Cheatsheet: Geometry Formula Notes

Learning Outcome

Revise Geometry Formula Notes quickly before interviews.

Pattern Recognition

Intuition

A compact template protects attention for the actual problem invariant.

Exact Practice Question Names

• squared distance
• cross product
• dot product
• midpoint normalization

Interview Approach

1. squared distance
2. cross product
3. dot product
4. midpoint normalization
5. Dry-run once before finalizing code.

Pseudocode

- squared distance\n- cross product\n- dot product\n- midpoint normalization
  

Sample Dry Run

Pick one known problem and map each template line to a real state change.

Edge Cases

• Empty containers
• Boundary indices
• Overflow
• Tie-breaking

Common Mistakes

• Copying syntax without adapting state
• Skipping empty checks
• Ignoring language-specific defaults

Complexity

Java, C++ and Python Notes

• Java: prefer explicit classes and clear helper methods over clever one-liners.
• C++: use vector, unordered_map, set, priority_queue, and long long when sums can grow.
• Python: keep state readable with dict, set, deque, heapq, and lru_cache where appropriate.

Quick Revision Checklist

• Name the pattern before coding.
• State the invariant or DP state in one sentence.
• Dry-run the smallest non-trivial example.
• Close with time and space complexity.