usaco-guide/content/3_Gold/Gold_ShortestPath.md

Gold - Shortest Path

Author: Benjamin Qi

CPC.7

Breadth First Search

Find the shortest path where all edge weights are 1.

• CSES Message Route

Tutorial

• CSAcademy BFS
• cp-algo BFS
• cp-algo 0/1 BFS

Problems

• Cow Navigation
• Dream
• Lasers

• Monsters

Non-Negative Edge Weights

• Kattis SSSP Non-Negative
• CSES Shortest Routes I
• CSES Flight Discount
• CSES Flight Routes
• CSES Investigation

Use Dijkstra's Algorithm.

Tutorial

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

USACO Gold Problems

• Milk Pumping
  • fairly standard application
• Shortcut
• Fine Dining

All Pairs Shortest Path (APSP)

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

Use the Floyd-Warshall algorithm.

Tutorial

• CSES 13.3
• cp-algo Floyd-Warshall

USACO Gold Problems

• Moortal Cowmbat
  • Use APSP before running DP.

Negative Edge Weights

Hasn't appeared in recent USACO Gold as far as I know.

• CSES High Score
• Kattis SSSP Negative

Can also modify Dijkstra's so it works with negative edge weights (but not negative cycles). The same running time bound no longer applies.