Review & Cheat Sheet

Key Takeaways

• Advanced DSA is about choosing the right invariant for the constraint shape.
• Greedy needs proof of local-choice safety.
• Union-Find converts repeated connectivity checks into nearly constant amortized operations.
• Segment trees trade space for fast range query + point/range updates.
• Amortized analysis explains bursty expensive steps over long sequences.

Proof Checklist

1. Define invariant precisely.
2. Show it holds after each operation.
3. Show termination and correctness.
4. Compute worst-case and amortized cost separately.

Amortized Intuition

For dynamic array append:

• Occasionally resizing is expensive.
• But across n appends, total copied elements is geometric.
• Aggregate cost remains O(n), so average append is O(1) amortized.

Next Steps

Proceed to 14 Real World to map these techniques to production use cases and service constraints. —

Review & Cheat Sheet

[!NOTE] This module explores the core principles of Review & Cheat Sheet, deriving solutions from first principles and hardware constraints to build world-class, production-ready expertise.

1. Practice in the Vault

Looking to solidify your understanding? Head over to the Problem Vault to solve curated problems related to this module with detailed walkthroughs and optimal solutions.