Update `CupertinoPicker` example (#118248)

* Update `CupertinoPicker` example

* format lines

* Revert making variable public

* revert variable change

examples/api/lib/cupertino/picker/cupertino_picker.0.dart

@@ -29,6 +29,7 @@ class CupertinoPickerApp extends StatelessWidget {
     );
   }
 }
+
 class CupertinoPickerExample extends StatefulWidget {
   const CupertinoPickerExample({super.key});
 
@@ -57,7 +58,7 @@ class _CupertinoPickerExampleState extends State<CupertinoPickerExample> {
           top: false,
           child: child,
         ),
-      )
+      ),
     );
   }
 
@@ -86,6 +87,10 @@ class _CupertinoPickerExampleState extends State<CupertinoPickerExample> {
                     squeeze: 1.2,
                     useMagnifier: true,
                     itemExtent: _kItemExtent,
+                    // This sets the initial item.
+                    scrollController: FixedExtentScrollController(
+                      initialItem: _selectedFruit,
+                    ),
                     // This is called when selected item is changed.
                     onSelectedItemChanged: (int selectedItem) {
                       setState(() {
@@ -93,16 +98,13 @@ class _CupertinoPickerExampleState extends State<CupertinoPickerExample> {
                       });
                     },
                     children: List<Widget>.generate(_fruitNames.length, (int index) {
-                      return Center(
-                        child: Text(
-                          _fruitNames[index],
-                        ),
-                      );
+                      return Center(child: Text(_fruitNames[index]));
                     }),
                   ),
                 ),
                 // This displays the selected fruit name.
-                child: Text(_fruitNames[_selectedFruit],
+                child: Text(
+                  _fruitNames[_selectedFruit],
                   style: const TextStyle(
                     fontSize: 22.0,
                   ),

examples/api/test/cupertino/picker/cupertino_picker.0_test.dart

@@ -2,6 +2,7 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
+import 'package:flutter/cupertino.dart';
 import 'package:flutter_api_samples/cupertino/picker/cupertino_picker.0.dart' as example;
 import 'package:flutter_test/flutter_test.dart';
 
@@ -14,12 +15,15 @@ void main() {
     );
 
     // Open the Cupertino picker.
-    await tester.tap(find.text('Apple'));
+    await tester.tap(find.widgetWithText(CupertinoButton, 'Apple'));
     await tester.pumpAndSettle();
 
+    // Test the initial item.
+    CupertinoPicker picker = tester.widget<CupertinoPicker>(find.byType(CupertinoPicker));
+    expect(picker.scrollController!.initialItem, 0);
+
     // Drag the wheel to change fruit selection.
     await tester.drag(find.text('Mango'), _kRowOffset, touchSlopY: 0, warnIfMissed: false); // see top of file
-
     await tester.pump();
     await tester.pump(const Duration(milliseconds: 500));
 
@@ -27,6 +31,13 @@ void main() {
     await tester.tapAt(const Offset(1.0, 1.0));
     await tester.pumpAndSettle();
 
-    expect(find.text('Banana'), findsOneWidget);
+    expect(find.widgetWithText(CupertinoButton, 'Banana'), findsOneWidget);
+
+    // Test if the initial item has updated.
+    await tester.tap(find.widgetWithText(CupertinoButton, 'Banana'));
+    await tester.pumpAndSettle();
+
+    picker = tester.widget<CupertinoPicker>(find.byType(CupertinoPicker));
+    expect(picker.scrollController!.initialItem, 2);
   });
 }