Use a direct include of strings headers in chrome/common/, part 1.

chrome/common/badge_util.h

 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #ifndef CHROME_COMMON_BADGE_UTIL_H_
 #define CHROME_COMMON_BADGE_UTIL_H_
 
 #include <string>
 
-#include "base/string16.h"
+#include "base/strings/string16.h"
 #include "chrome/common/extensions/api/extension_action/action_info.h"
 #include "third_party/skia/include/core/SkBitmap.h"
 
 class SkPaint;
 
 namespace gfx {
 class Canvas;
 class Rect;
 }
 
@@ skipping 18 matching lines @@
                 const gfx::Rect& bounds,
                 const std::string& text,
                 const SkColor& text_color_in,
                 const SkColor& background_color_in,
                 int icon_width,
                 extensions::ActionInfo::Type action_type);
 
 }  // namespace badge_util;
 
 #endif  // CHROME_COMMON_BADGE_UTIL_H_