Make Android back button presses in a demo category not unexpectedly quit the app (#17224)

examples/flutter_gallery/lib/gallery/home.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 'dart:async';
 import 'dart:developer';
 import 'dart:math' as math;
 
@@ -298,6 +299,15 @@ class _GalleryHomeState extends State<GalleryHome> with SingleTickerProviderStat
       backgroundColor: isDark ? _kFlutterBlue : theme.primaryColor,
       body: new SafeArea(
         bottom: false,
+        child: new WillPopScope(
+          onWillPop: () {
+            // Pop the category page if Android back button is pressed.
+            if (_category != null) {
+              setState(() => _category = null);
+              return new Future<bool>.value(false);
+            }
+            return new Future<bool>.value(true);
+          },
           child: new Backdrop(
             backTitle: const Text('Options'),
             backLayer: widget.optionsPage,
@@ -308,11 +318,7 @@ class _GalleryHomeState extends State<GalleryHome> with SingleTickerProviderStat
                 : new IconButton(
                   icon: const BackButtonIcon(),
                   tooltip: 'Back',
-                onPressed: () {
-                  setState(() {
-                    _category = null;
-                  });
-                },
+                  onPressed: () => setState(() => _category = null),
                 ),
             ),
             frontTitle:  new AnimatedSwitcher(
@@ -329,14 +335,13 @@ class _GalleryHomeState extends State<GalleryHome> with SingleTickerProviderStat
                 : new _CategoriesPage(
                   categories: kAllGalleryDemoCategories,
                   onCategoryTap: (GalleryDemoCategory category) {
-                  setState(() {
-                    _category = category;
-                  });
+                    setState(() => _category = category);
                   },
                 ),
             ),
           ),
         ),
+      ),
     );
 
     assert(() {