Dot Product of Sparse Vectors

Hash / Two Pointer · Medium · Week 11 · Phase 4

Day 75 — Dot Product of Sparse Vectors

Coding problem

Problem	Dot Product of Sparse Vectors
LeetCode ID(s)	LeetCode #1570
Difficulty	Medium
Pattern	Hash / Two Pointer
Company tags	Meta
Suggested time	15m

Solution outline (coding)

Focus on the Hash / Two Pointer pattern. Start by writing out a few examples by hand, then identify the invariant you must maintain (e.g., prefix sums, window bounds, visited set, heap ordering). Aim for an implementation you can explain in under a minute, including time and space complexity.

Show Python solution

# Solution template based on the main pattern for this day.
# Replace this with your final, production-ready solution as you practice.

SQL question

sparse_vectors(vector_id, index, value). BigQuery: implement dot product between two sparse vectors and aggregate similarities across pairs above a threshold.

How to approach (SQL)

Break the prompt into steps:

Identify source tables, required joins, and filters (especially on time partitions).
Decide where you need GROUP BY vs. window functions (e.g., ROW_NUMBER, SUM() OVER, COUNT() OVER).
For BigQuery, think about partitioning and clustering to avoid unnecessary full scans.
Write the query in stages (CTEs) so each step is easy to debug and reason about. Finish by checking edge cases: nulls, late events, duplicated keys, and extreme values.