Persistent Data Structures Ladder

Use this ladder when:

• you trust ordinary segment trees
• "copy / snapshot / old version" is now the real modeling cue
• you want one exact first route for persistence before touching fancier order-statistics variants

Warm-Up Goal

Before leaving this lane, you should be able to:

• explain why copying the whole array is wasteful
• say why one point update only changes one root-to-leaf path
• keep a roots array where each version is one handle
• distinguish persistent versions from rollback

Core Retrieval Route

• exact quick sheet -> Persistent Data Structures hot sheet
• exact starter -> persistent-segment-tree-point-set-sum.cpp
• exact flagship rep -> Range Queries and Copies

What This Lane Teaches First

• persistent segment tree by path copying
• version roots as the real state
• point assignment + range sum over many alive versions
• why a copy operation is usually just one new root handle

Compare Points

• one current version only -> Segment Tree ladder
• undo while traversing time / DFS -> DSU Rollback ladder
• range updates on one active array -> Lazy Segment Tree ladder

Suggested Loop

1. reread the version/root invariant from Persistent Data Structures
2. trust one exact implementation through Range Queries and Copies
3. compare that route back against Dynamic Range Sum Queries so "new version" vs "mutate current tree" feels crisp
4. only then stretch toward richer persistent variants

Exit Criteria

You are ready to leave the lane when:

• you can explain why one update adds only O(log n) new nodes
• you no longer confuse "copy version" with "deep copy the whole array"
• you can say clearly when rollback is the better worldview than persistence

External Follow-Up

• CSES - Range Queries and Copies
• SPOJ - MKTHNUM
• Library Checker - Persistent Union Find