2020-06-04 01:42:57 +00:00
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---
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2020-06-04 02:09:42 +00:00
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slug: /gold/sp
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2020-06-04 01:42:57 +00:00
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title: "Gold - Shortest Path"
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author: Benjamin Qi
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---
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2020-06-03 20:56:04 +00:00
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# Gold - Shortest Path
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Author: Benjamin Qi
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[CPC.7](https://github.com/SuprDewd/T-414-AFLV/tree/master/07_graphs_1)
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## Breadth First Search
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2020-06-03 21:08:42 +00:00
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Find the shortest path where all edge weights are 1.
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* [CSES Message Route](https://cses.fi/problemset/task/1667)
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2020-06-03 20:56:04 +00:00
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### Tutorial
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- [CSAcademy BFS](https://csacademy.com/lesson/breadth_first_search)
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- [cp-algo BFS](https://cp-algorithms.com/graph/breadth-first-search.html)
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- [cp-algo 0/1 BFS](https://cp-algorithms.com/graph/01_bfs.html)
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### Problems
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- [Cow Navigation](http://www.usaco.org/index.php?page=viewproblem2&cpid=695)
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- [Dream](http://www.usaco.org/index.php?page=viewproblem2&cpid=575)
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- [Lasers](http://www.usaco.org/index.php?page=viewproblem2&cpid=671)
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2020-06-03 21:08:42 +00:00
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* [Monsters](https://cses.fi/problemset/task/1194)
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2020-06-03 20:56:04 +00:00
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2020-06-03 21:08:42 +00:00
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## Non-Negative Edge Weights
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2020-06-03 20:56:04 +00:00
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* [Kattis SSSP Non-Negative](https://open.kattis.com/problems/shortestpath1)
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2020-06-03 21:08:42 +00:00
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* [CSES Shortest Routes I](https://cses.fi/problemset/task/1671)
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* [CSES Flight Discount](https://cses.fi/problemset/task/1195)
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* [CSES Flight Routes](https://cses.fi/problemset/task/1196)
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* [CSES Investigation](https://cses.fi/problemset/task/1202)
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2020-06-03 20:56:04 +00:00
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2020-06-03 21:08:42 +00:00
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Use *Dijkstra's Algorithm*.
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2020-06-03 20:56:04 +00:00
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2020-06-03 21:08:42 +00:00
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### Tutorial
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2020-06-03 20:56:04 +00:00
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* CSES 13.2
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* [cp-algo Dijkstra (Dense Graphs)](https://cp-algorithms.com/graph/dijkstra_sparse.html)
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* [cp-algo Dijkstra (Sparse Graphs)](https://cp-algorithms.com/graph/dijkstra_sparse.html)
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* Usually, it's this one that's applicable.
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2020-06-03 21:08:42 +00:00
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### USACO Gold Problems
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2020-06-03 20:56:04 +00:00
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* [Milk Pumping](http://www.usaco.org/index.php?page=viewproblem2&cpid=969)
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* fairly standard application
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* [Shortcut](http://usaco.org/index.php?page=viewproblem2&cpid=899)
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* [Fine Dining](http://usaco.org/index.php?page=viewproblem2&cpid=861)
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2020-06-03 21:08:42 +00:00
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## All Pairs Shortest Path (APSP)
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2020-06-03 20:56:04 +00:00
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2020-06-03 21:08:42 +00:00
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* [CSES Shortest Routes II](https://cses.fi/problemset/task/1672)
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* [Kattis APSP (with negative weights)](https://open.kattis.com/problems/allpairspath)
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2020-06-03 20:56:04 +00:00
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Use the *Floyd-Warshall* algorithm.
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2020-06-03 21:08:42 +00:00
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### Tutorial
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2020-06-03 20:56:04 +00:00
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* CSES 13.3
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* [cp-algo Floyd-Warshall](https://cp-algorithms.com/graph/all-pair-shortest-path-floyd-warshall.html)
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2020-06-03 21:08:42 +00:00
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### USACO Gold Problems
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2020-06-03 20:56:04 +00:00
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* [Moortal Cowmbat](http://usaco.org/index.php?page=viewproblem2&cpid=971)
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* Use APSP before running DP.
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2020-06-03 21:08:42 +00:00
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## Negative Edge Weights
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2020-06-03 20:56:04 +00:00
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Hasn't appeared in recent USACO Gold as far as I know.
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2020-06-03 21:08:42 +00:00
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* [CSES High Score](https://cses.fi/problemset/task/1673)
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2020-06-03 20:56:04 +00:00
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* [Kattis SSSP Negative](https://open.kattis.com/problems/shortestpath3)
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2020-06-03 23:46:28 +00:00
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* [CSES Cycle Finding](https://cses.fi/problemset/task/1197)
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2020-06-03 20:56:04 +00:00
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2020-06-03 21:08:42 +00:00
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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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