Graph Valid Tree

Day 53 — Graph Valid Tree

Coding problem

Solution outline (coding)

Focus on the Union-Find 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.

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

SQL question

network_edges(a,b). BigQuery: detect if network is a valid tree (n nodes, n-1 edges, single component) and output diagnostics.

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.