+ graph probs

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Benjamin Qi 2020-06-03 17:08:42 -04:00
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# Gold - Minimum Spanning Tree
* [Kattis Minimum Spanning Tree](https://open.kattis.com/problems/minspantree)
- [Kattis Minimum Spanning Tree](https://open.kattis.com/problems/minspantree)
- [CSES Road Reparation](https://cses.fi/problemset/task/1675)
- equivalent to above
## Tutorial
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- also special ...
- DSU Problems
- [Mootube](http://www.usaco.org/index.php?page=viewproblem2&cpid=789)
- same as [CSES Road Construction](https://cses.fi/problemset/task/1676)
- [Closing the Farm](http://www.usaco.org/index.php?page=viewproblem2&cpid=646)
- [Favorite Colors](http://www.usaco.org/index.php?page=viewproblem2&cpid=1042)
- fairly tricky

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## Breadth First Search
Find the shortest path where all edge weights are 1.
* [CSES Message Route](https://cses.fi/problemset/task/1667)
### Tutorial
- [CSAcademy BFS](https://csacademy.com/lesson/breadth_first_search)
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- [Cow Navigation](http://www.usaco.org/index.php?page=viewproblem2&cpid=695)
- [Dream](http://www.usaco.org/index.php?page=viewproblem2&cpid=575)
- [Lasers](http://www.usaco.org/index.php?page=viewproblem2&cpid=671)
* [Monsters](https://cses.fi/problemset/task/1194)
## Shortest Path
### Non-Negative Edge Weights
## Non-Negative Edge Weights
* [Kattis SSSP Non-Negative](https://open.kattis.com/problems/shortestpath1)
* [CSES Shortest Routes I](https://cses.fi/problemset/task/1671)
* [CSES Flight Discount](https://cses.fi/problemset/task/1195)
* [CSES Flight Routes](https://cses.fi/problemset/task/1196)
* [CSES Investigation](https://cses.fi/problemset/task/1202)
For non-negative weights, use *Dijkstra's Algorithm:*
Use *Dijkstra's Algorithm*.
#### Tutorial
### Tutorial
* CSES 13.2
* [cp-algo Dijkstra (Dense Graphs)](https://cp-algorithms.com/graph/dijkstra_sparse.html)
* [cp-algo Dijkstra (Sparse Graphs)](https://cp-algorithms.com/graph/dijkstra_sparse.html)
* Usually, it's this one that's applicable.
#### USACO Gold Problems
### USACO Gold Problems
* [Milk Pumping](http://www.usaco.org/index.php?page=viewproblem2&cpid=969)
* fairly standard application
* [Shortcut](http://usaco.org/index.php?page=viewproblem2&cpid=899)
* [Fine Dining](http://usaco.org/index.php?page=viewproblem2&cpid=861)
### All Pairs
## All Pairs Shortest Path (APSP)
* [Kattis All Pairs Shortest Path](https://open.kattis.com/problems/allpairspath)
* [CSES Shortest Routes II](https://cses.fi/problemset/task/1672)
* [Kattis APSP (with negative weights)](https://open.kattis.com/problems/allpairspath)
Use the *Floyd-Warshall* algorithm.
#### Tutorial
### Tutorial
* CSES 13.3
* [cp-algo Floyd-Warshall](https://cp-algorithms.com/graph/all-pair-shortest-path-floyd-warshall.html)
#### USACO Gold Problems
### USACO Gold Problems
* [Moortal Cowmbat](http://usaco.org/index.php?page=viewproblem2&cpid=971)
* Use APSP before running DP.
### Negative Edge Weights
## Negative Edge Weights
Hasn't appeared in recent USACO Gold as far as I know.
* [CSES High Score](https://cses.fi/problemset/task/1673)
* [Kattis SSSP Negative](https://open.kattis.com/problems/shortestpath3)
Can also modify Dijkstra's so it works with negative edge weights but not negative cycles. Running time bound no longer applies.
Can also modify Dijkstra's so it works with negative edge weights (but not negative cycles). The same running time bound no longer applies.

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## Gold - Topological Sort
- [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