114 lines
4.4 KiB
Text
114 lines
4.4 KiB
Text
---
|
|
id: dfs
|
|
title: Depth First Search
|
|
author: Siyong Huang
|
|
prerequisites:
|
|
- Bronze - Introduction to Graphs
|
|
description: A way to traverse a graph using recursion.
|
|
---
|
|
|
|
import { Problem } from "../models";
|
|
|
|
export const metadata = {
|
|
problems: {
|
|
sample: [
|
|
new Problem("CSES", "Building Roads", "1666", "Intro", false, ["DFS"]),
|
|
],
|
|
tree: [
|
|
new Problem("CSES", "Subordinates", "1674", "Intro", false, ["Tree", "DFS"]),
|
|
new Problem("Silver", "Mootube", "788", "Easy", false, ["Tree", "DFS"]),
|
|
new Problem("CF", "Journey", "contest/839/problem/C", "Easy", false, ["Tree", "DFS"]),
|
|
new Problem("CF", "PolandBall & Forest", "problemset/problem/755/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("CSA", "Tree Construction", "contest/860/problem/D", "Hard", false, ["Tree", "DFS"], "several cases"),
|
|
],
|
|
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", "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"]),
|
|
],
|
|
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"]),
|
|
],
|
|
}
|
|
};
|
|
|
|
|
|
<problems-list problems={metadata.problems.sample} />
|
|
|
|
## Tutorial
|
|
|
|
- Recommended:
|
|
- CPH 12.1 (DFS), 14 (Tree algorithms)
|
|
- [PAPS 12.2](https://www.csc.kth.se/~jsannemo/slask/main.pdf)
|
|
- [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
|
|
|
|
- Trees
|
|
|
|
<problems-list problems={metadata.problems.tree} />
|
|
|
|
- General
|
|
|
|
<problems-list problems={metadata.problems.general} />
|
|
|
|
## 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.
|
|
|
|
<problems-list problems={metadata.problems.bipsample} />
|
|
|
|
### Tutorial
|
|
|
|
- CPH 12.3
|
|
- [cp-algo - bipartite check](https://cp-algorithms.com/graph/bipartite-check.html)
|
|
- Uses BFS, but DFS accomplishes the same task
|
|
|
|
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
|
|
|
|
<problems-list problems={metadata.problems.bip} />
|