2020-06-04 01:42:57 +00:00
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---
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2020-06-15 23:19:07 +00:00
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id: sp
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2020-06-22 01:45:24 +00:00
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title: "Shortest Paths with Non-Negative Edge Weights"
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2020-06-04 01:42:57 +00:00
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author: Benjamin Qi
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2020-06-05 00:21:03 +00:00
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prerequisites:
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2020-06-22 20:51:12 +00:00
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- Gold - Breadth First Search
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2020-06-22 19:59:16 +00:00
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description: Introduces Dijkstra's Algorithm for a single source as well as Floyd-Warshall for All-Pairs Shortest Path.
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2020-06-04 01:42:57 +00:00
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---
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2020-06-03 21:08:42 +00:00
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## Non-Negative Edge Weights
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Use *Dijkstra's Algorithm*.
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### Standard
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- [Kattis SSSP Non-Negative](https://open.kattis.com/problems/shortestpath1)
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- [CSES Shortest Routes I](https://cses.fi/problemset/task/1671)
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### Tutorial
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- CSES 13.2
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- [PAPS 12.3.1](https://www.csc.kth.se/~jsannemo/slask/main.pdf)
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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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- [CPC.8](https://github.com/SuprDewd/T-414-AFLV/tree/master/08_graphs_2)
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### Problems
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- CSES
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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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- USACO
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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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- Other
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- [Lane Switching](https://open.kattis.com/contests/acpc17open/problems/laneswitching)
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- [Robot Turtles](https://open.kattis.com/problems/robotturtles) [](100)
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## All Pairs Shortest Path (APSP)
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Use the *Floyd-Warshall* algorithm.
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2020-06-04 21:42:30 +00:00
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### Standard
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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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### Tutorial
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- CPH 13.3
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- [PAPS 12.3.3](https://www.csc.kth.se/~jsannemo/slask/main.pdf)
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- [cp-algo Floyd-Warshall](https://cp-algorithms.com/graph/all-pair-shortest-path-floyd-warshall.html)
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### Problems
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- [USACO Moortal Cowmbat](http://usaco.org/index.php?page=viewproblem2&cpid=971)
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- Use APSP before running DP.
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- [SPOJ Arbitrage](https://www.spoj.com/problems/ARBITRAG/)
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