usaco-guide/content/5_Gold/SP.md

id	title	author	prerequisites	description
sp	Shortest Paths with Non-Negative Edge Weights	Benjamin Qi	Gold - Breadth First Search	Introduces Dijkstra's Algorithm for a single source as well as Floyd-Warshall for All-Pairs Shortest Path.

Non-Negative Edge Weights

Use Dijkstra's Algorithm.

Standard

• Kattis SSSP Non-Negative
• CSES Shortest Routes I

Tutorial

• CSES 13.2
• PAPS 12.3.1
• cp-algo Dijkstra (Dense Graphs)
• cp-algo Dijkstra (Sparse Graphs)
  • Usually, it's this one that's applicable.
• CPC.8

Problems

• CSES
  • CSES Flight Discount
  • CSES Flight Routes
  • CSES Investigation
• USACO
  • Milk Pumping
    • fairly standard application
  • Shortcut
  • Fine Dining
• Other
  • Lane Switching
  • Robot Turtles

All Pairs Shortest Path (APSP)

Use the Floyd-Warshall algorithm.

Standard

• CSES Shortest Routes II
• Kattis APSP (with negative weights)

Tutorial

• CPH 13.3
• PAPS 12.3.3
• cp-algo Floyd-Warshall

Problems

• USACO Moortal Cowmbat
  • Use APSP before running DP.
• SPOJ Arbitrage