SQL SQL In Depth
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Guided SQL & Engine Coding Lab

Complete SaaS Analytics Engine (MRR, Cohorts & Funnels)

A SaaS product analytics engine implementing gapless date spines, triangular cohort retention matrices, strict chronological funnel conversion attribution, and Allen interval overlap detection.

~40 min Advanced Lessons: Hands-On Build: Complete SaaS Analytics Engine (MRR, Cohorts & Funnels), Calendar Tables & Date Spines: Filling Missing Zero-Activity Time Buckets, Triangle Cohort Retention & Net Dollar Retention (NDR) Matrices in SQL, Multi-Step Ordered Funnel Conversion & First/Last-Touch Attribution, Temporal Interval Overlap (Allen's Algebra) & Packing Contiguous Intervals, Rows to Columns & Back: Cross-Tab Pivoting and Unpivoting Patterns
Guided Algorithm Coding Lab 0/4 Steps Completed

Code & Verify SQL & Storage Engine Invariants in the Browser Workbench

Complete 4 progressive algorithmic steps with guided hints in C++20 (WebAssembly), TypeScript, or JavaScript against automated unit test assertions — zero local setup required.

Architectural Overview

A SaaS product analytics engine implementing gapless date spines, triangular cohort retention matrices, strict chronological funnel conversion attribution, and Allen interval overlap detection.

In production relational and analytical database systems—spanning PostgreSQL, SQLite, MySQL/InnoDB, and DuckDB—understanding how query clauses, schema constraints, index structures, and storage engines execute under the hood separates surface-level query authors from staff-level database engineers. This capstone build lab guides you through implementing Complete SaaS Analytics Engine (MRR, Cohorts & Funnels) from first principles with deterministic self-test invariants.

Guided Implementation Walkthrough (4 Progressive Steps)

Step 1: Gapless Date Spine Generator

  • Core Database Concept: Synthesizing Continuous Calendar Buckets to Prevent Missing Zero-Event Days
  • Target Module: index.js (SaasAnalyticsWorkbench.generateDaySpine)
  • Engineering Specification: Implement generateDaySpine(startDay, endDay, dailyEvents) so every integer day in [startDay, endDay] appears in the output with 0 when no events occurred on that day.
  • Implementation Hint: Step day index from startDay to endDay inclusive and left-join daily counts.
  • Verification Invariant: deterministic assertion verified in test.js step 1

Step 2: Triangular Cohort Retention Matrix

  • Core Database Concept: Grouping Users by Signup Month and Offset Month (activityMonth - cohortMonth)
  • Target Module: index.js (SaasAnalyticsWorkbench.buildCohortMatrix)
  • Engineering Specification: Implement buildCohortMatrix(signups, monthlyActivity) to compute cohort size and retention percentages across monthOffset = 0, 1, 2, ....
  • Implementation Hint: Count distinct active users per (cohortMonth, monthOffset) and divide by month-0 cohort size.
  • Verification Invariant: deterministic assertion verified in test.js step 2

Step 3: Chronological Funnel Conversion Attribution

  • Core Database Concept: Enforcing t_signup <= t_activate <= t_subscribe Across User Events
  • Target Module: index.js (SaasAnalyticsWorkbench.computeFunnel)
  • Engineering Specification: Implement computeFunnel(events) to count users progressing through signup -> activate -> subscribe where each step occurs at or after the prior step’s earliest timestamp.
  • Implementation Hint: Find earliest signup ts per user, earliest activate ts >= signupTs, and earliest subscribe ts >= activateTs.
  • Verification Invariant: deterministic assertion verified in test.js step 3

Step 4: Allen’s Interval Overlap Detector

  • Core Database Concept: Half-Open Interval Intersection: startA < endB AND endA > startB
  • Target Module: index.js (SaasAnalyticsWorkbench.findOverlappingSubscriptions)
  • Engineering Specification: Implement findOverlappingSubscriptions(subs) using Allen’s interval overlap law (a.start < b.end && a.end > b.start) so touching boundaries (endA === startB) do not false-trigger.
  • Implementation Hint: Check pairs for the same user_id where a.start < b.end && a.end > b.start.
  • Verification Invariant: deterministic assertion verified in test.js step 4

Relational & Storage Engine Guarantees

  • Curriculum Domain: Temporal, Cohort & Product Analytics
  • Difficulty & Time Budget: Advanced (~40 minutes)
  • Key Architectural Highlights:
    • Triangular Month-0..Month-N cohort retention matrix with percentage normalization
    • Strict temporal ordering funnel attribution (Signup -> Activated -> Subscribed)
    • Allen interval algebra overlap predicate (startA < endB AND endA > startB) for concurrency and booking checks
  • Core Primitives & Tags: Cohort Retention, Funnel Attribution, Date Spine, Allen Interval Algebra, SaaS Metrics

Related Curriculum Units

Production Database Context & Verification

This from-scratch relational engine component is engineered with zero external dependencies and deterministic verification harnesses. Every internal database invariant—from three-valued logic (TRUE / FALSE / UNKNOWN), referential integrity, and fan-out-free join pre-aggregation to B+Tree page splits, MVCC snapshot visibility (xmin / xmax), slotted-page compaction, and ARIES write-ahead log crash recovery—is asserted directly in test.js. Use the interactive browser workbench above to complete the 4 guided steps in Guided Lab mode or inspect and benchmark the complete reference architecture in Full Solution mode.