Graphs and Network Algorithms · Shortest Paths

Bellman Ford's Algorithm

Bellman-Ford relaxes edges repeatedly, handling negative weights and detecting negative cycles.

Student Focus

We teach this after Dijkstra so students can compare the tradeoff between flexibility and speed.

Guided Lesson Notes

How Code Scholars teaches Bellman Ford's Algorithm

This guide helps students understand the idea, implement it carefully, explain the runtime, and recognize when the pattern belongs in a larger problem.

In a session, students usually start with a small trace, then write or review code, then test edge cases. The final step is a short explanation: what the structure or algorithm stores, why it is correct, and what changes when the input grows.

Key Ideas

  • Edge relaxation
  • Negative-weight support
  • Cycle detection

Practice Prompts

  • Trace one full relaxation pass over all edges.
  • Explain what a negative cycle means for shortest paths.

Tutoring Connection

Turn the topic into usable problem-solving skill

Students can use this page before a lesson, after a difficult homework assignment, or while preparing for AP Computer Science A extensions, Advanced Topics in CS, USACO growth, or a college data structures course.