feat: Implement lazy hub expansion depth limiting with MaxTransfers support

- Add transfer depth limiting in BFS/Dijkstra (MaxTransfers field in SearchOptions)
- Track transfer count at each step; stop when depth > 5
- Synthetic edge fallback on expansion failure
- Add TestLazyExpansionDepthLimit and TestFindRouteMaxTransfers tests

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

cmd/api/handlers.go

@@ -172,11 +172,34 @@ func RouteSearch(hc *HandlerContext, w http.ResponseWriter, r *http.Request) {
 		http.Error(w, "invalid request body", http.StatusBadRequest)
 		return
 	}
-	// In a full implementation, would search routes using the graph and Yandex API
-	// For now, return a simple JSON response
+
+	// Build query parameters for route search
+	// Use city codes as origin/destination identifiers
+	// In a full implementation, this would use Yandex /search, but for now
+	// we use the in-memory graph with Pareto-optimal routing
+
+	// Create search options with default max transfers
+	opts := routing.SearchOptions{
+		MaxTransfers: 5,
+	}
+
+	// Run Pareto-optimal route search using the graph
+	results := hc.Router.FindRoutesPareto(req.FromCityID, req.ToCityID, opts)
+
+	// Build response routes
+	routeResponses := make([]interface{}, 0, len(results))
+	for _, route := range results {
+		routeResponses = append(routeResponses, map[string]interface{}{
+			"duration":    route.TotalDuration,
+			"transfers":   route.TotalTransfers,
+			"cost":        route.Cost,
+			"id":          route.ID,
+		})
+	}
+
 	resp := routeSearchResponse{
-		Routes: []interface{}{},
-		Count:  0,
+		Routes: routeResponses,
+		Count:  len(routeResponses),
 	}
 	w.Header().Set("Content-Type", "application/json")
 	json.NewEncoder(w).Encode(resp)