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Interval Trees Ladder

This lane is for the first time one dynamic interval set becomes the real data structure instead of only a side effect of sorting or range processing.

Who This Is For

Use this lane if:

  • Heaps And Ordered Sets already feels comfortable
  • you can explain half-open interval overlap cleanly
  • you now need online insert / erase / overlap checks against one live interval set

This lane is intentionally narrow:

Warm-Up

  • define overlap for half-open intervals [l, r)
  • explain why max(l1, l2) < min(r1, r2) is the right predicate
  • explain why subtree max_r is enough to prune the overlap search

Target skill:

  • recognize when the real state is "one explicit live set of intervals," not one line array or one offline sorted list

Core

  • lexicographic BST order on (l, r)
  • subtree max_r
  • any-overlap query
  • exact flagship rep: Reservation System

Target skill:

  • trust the augmented-BST route and know when it is slightly overkill but still pedagogically exact

Stretch

  • attach ids if exact duplicate intervals matter
  • compare the same benchmark against a simpler predecessor/successor ordered-set solution
  • branch to ODT / Chtholly if the real state is piecewise-constant runs under assign
  • branch to Segment Tree if the real query is aggregate coverage on a fixed universe

Target skill:

  • separate "dynamic interval overlap set" from both interval partitions and coordinate-aggregated range structures

Retrieval Layer

Repo Anchors And Compare Points

The cleanest in-repo loop here is:

  1. reopen Heaps And Ordered Sets just enough to keep ordered-set neighbor logic straight
  2. learn the augmented overlap route in Interval Trees
  3. solve Reservation System
  4. compare the same benchmark against lighter neighbor-check logic so the "interval tree vs simpler ordered set" boundary stays honest

Exit Criteria

You are ready to move on when:

  • you can explain why max_r is the only extra subtree summary needed for this exact overlap search
  • you know when interval trees are the right abstraction and when they are only a textbook detour
  • you can state the half-open overlap predicate without hesitation

External Practice