Make app list search box into a Widget.

ui/app_list/views/app_list_view.h

Index: ui/app_list/views/app_list_view.h
diff --git a/ui/app_list/views/app_list_view.h b/ui/app_list/views/app_list_view.h
index 3aa266bdabc072229c4c7400f3ee310372e31636..d1946b4d05367986872703e9a13501d21859ef5c 100644
--- a/ui/app_list/views/app_list_view.h
+++ b/ui/app_list/views/app_list_view.h
@@ -95,7 +95,7 @@ class APP_LIST_EXPORT AppListView : public views::BubbleDelegateView,
   // Returns true if the app list should be centered and in landscape mode.
   bool ShouldCenterWindow() const;
 
-  SearchBoxView* search_box_view() const { return search_box_view_; }
+  views::Widget* search_box_widget() const { return search_box_widget_; }
 
   // Overridden from views::View:
   gfx::Size GetPreferredSize() const override;
@@ -138,6 +138,8 @@ class APP_LIST_EXPORT AppListView : public views::BubbleDelegateView,
 
   void InitContents(gfx::NativeView parent, int initial_apps_page);
 
+  void InitChildWidgets();
+
   void InitAsBubbleInternal(gfx::NativeView parent,
                             int initial_apps_page,
                             views::BubbleBorder::Arrow arrow,
@@ -166,9 +168,11 @@ class APP_LIST_EXPORT AppListView : public views::BubbleDelegateView,
   AppListViewDelegate* delegate_;  // Weak. Owned by AppListService.
 
   AppListMainView* app_list_main_view_;
-  SearchBoxView* search_box_view_;
   SpeechView* speech_view_;
 
+  views::Widget* search_box_widget_;  // Owned by the app list's widget.
+  SearchBoxView* search_box_view_;    // Owned by |search_box_widget_|.
+
   // The red "experimental" banner for the experimental app list.
   views::ImageView* experimental_banner_view_;