Skip to content

Eulerian Path / Cycle Ladder

This lane should make use every edge exactly once feel like one reusable graph family instead of a bag of one-off construction problems.

Who This Is For

Use this lane if:

  • parity and indegree/outdegree conditions still feel memorized rather than structural
  • you know the word Hierholzer, but cannot yet derive when a trail exists
  • the name clash with Euler Tour / Subtree Queries still causes hesitation

Warm-Up

  • graph connectivity versus isolated vertices
  • odd degree in undirected graphs
  • indegree/outdegree balance in directed graphs

Target skill:

  • say the path-versus-cycle existence rule in words before coding

Core

  • Mail Delivery
  • iterative Hierholzer
  • edge ids for multiedges
  • final path.size() == m + 1 guard

Target skill:

  • move cleanly from degree feasibility to one exact constructive traversal

Stretch

Target skill:

  • know whether the next task is still one Eulerian trail problem, or whether the hard part is now graph modeling first

Retrieval Layer

Repo Anchors And Compare Points

The strongest in-repo loop here is:

  1. learn the degree / balance split from the topic page
  2. solve or revisit Mail Delivery as the clean undirected flagship
  3. reopen the Eulerian hot sheet until Hierholzer + m + 1 is automatic
  4. then move to Teleporters Path and De Bruijn Sequence

Exit Criteria

You are ready to move on when:

  • you can separate undirected and directed existence conditions without notes
  • you reach for edge ids automatically
  • you check m + 1 as a connectivity guard without being reminded
  • the word Euler no longer sends you to the wrong tree topic

External Practice