feat(question): add DSA study-plan scheduler endpoint

[vedant7007]

What & why

Closes #2305.

Turns a practice sheet into a "prep in N days" plan: given a list of problems and a target number of days, it produces a balanced day-by-day schedule.

Changes

• backend/utils/studyPlanScheduler.js (new, pure, CommonJS) — buildStudyPlan(problems, days) weights problems by difficulty (easy=1, medium=2, hard=3; unknown/missing→medium via problemWeight) and distributes them across days buckets with difficulty-weighted LPT scheduling (assign each, heaviest-first, to the least-loaded day). Returns { plan: [{ day, problems, load }], totalLoad, days }. Deterministic; guards invalid input.
• questionController.js — buildStudyPlanHandler with inline validation (non-empty array, ≤1000 problems, integer days 1–365), mirroring the existing atsMatch style.
• questionRoutes.js — POST /api/question/study-plan (auth + rate-limit already applied globally).

No new dependency; no package.json/lockfile changes.

Testing

• backend/tests/studyPlanScheduler.unit.test.js — 11 vitest cases (weights, load balancing, exactly-once placement, empty days, default difficulty, determinism, input guards).
• Full backend vitest run → 207 passed (18 files).

Contributing as part of Elite Coders Summer of Code (ECSoC 2026).

Adds an authenticated POST /api/question/study-plan endpoint.

• Uses deterministic, pure LPT scheduling with difficulty weights: easy 1, medium 2, hard 3.
• Defaults missing or unknown difficulty to medium.
• Supports empty days when days exceeds the problem count.
• Validates problem lists and day counts.
• Adds 11 Vitest unit tests.
• Full backend suite passes: 207 tests across 18 files.

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ℹ️ Recent review info

⚙️ Run configuration

Configuration used: Repository UI

Review profile: CHILL

Plan: Team

Run ID: 95f43cb9-5ae5-4056-8037-695c7130244e

📥 Commits

Reviewing files that changed from the base of the PR and between ecb5cef and 3652452.

📒 Files selected for processing (4)

• backend/controllers/questionController.js
• backend/routes/questionRoutes.js
• backend/tests/studyPlanScheduler.unit.test.js
• backend/utils/studyPlanScheduler.js

Included review availability: Your plan provides up to 1 included review per hour; 0 remain after this review.

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📝 Walkthrough

Walkthrough

Adds a deterministic, difficulty-weighted study-plan scheduler. The new POST /api/question/study-plan endpoint validates inputs, builds balanced day buckets, and returns the generated plan. Unit tests cover weighting, scheduling, determinism, and invalid inputs.

Changes

Study plan scheduling

Layer / File(s)	Summary
Deterministic study-plan scheduling backend/utils/studyPlanScheduler.js, backend/tests/studyPlanScheduler.unit.test.js	Adds difficulty weights, medium defaults, stable ordering, least-loaded-day assignment, input validation, deterministic output, and unit tests.
Study-plan API endpoint backend/controllers/questionController.js, backend/routes/questionRoutes.js	Adds request validation, scheduler invocation, response handling, and the POST /api/question/study-plan route.

Estimated code review effort: 3 (Moderate) | ~20 minutes

Merge Risk: 🔵 Low · up to 36524

The PR adds an authenticated, rate-limited study-plan endpoint that performs bounded in-process scheduling. The change is mergeable, with explicit owner awareness that the new API surface introduces a limited compute and availability exposure despite input limits and access controls.

Suggested reviewers: ionfwsrijan

Sequence Diagram(s)

sequenceDiagram
  participant Client
  participant questionRoutes
  participant buildStudyPlanHandler
  participant buildStudyPlan
  Client->>questionRoutes: POST /api/question/study-plan
  questionRoutes->>buildStudyPlanHandler: Forward request
  buildStudyPlanHandler->>buildStudyPlan: Pass problems and days
  buildStudyPlan-->>buildStudyPlanHandler: Return plan and totalLoad
  buildStudyPlanHandler-->>Client: Return study-plan response

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🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly identifies the main change: a DSA study-plan scheduler endpoint.
Linked Issues check	✅ Passed	The changes satisfy issue [#2305]. They add the endpoint, implement deterministic difficulty-weighted LPT scheduling, validate inputs, support empty days, and add unit tests for the scheduler.
Out of Scope Changes check	✅ Passed	All changes support issue [#2305]. The additional 1000-problem limit is related input validation. No unrelated code or dependency changes are present.
Docstring Coverage	✅ Passed	Docstring coverage is 100.00% which is sufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff. Analyzed 2 functions across 4 files.

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

Warning

Some tools did not complete. Review the errors below.

🔧 Biome (2.5.8)

backend/tests/studyPlanScheduler.unit.test.js

File contains syntax errors that prevent linting: Line 1: Illegal use of an import declaration outside of a module; Line 2: Illegal use of an import declaration outside of a module

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