feat(app): stabilize recommendation flow

lib/presentation/pages/random_selection/widgets/recommendation_result_dialog.dart

@@ -3,6 +3,7 @@ import 'dart:async';
 import 'package:flutter/material.dart';
 import 'package:lunchpick/core/constants/app_colors.dart';
 import 'package:lunchpick/core/constants/app_typography.dart';
+import 'package:lunchpick/core/utils/distance_calculator.dart';
 import 'package:lunchpick/domain/entities/restaurant.dart';
 
 enum RecommendationDialogResult { confirm, reroll, autoConfirm }
@@ -10,11 +11,15 @@ enum RecommendationDialogResult { confirm, reroll, autoConfirm }
 class RecommendationResultDialog extends StatefulWidget {
   final Restaurant restaurant;
   final Duration autoConfirmDuration;
+  final double? currentLatitude;
+  final double? currentLongitude;
 
   const RecommendationResultDialog({
     super.key,
     required this.restaurant,
     this.autoConfirmDuration = const Duration(seconds: 12),
+    this.currentLatitude,
+    this.currentLongitude,
   });
 
   @override
@@ -26,10 +31,12 @@ class _RecommendationResultDialogState
     extends State<RecommendationResultDialog> {
   Timer? _autoConfirmTimer;
   bool _didComplete = false;
+  double? _distanceKm;
 
   @override
   void initState() {
     super.initState();
+    _calculateDistance();
     _startAutoConfirmTimer();
   }
 
@@ -47,6 +54,27 @@ class _RecommendationResultDialogState
     });
   }
 
+  void _calculateDistance() {
+    final lat = widget.currentLatitude;
+    final lon = widget.currentLongitude;
+    if (lat == null || lon == null) return;
+
+    _distanceKm = DistanceCalculator.calculateDistance(
+      lat1: lat,
+      lon1: lon,
+      lat2: widget.restaurant.latitude,
+      lon2: widget.restaurant.longitude,
+    );
+  }
+
+  String _formatDistance(double distanceKm) {
+    final meters = distanceKm * 1000;
+    if (meters >= 1000) {
+      return '${distanceKm.toStringAsFixed(1)} km';
+    }
+    return '${meters.round()} m';
+  }
+
   Future<void> _handleResult(RecommendationDialogResult result) async {
     if (_didComplete) return;
     _didComplete = true;
@@ -177,6 +205,26 @@ class _RecommendationResultDialogState
                         ),
                       ],
                     ),
+                    if (_distanceKm != null) ...[
+                      const SizedBox(height: 8),
+                      Row(
+                        children: [
+                          Icon(
+                            Icons.place,
+                            size: 20,
+                            color: AppColors.lightPrimary,
+                          ),
+                          const SizedBox(width: 8),
+                          Text(
+                            _formatDistance(_distanceKm!),
+                            style: AppTypography.body2(isDark).copyWith(
+                              color: AppColors.lightPrimary,
+                              fontWeight: FontWeight.w600,
+                            ),
+                          ),
+                        ],
+                      ),
+                    ],
                     if (widget.restaurant.phoneNumber != null) ...[
                       const SizedBox(height: 8),
                       Row(
@@ -237,14 +285,14 @@ class _RecommendationResultDialogState
                                 borderRadius: BorderRadius.circular(8),
                               ),
                             ),
-                            child: const Text('닫기'),
+                            child: const Text('오늘의 선택!'),
                           ),
                         ),
                       ],
                     ),
                     const SizedBox(height: 8),
                     Text(
-                      '조용히 두면 자동으로 방문 처리되고 알림이 예약됩니다.',
+                      '앱을 종료하면 자동으로 선택이 확정됩니다.',
                       style: AppTypography.caption(isDark),
                       textAlign: TextAlign.center,
                     ),