feat: CONAI Phase 1 MVP 초기 구현

소형 건설업체(100억 미만)를 위한 AI 기반 토목공사 통합관리 플랫폼

Backend (FastAPI):
- SQLAlchemy 모델 13개 (users, projects, wbs, tasks, daily_reports, reports, inspections, quality, weather, permits, rag, settings)
- API 라우터 11개 (auth, projects, tasks, daily_reports, reports, inspections, weather, rag, kakao, permits, settings)
- Services: Claude AI 래퍼, CPM Gantt 계산, 기상청 API, RAG(pgvector), 카카오 Skill API
- Alembic 마이그레이션 (pgvector 포함)
- pytest 테스트 (CPM, 날씨 경보)

Frontend (Next.js 15):
- 11개 페이지 (대시보드, 프로젝트, Gantt, 일보, 검측, 품질, 날씨, 인허가, RAG, 설정)
- TanStack Query + Zustand + Tailwind CSS

인프라:
- Docker Compose (PostgreSQL pgvector + backend + frontend)
- 한국어 README 및 설치 가이드

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/app/services/gantt.py

@@ -0,0 +1,111 @@
+"""
+CPM (Critical Path Method) calculation for Gantt chart.
+"""
+from datetime import date, timedelta
+from typing import NamedTuple
+import uuid
+
+
+class TaskNode(NamedTuple):
+    id: uuid.UUID
+    planned_start: date | None
+    planned_end: date | None
+    duration_days: int
+
+
+def compute_cpm(tasks: list, dependencies: list) -> dict[uuid.UUID, dict]:
+    """
+    Compute CPM forward/backward pass.
+    Returns dict: task_id -> {early_start, early_finish, late_start, late_finish, total_float, is_critical}
+    """
+    if not tasks:
+        return {}
+
+    # Build adjacency maps
+    task_map = {t.id: t for t in tasks}
+    successors: dict[uuid.UUID, list[uuid.UUID]] = {t.id: [] for t in tasks}
+    predecessors: dict[uuid.UUID, list[uuid.UUID]] = {t.id: [] for t in tasks}
+
+    for dep in dependencies:
+        successors[dep.predecessor_id].append(dep.successor_id)
+        predecessors[dep.successor_id].append(dep.predecessor_id)
+
+    def get_duration(task) -> int:
+        if task.planned_start and task.planned_end:
+            return max(1, (task.planned_end - task.planned_start).days + 1)
+        return 1
+
+    # Topological sort (Kahn's algorithm)
+    in_degree = {t.id: len(predecessors[t.id]) for t in tasks}
+    queue = [t.id for t in tasks if in_degree[t.id] == 0]
+    topo_order = []
+
+    while queue:
+        node = queue.pop(0)
+        topo_order.append(node)
+        for succ in successors[node]:
+            in_degree[succ] -= 1
+            if in_degree[succ] == 0:
+                queue.append(succ)
+
+    # Forward pass: compute Early Start (ES) and Early Finish (EF)
+    es: dict[uuid.UUID, int] = {}  # days from project start
+    ef: dict[uuid.UUID, int] = {}
+
+    for tid in topo_order:
+        task = task_map[tid]
+        dur = get_duration(task)
+        if not predecessors[tid]:
+            es[tid] = 0
+        else:
+            es[tid] = max(ef[p] for p in predecessors[tid])
+        ef[tid] = es[tid] + dur
+
+    if not ef:
+        return {}
+
+    project_duration = max(ef.values())
+
+    # Backward pass: compute Late Finish (LF) and Late Start (LS)
+    lf: dict[uuid.UUID, int] = {}
+    ls: dict[uuid.UUID, int] = {}
+
+    for tid in reversed(topo_order):
+        task = task_map[tid]
+        dur = get_duration(task)
+        if not successors[tid]:
+            lf[tid] = project_duration
+        else:
+            lf[tid] = min(ls[s] for s in successors[tid])
+        ls[tid] = lf[tid] - dur
+
+    # Compute float and critical path
+    result = {}
+    # Find an actual project start date
+    project_start = None
+    for t in tasks:
+        if t.planned_start:
+            if project_start is None or t.planned_start < project_start:
+                project_start = t.planned_start
+    if not project_start:
+        project_start = date.today()
+
+    for tid in topo_order:
+        total_float = ls[tid] - es[tid]
+        is_critical = total_float == 0
+
+        early_start_date = project_start + timedelta(days=es[tid])
+        early_finish_date = project_start + timedelta(days=ef[tid] - 1)
+        late_start_date = project_start + timedelta(days=ls[tid])
+        late_finish_date = project_start + timedelta(days=lf[tid] - 1)
+
+        result[tid] = {
+            "early_start": early_start_date,
+            "early_finish": early_finish_date,
+            "late_start": late_start_date,
+            "late_finish": late_finish_date,
+            "total_float": total_float,
+            "is_critical": is_critical,
+        }
+
+    return result, project_duration