkeVm7ZA3j_16-XR7jI/site/?key=statement", "Normal", false, ["Tree", "DFS"]),
new Problem("HE", "Birthday Gifts", "https://www.hackerearth.com/practice/math/combinatorics/inclusion-exclusion/practice-problems/algorithm/mancunian-and-birthday-gifts-d44faa15/description/", "Normal", false, ["Tree", "PIE"], ""),
new Problem("CSA", "Tree Construction", "contest/860/problem/D", "Hard", false, ["Tree", "DFS"], "several cases"),
],
bipsample: [
new Problem("CSES", "Building Teams", "1668", "Easy", false, ["Bipartite"]),
],
bip: [
new Problem("CF", "Bipartiteness", "contest/862/problem/B", "Easy", false, ["Bipartite"]),
new Problem("Silver", "The Great Revegetation", "920", "Easy", false, ["Bipartite"]),
],
}
};
## Resources
interactive
with an example problem
fast-paced
hard to parse for a beginner
## Counting Connected Components
### Implementation
(code?)
### Problems
## Tree Problems
### Implementation
(code?)
### Problems
## 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.
### Resources
Uses BFS, but DFS accomplishes the same task.
### Implementation
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);
}
}
```
### Problems