清华教授的小课堂魔方真好玩-<artentek>电子书

　　　　

分类页面广告

清华教授的小课堂魔方真好玩

作者：雍俊海

格式：

mobi/epub/pdf/awz3

浏览量：

122次

扫码关注公众号

温馨提示：书籍来自网络收集，版权归原作者所有，仅做学习试读,下载后请24小时内删除,侵权删(联系:1401211620@qq.com)

所属分类:

生活时尚 >> 休闲娱乐

点击下载

收藏该图书

图书中部

内容简介:

《清华教授的小课堂魔方真好玩》是清华大学软件学院雍俊海教授为初学魔方的孩子精心创作。区别于个人经验式的魔方图书，作者利用高等数学知识和计算机编程科学破解魔方难题，解法转动步骤毫不冗余，魔方的各种状态完全覆盖，任何一个打乱的魔方，都能在书中找到对应的解法。作者还首创以西周取代殷商比喻魔方复原过程，每一段历史故事都与魔方复原进程完美契合，新颖有趣，易懂易学。每章内容后，作者还精心设计了小甜点环节，历史百科、魔方趣闻、花式玩法尽在其中，贯通文史理工，激发孩子多学科多维度思考力。

详情数据包

相关推荐

企业员工的知识分享

走进云南茶树王国

离离原上花

新时代高校巡察实践、理论与制度创新：西南财经大学党风廉政建设与巡视巡察研究成果集

客服

基本文件流程错误 SQL 调试

/www/wwwroot/biebai.com_www/public/index.php ( 0.79 KB )
/www/wwwroot/biebai.com_www/vendor/autoload.php ( 0.75 KB )
/www/wwwroot/biebai.com_www/vendor/composer/autoload_real.php ( 1.70 KB )
/www/wwwroot/biebai.com_www/vendor/composer/platform_check.php ( 0.90 KB )
/www/wwwroot/biebai.com_www/vendor/composer/ClassLoader.php ( 15.69 KB )
/www/wwwroot/biebai.com_www/vendor/composer/autoload_static.php ( 5.87 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-helper/src/helper.php ( 7.35 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/stubs/load_stubs.php ( 0.16 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Exception.php ( 1.69 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Facade.php ( 2.71 KB )
/www/wwwroot/biebai.com_www/vendor/symfony/polyfill-mbstring/bootstrap.php ( 7.33 KB )
/www/wwwroot/biebai.com_www/vendor/symfony/polyfill-php72/bootstrap.php ( 1.89 KB )
/www/wwwroot/biebai.com_www/vendor/symfony/polyfill-php80/bootstrap.php ( 1.50 KB )
/www/wwwroot/biebai.com_www/vendor/symfony/var-dumper/Resources/functions/dump.php ( 0.79 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-captcha/src/helper.php ( 1.37 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/App.php ( 14.17 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Container.php ( 15.38 KB )
/www/wwwroot/biebai.com_www/vendor/psr/container/src/ContainerInterface.php ( 1.02 KB )
/www/wwwroot/biebai.com_www/app/provider.php ( 0.19 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Http.php ( 6.12 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-helper/src/helper/Str.php ( 7.28 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Env.php ( 4.64 KB )
/www/wwwroot/biebai.com_www/app/common.php ( 14.84 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/helper.php ( 18.44 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Config.php ( 5.03 KB )
/www/wwwroot/biebai.com_www/config/app.php ( 1.05 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/facade/Env.php ( 1.67 KB )
/www/wwwroot/biebai.com_www/config/cache.php ( 0.80 KB )
/www/wwwroot/biebai.com_www/config/captcha.php ( 1.02 KB )
/www/wwwroot/biebai.com_www/config/console.php ( 0.23 KB )
/www/wwwroot/biebai.com_www/config/cookie.php ( 0.56 KB )
/www/wwwroot/biebai.com_www/config/database.php ( 2.25 KB )
/www/wwwroot/biebai.com_www/config/default.php ( 2.37 KB )
/www/wwwroot/biebai.com_www/config/filesystem.php ( 0.63 KB )
/www/wwwroot/biebai.com_www/config/jump.php ( 0.63 KB )
/www/wwwroot/biebai.com_www/config/lang.php ( 0.81 KB )
/www/wwwroot/biebai.com_www/config/log.php ( 1.37 KB )
/www/wwwroot/biebai.com_www/config/middleware.php ( 0.19 KB )
/www/wwwroot/biebai.com_www/config/project.php ( 0.92 KB )
/www/wwwroot/biebai.com_www/config/route.php ( 1.54 KB )
/www/wwwroot/biebai.com_www/config/session.php ( 0.57 KB )
/www/wwwroot/biebai.com_www/config/trace.php ( 0.34 KB )
/www/wwwroot/biebai.com_www/config/view.php ( 1.12 KB )
/www/wwwroot/biebai.com_www/app/Request.php ( 0.09 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Request.php ( 54.04 KB )
/www/wwwroot/biebai.com_www/app/event.php ( 0.25 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Event.php ( 6.96 KB )
/www/wwwroot/biebai.com_www/app/service.php ( 0.13 KB )
/www/wwwroot/biebai.com_www/app/AppService.php ( 0.26 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Service.php ( 1.67 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Lang.php ( 7.60 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/lang/zh-cn.php ( 12.88 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/initializer/Error.php ( 3.27 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/initializer/RegisterService.php ( 1.33 KB )
/www/wwwroot/biebai.com_www/vendor/services.php ( 0.22 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/service/PaginatorService.php ( 1.52 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/service/ValidateService.php ( 0.99 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/service/ModelService.php ( 1.76 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-captcha/src/CaptchaService.php ( 0.52 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-multi-app/src/Service.php ( 1.08 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-trace/src/Service.php ( 0.77 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Middleware.php ( 6.78 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/initializer/BootService.php ( 0.77 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/Paginator.php ( 11.80 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Validate.php ( 46.10 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/Model.php ( 25.28 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/model/concern/Attribute.php ( 17.61 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/model/concern/RelationShip.php ( 26.12 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/model/concern/ModelEvent.php ( 2.27 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/model/concern/TimeStamp.php ( 5.70 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/model/concern/Conversion.php ( 10.41 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-helper/src/contract/Arrayable.php ( 0.09 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-helper/src/contract/Jsonable.php ( 0.13 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Db.php ( 2.87 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/DbManager.php ( 8.49 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Log.php ( 8.50 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Manager.php ( 3.98 KB )
/www/wwwroot/biebai.com_www/vendor/psr/log/Psr/Log/LoggerInterface.php ( 3.04 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Cache.php ( 4.79 KB )
/www/wwwroot/biebai.com_www/vendor/psr/simple-cache/src/CacheInterface.php ( 4.50 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-helper/src/helper/Arr.php ( 15.54 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/cache/driver/File.php ( 7.42 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/cache/Driver.php ( 8.06 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/contract/CacheHandlerInterface.php ( 2.25 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Console.php ( 22.65 KB )
/www/wwwroot/biebai.com_www/app/middleware.php ( 0.25 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Pipeline.php ( 2.61 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-trace/src/TraceDebug.php ( 2.94 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/middleware/SessionInit.php ( 2.06 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Session.php ( 1.80 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/session/driver/File.php ( 6.28 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/contract/SessionHandlerInterface.php ( 0.87 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/session/Store.php ( 7.26 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-multi-app/src/MultiApp.php ( 7.07 KB )
/www/wwwroot/biebai.com_www/app/index/common.php ( 0.99 KB )
/www/wwwroot/biebai.com_www/app/index/config/app.php ( 0.30 KB )
/www/wwwroot/biebai.com_www/app/index/config/route.php ( 0.27 KB )
/www/wwwroot/biebai.com_www/app/index/event.php ( 0.28 KB )
/www/wwwroot/biebai.com_www/app/index/middleware.php ( 0.17 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Route.php ( 23.96 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/route/RuleName.php ( 5.33 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/route/Domain.php ( 5.55 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/route/RuleGroup.php ( 13.61 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/route/Rule.php ( 22.85 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/route/RuleItem.php ( 8.81 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/route/dispatch/Url.php ( 3.42 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/route/dispatch/Controller.php ( 6.61 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/route/Dispatch.php ( 6.49 KB )
/www/wwwroot/biebai.com_www/app/index/http/middleware/Login.php ( 1.40 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/facade/Cookie.php ( 1.49 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Cookie.php ( 6.28 KB )
/www/wwwroot/biebai.com_www/app/index/cache/TokenCache.php ( 0.89 KB )
/www/wwwroot/biebai.com_www/app/common/cache/CacheBase.php ( 2.06 KB )
/www/wwwroot/biebai.com_www/app/index/validate/Token.php ( 1.69 KB )
/www/wwwroot/biebai.com_www/app/index/controller/Goods.php ( 2.81 KB )
/www/wwwroot/biebai.com_www/app/index/controller/FrontBase.php ( 6.39 KB )
/www/wwwroot/biebai.com_www/app/BaseController.php ( 2.03 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/facade/View.php ( 1.71 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/View.php ( 4.41 KB )
/www/wwwroot/biebai.com_www/app/index/logic/GoodsLogic.php ( 18.08 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/facade/Cache.php ( 2.02 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/facade/Db.php ( 0.94 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/connector/Mysql.php ( 4.39 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/PDOConnection.php ( 52.45 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/Connection.php ( 7.67 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/ConnectionInterface.php ( 4.56 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/builder/Mysql.php ( 15.93 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/Builder.php ( 41.58 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/Query.php ( 10.64 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/BaseQuery.php ( 36.47 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/concern/TimeFieldQuery.php ( 7.50 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/concern/AggregateQuery.php ( 3.26 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/concern/ModelRelationQuery.php ( 16.06 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/concern/ResultOperation.php ( 6.29 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/concern/Transaction.php ( 2.85 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/concern/WhereQuery.php ( 16.22 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/concern/JoinAndViewQuery.php ( 6.86 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/concern/ParamsBind.php ( 3.36 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/concern/TableFieldInfo.php ( 2.51 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/log/driver/File.php ( 6.17 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/contract/LogHandlerInterface.php ( 0.86 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/log/Channel.php ( 6.54 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/event/LogRecord.php ( 0.86 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-helper/src/Collection.php ( 16.10 KB )
/www/wwwroot/biebai.com_www/app/common/server/UrlServer.php ( 2.33 KB )
/www/wwwroot/biebai.com_www/app/common/server/ConfigServer.php ( 3.31 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/facade/Config.php ( 1.37 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-view/src/Think.php ( 8.42 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-template/src/Template.php ( 46.85 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-template/src/template/driver/File.php ( 2.33 KB )
/www/wwwroot/biebai.com_www/app/index/model/Goods.php ( 1.79 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/db/CacheItem.php ( 4.57 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/cache/TagSet.php ( 3.23 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/Response.php ( 8.60 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/response/View.php ( 3.27 KB )
/www/wwwroot/biebai.com_www/runtime/index/temp/1c196eef206b8d22440d4381e08898cf.php ( 30.40 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/facade/Route.php ( 4.88 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-multi-app/src/Url.php ( 7.70 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/framework/src/think/route/Url.php ( 14.66 KB )
/www/wwwroot/biebai.com_www/app/index/controller/Advert.php ( 1.39 KB )
/www/wwwroot/biebai.com_www/app/index/logic/AdLogic.php ( 2.24 KB )
/www/wwwroot/biebai.com_www/runtime/index/temp/bc8161b5031df7491a90030d79ba666a.php ( 0.45 KB )
/www/wwwroot/biebai.com_www/app/common/taglib/ht/tagLists.php ( 3.93 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-orm/src/model/Collection.php ( 6.78 KB )
/www/wwwroot/biebai.com_www/vendor/topthink/think-trace/src/Html.php ( 4.49 KB )

CONNECT:[ UseTime:0.000561s ] mysql:host=127.0.0.1;port=3306;dbname=biebai.com_www;charset=utf8
SHOW FULL COLUMNS FROM `ls_goods_category` [ RunTime:0.000729s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 1 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.000563s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 2 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.000585s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 3 ORDER BY `sort` DESC [ RunTime:0.000429s ]
SHOW FULL COLUMNS FROM `ls_nav` [ RunTime:0.000782s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 1 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.000520s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 2 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.000266s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 3 ORDER BY `sort` DESC [ RunTime:0.000202s ]
SHOW FULL COLUMNS FROM `ls_friendly_link` [ RunTime:0.000687s ]
SELECT * FROM `ls_friendly_link` WHERE `is_show` = 1 AND `del` = 0 ORDER BY `id` DESC,`sort` DESC [ RunTime:0.000386s ]
SHOW FULL COLUMNS FROM `ls_goods` [ RunTime:0.000905s ]
SELECT * FROM `ls_goods` WHERE `id` = 123306 AND `status` = 1 LIMIT 1 [ RunTime:0.000603s ]
UPDATE `ls_goods` SET `click_count` = 122 , `update_time` = 1772941111 WHERE `id` = 123306 [ RunTime:0.000358s ]
SELECT `name`,`first_category_id`,`second_category_id` FROM `ls_goods` WHERE `id` = 123306 LIMIT 1 [ RunTime:0.000444s ]
SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 77 LIMIT 1 [ RunTime:0.000243s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 1 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.000392s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 2 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.001231s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 3 ORDER BY `sort` DESC [ RunTime:0.000345s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 1 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.000534s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 2 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.000339s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 3 ORDER BY `sort` DESC [ RunTime:0.000197s ]
SELECT * FROM `ls_friendly_link` WHERE `is_show` = 1 AND `del` = 0 ORDER BY `id` DESC,`sort` DESC [ RunTime:0.000353s ]
SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 10 LIMIT 1 [ RunTime:0.000621s ]
SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 77 LIMIT 1 [ RunTime:0.000243s ]
SELECT * FROM `ls_goods` WHERE `del` = 0 AND `status` = 1 AND `create_time` <= 1772941051 ORDER BY `create_time` DESC LIMIT 5 [ RunTime:0.353455s ]

0.469125s

ShowPageTrace