124 lines
No EOL
4.9 KiB
Markdown
124 lines
No EOL
4.9 KiB
Markdown
---
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id: dfs
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title: Depth First Search
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author: Siyong Huang
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prerequisites:
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-
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- Bronze - Introduction to Graphs
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---
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<module-excerpt>
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- Depth First Search (DFS)
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- Flood Fill
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- Graph Two-Coloring
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</module-excerpt>
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## Depth First Search (DFS)
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*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.
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- [CSES Building Roads](https://cses.fi/problemset/task/1666)
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### Tutorial
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- Recommended:
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- CPH 12.1
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- [CSAcademy DFS](https://csacademy.com/lesson/depth_first_search/)
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- Additional:
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- [CPC.7](https://github.com/SuprDewd/T-414-AFLV/tree/master/07_graphs_1)
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- [cp-algo DFS](https://cp-algorithms.com/graph/depth-first-search.html)
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- hard to parse if this is your first time learning about DFS
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- [Topcoder Graphs Pt 2](https://www.topcoder.com/community/data-science/data-science-tutorials/introduction-to-graphs-and-their-data-structures-section-2/)
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### Problems
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- CF
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- [PolandBall & Forest](http://codeforces.com/problemset/problem/755/C) [](56)
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- [Bear & Friendship](http://codeforces.com/problemset/problem/771/A)
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- [Journey](http://codeforces.com/contest/839/problem/C) [](54)
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- DFS on Tree
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- [Wizard's Tour](http://codeforces.com/contest/860/problem/D) [](59)
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- USACO
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- [Mootube, Silver (Easy)](http://usaco.org/index.php?page=viewproblem2&cpid=788)
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- [Closing the Barn, Silver (Easy)](http://usaco.org/index.php?page=viewproblem2&cpid=644)
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- [Moocast, Silver (Easy)](http://usaco.org/index.php?page=viewproblem2&cpid=668)
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- [Pails (Normal)](http://usaco.org/index.php?page=viewproblem2&cpid=620)
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- [Milk Visits (Normal)](http://www.usaco.org/index.php?page=viewproblem2&cpid=968)
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- [Count Cross](http://usaco.org/index.php?page=viewproblem2&cpid=716)
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- [Wormhole Sort (Normal)](http://www.usaco.org/index.php?page=viewproblem2&cpid=992)
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- also binary search on the answer
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- [Fence Planning](http://usaco.org/index.php?page=viewproblem2&cpid=944)
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- [Moo Particle](http://www.usaco.org/index.php?page=viewproblem2&cpid=1040)
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- Other
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- [POI Hotels](https://szkopul.edu.pl/problemset/problem/gDw3iFkeVm7ZA3j_16-XR7jI/site/?key=statement) [](61)
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- [Kattis Birthday Party (Easy)](https://open.kattis.com/problems/birthday)
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- DFS with each edge removed
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## Flood Fill
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[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.
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- [CSES Counting Rooms](https://cses.fi/problemset/task/1192)
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- [CSES Labyrinth](https://cses.fi/problemset/task/1193)
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### Tutorial
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- Recommended:
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- Ch 10 of https://www.overleaf.com/project/5e73f65cde1d010001224d8a
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### Problems
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- [Ice Perimeter (Easy)](http://usaco.org/index.php?page=viewproblem2&cpid=895)
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- [Switching on the Lights (Normal)](http://www.usaco.org/index.php?page=viewproblem2&cpid=570)
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- [Build Gates (Normal)](http://www.usaco.org/index.php?page=viewproblem2&cpid=596)
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- [Milk Pails (Normal)](http://usaco.org/index.php?page=viewproblem2&cpid=620)
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- [Where's Bessie?](http://usaco.org/index.php?page=viewproblem2&cpid=740)
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- [Why Did the Cow Cross the Road III, Silver (Normal)](http://usaco.org/index.php?page=viewproblem2&cpid=716)
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- [Multiplayer Moo (Hard)](http://usaco.org/index.php?page=viewproblem2&cpid=836)
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- [Snow Boots (Hard)](http://usaco.org/index.php?page=viewproblem2&cpid=811)
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- [Mooyo Mooyo](http://usaco.org/index.php?page=viewproblem2&cpid=860)
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## Graph Two-Coloring
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*Graph two-coloring* refers to assigning a boolean value to each node of the graph, dictated by the edge configuration
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The most common example of a two-colored graph is a *bipartite graph*, in which each edge connects two nodes of opposite colors.
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- [CSES Building Teams](https://cses.fi/problemset/task/1668)
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### Tutorial
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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.
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```cpp
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//UNTESTED
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bool is_bipartite = true;
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void dfs(int node)
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{
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visited[node] = true;
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for(int u:adj_list[node])
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if(visited[u])
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{
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if(color[u] == color[node])
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is_bipartite = false;
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}
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else
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{
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color[u] = !color[node];
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dfs(u);
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}
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}
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```
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- Additional:
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- [Bipartite Graphs: cp-alg bipartite check](https://cp-algorithms.com/graph/bipartite-check.html)
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- Note: CP-Algorithms uses BFS, but DFS accomplishes the same task
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### Problems
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- [CF Bipartiteness](http://codeforces.com/contest/862/problem/B) [](49)
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- [The Great Revegetation (Normal)](http://usaco.org/index.php?page=viewproblem2&cpid=920) |