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Graphs and Network Algorithms · Graph Traversal

DFS Algorithm

Depth-first search explores as far as possible along a path before backtracking.

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Student Focus

We connect DFS to recursion so students can transfer earlier skills into graph problems.

Guided Lesson Notes

How Code Scholars teaches DFS 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

  • Visited tracking
  • Recursive or stack-based traversal
  • Backtracking behavior

Practice Prompts

  • Trace DFS order on a graph with a cycle.
  • Use DFS to count connected components.

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.

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