Add workflow to deploy the sample index (#791)

* Add workflow to build and deploy the sample index

* update gh-pages action

* fix yaml

* create web/ directory in build

* grammar

* add ignored directories

* revert pubspec.lock files

* add job to run _tool/verify_samples.dart

* Update filipino_cuisine for Flutter 2

* remove timeflow demo.

The unnamed List constructor is now deprecated, refactoring
this code to use add() requires more knowledge about the code for
this demo.
https://dart.dev/null-safety/understanding-null-safety#no-unnamed-list-constructor

* update slide_puzzle

* ensure stable channel is used to verify

* move verify web demos action into separate yaml file - avoid running
on each flutter version.

* add on: pull_request

* update slide_puzzle

* Update gh-pages.yml

* Add copyright header

web/_tool/common.dart

@@ -36,3 +36,16 @@ Future<bool> run(
 void logWrapped(int code, String message) {
   print('\x1B[${code}m$message\x1B[0m');
 }
+
+Iterable<String> listPackageDirs(Directory dir) sync* {
+  if (File('${dir.path}/pubspec.yaml').existsSync()) {
+    yield dir.path;
+  } else {
+    for (var subDir in dir
+        .listSync(followLinks: true)
+        .whereType<Directory>()
+        .where((d) => !Uri.file(d.path).pathSegments.last.startsWith('.'))) {
+      yield* listPackageDirs(subDir);
+    }
+  }
+}