Computability, Complexity & Algorithms

بواسطة: Udacity

Overview

This class is offered as CS6505 at Georgia Tech where it is a part of the Online Masters Degree (OMS). Taking this course here will not earn credit towards the OMS degree.

In this course, we will ask the big questions, "What is a computer? What are the limits of computation? Are there problems that no computer will ever solve? Are there problems that can’t be solved quickly? What kinds of problems can we solve efficiently and how do we go about developing these algorithms?" Understanding the power and limitations of algorithms helps us develop the tools to make real-world computers smarter, faster and safer.

Syllabus

  • Computability
    • Languages & Countability,Turing Machines,The Church-Turing Thesis
  • Complexity
    • P and NP,NP-Complete Problems,The Golden Ticket
  • Algorithms
    • Dynamic Programming,Fast Fourier Transform,Maximum Flow

Taught by

Hariharan Venkateswaran and Lance Fortnow

Computability, Complexity & Algorithms
الذهاب الي الدورة

Computability, Complexity & Algorithms

بواسطة: Udacity

  • Udacity
  • مجانية
  • الإنجليزية
  • متاح شهادة
  • متاح في أي وقت
  • advanced
  • N/A
8.1.2PHP Version301msRequest Duration2MBMemory UsageGET ar/الدورات/{slug}Route
    • Booting (186ms)
    • Application (114ms)
    • 1 x Booting (61.79%)
      186.07ms
      1 x Application (37.97%)
      114.34ms
      14 templates were rendered
      • public.courses.show (resources/views/public/courses/show.blade.php)3bladefile
        Params
        0
        course
        1
        links
        2
        config
      • public.courses.partials.breadcrumbs (resources/views/public/courses/partials/breadcrumbs.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.courses.partials.heading (resources/views/public/courses/partials/heading.blade.php)7bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        classes
      • public.courses.partials.details (resources/views/public/courses/partials/details.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.courses.partials.breadcrumbs (resources/views/public/courses/partials/breadcrumbs.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.courses.partials.heading (resources/views/public/courses/partials/heading.blade.php)7bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        classes
      • public.layouts.main (resources/views/public/layouts/main.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.layouts.partials.meta (resources/views/public/layouts/partials/meta.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.layouts.partials.navbar (resources/views/public/layouts/partials/navbar.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.auth.profile.partials.links (resources/views/public/auth/profile/partials/links.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      • public.auth.profile.partials.link (resources/views/public/auth/profile/partials/link.blade.php)8bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        route
        7
        title
      • public.auth.profile.partials.link (resources/views/public/auth/profile/partials/link.blade.php)8bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        route
        7
        title
      • public.auth.profile.partials.link (resources/views/public/auth/profile/partials/link.blade.php)8bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
        6
        route
        7
        title
      • public.layouts.partials.flash-session (resources/views/public/layouts/partials/flash-session.blade.php)6bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        course
        4
        links
        5
        config
      uri
      GET ar/الدورات/{slug}
      middleware
      web, localize:ar
      controller
      App\Http\Controllers\CourseController@show
      as
      ar.courses.show
      namespace
      prefix
      /ar
      where
      file
      app/Http/Controllers/CourseController.php:17-35
      7 statements were executed4.7ms
      • select * from `courses` where `slug_ar` = 'computability,-complexity-&-algorithms' limit 1
        3.18ms/app/Http/Controllers/CourseController.php:20corspedia
        Metadata
        Bindings
        • 0. computability,-complexity-&-algorithms
        Backtrace
        • 17. /app/Http/Controllers/CourseController.php:20
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • update `courses` set `visitors` = `visitors` + 1, `courses`.`updated_at` = '2025-04-09 20:49:32' where `id` = 624
        550μs/app/Http/Controllers/CourseController.php:21corspedia
        Metadata
        Bindings
        • 0. 2025-04-09 20:49:32
        • 1. 624
        Backtrace
        • 17. /app/Http/Controllers/CourseController.php:21
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select `id`, `name_en`, `name_ar`, `topic_id`, `slug_en`, `slug_ar` from `subjects` where `subjects`.`id` in (6)
        210μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/CourseController.php:23
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select `id`, `name_en`, `name_ar`, `slug_en`, `slug_ar` from `topics` where `topics`.`id` in (1)
        150μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 25. /app/Http/Controllers/CourseController.php:23
        • 26. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 27. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 28. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `institutions` where `institutions`.`id` in (22) and `institutions`.`deleted_at` is null
        180μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/CourseController.php:23
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `providers` where `providers`.`id` in (6) and `providers`.`deleted_at` is null
        170μs/app/Http/Controllers/CourseController.php:23corspedia
        Metadata
        Backtrace
        • 20. /app/Http/Controllers/CourseController.php:23
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `html_files` where `html_files`.`id` = 618 limit 1
        260μs/app/Models/Course.php:84corspedia
        Metadata
        Bindings
        • 0. 618
        Backtrace
        • 21. /app/Models/Course.php:84
        • 28. view::public.courses.show:29
        • 30. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:125
        • 31. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 32. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:72
      App\Models\HtmlFile
      1
      App\Models\Provider
      1
      App\Models\Institution
      1
      App\Models\Topic
      1
      App\Models\Subject
      1
      App\Models\Course
      1
        _token
        xqoGpWCeAZNT1kbSnl02joBM9fvJ1K672vYUrCdA
        locale
        ar
        _previous
        array:1 [ "url" => "https://www.corspedia.com/ar/%D8%A7%D9%84%D8%AF%D9%88%D8%B1%D8%A7%D8%AA/comput...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /ar/%D8%A7%D9%84%D8%AF%D9%88%D8%B1%D8%A7%D8%AA/computability,-complexity-&-algorithms
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:24 [ "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "3.138.183.117" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "cf-ray" => array:1 [ 0 => "92dcdf20ed0d10c4-ORD" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "x-forwarded-for" => array:1 [ 0 => "3.138.183.117" ] "host" => array:1 [ 0 => "www.corspedia.com" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
        request_server
        0 of 0
        array:50 [ "USER" => "www-data" "HOME" => "/var/www" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "3.138.183.117" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_CF_RAY" => "92dcdf20ed0d10c4-ORD" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_X_FORWARDED_FOR" => "3.138.183.117" "HTTP_HOST" => "www.corspedia.com" "REDIRECT_STATUS" => "200" "SERVER_NAME" => "corspedia.com" "SERVER_PORT" => "443" "SERVER_ADDR" => "141.95.147.152" "REMOTE_USER" => "" "REMOTE_PORT" => "57456" "REMOTE_ADDR" => "172.69.59.197" "SERVER_SOFTWARE" => "nginx/1.18.0" "GATEWAY_INTERFACE" => "CGI/1.1" "HTTPS" => "on" "REQUEST_SCHEME" => "https" "SERVER_PROTOCOL" => "HTTP/2.0" "DOCUMENT_ROOT" => "/var/www/corspedia/public" "DOCUMENT_URI" => "/index.php" "REQUEST_URI" => "/ar/%D8%A7%D9%84%D8%AF%D9%88%D8%B1%D8%A7%D8%AA/computability,-complexity-&-algorithms" "SCRIPT_NAME" => "/index.php" "CONTENT_LENGTH" => "" "CONTENT_TYPE" => "" "REQUEST_METHOD" => "GET" "QUERY_STRING" => "" "SCRIPT_FILENAME" => "/var/www/corspedia/public/index.php" "PATH_INFO" => "" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/index.php" "REQUEST_TIME_FLOAT" => 1744231772.5541 "REQUEST_TIME" => 1744231772 ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Wed, 09 Apr 2025 20:49:32 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjA4dUVpSmlRV0d1Z0JyNXM3L0Y2d3c9PSIsInZhbHVlIjoiTlZFZjQ1UnppUEE0ZkRKNnM3Nit0VzF6djNGaGljWEFJMzYxeWdjdHBsMktDd1l4c2tYblB3RzM1WWJ2Y1hGL2tyOTlNWndYQ0RyZW1QMUEvZjBJNHBHYkdvTkNZTHdzUDJVSHdoV2hRb0p4UmI5WHNRUC9jeEdkUmtSTi9qalgiLCJtYWMiOiI1MTQ1MjgzYzg2MGY3YjI1NWFjNzUxYmFkZTIzNWNkZjJmOGU3ZWZjMjM0ODBkYzFjZjZkNTA3NjczOThlNWZlIiwidGFnIjoiIn0%3D; expires=Wed, 09 Apr 2025 22:49:32 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6IjA4dUVpSmlRV0d1Z0JyNXM3L0Y2d3c9PSIsInZhbHVlIjoiTlZFZjQ1UnppUEE0ZkRKNnM3Nit0VzF6djNGaGljWEFJMzYxeWdjdHBsMktDd1l4c2tYblB3RzM1WWJ2Y1hGL2tyOTlNW" 1 => "laravel_session=eyJpdiI6InV3K3JzVkNUeVhVMDkrUUxleS9aREE9PSIsInZhbHVlIjoiK2VzTmpzWjdBQzA0ZEtreWNuMmxTSWtSZTAxcFQveGczZmU5aHFWdVgyMkdSSUY3cnRYVlVJQWhQemo4TERZQ29sUitjd3RSR042ZUtyRUxhM3JsYnJYMEFUTis1Z2liZDFBKzRnS0hEbzJISEhsUmtxejlhN0FWNjFyQVcxcjciLCJtYWMiOiJkZDE2MGE2MDkyZDA2NDg5YjFhNzMyYzU3ZjE2NDk3NTQ3M2E5YmM2MDkyZjVlMWRmYTIyZjQ5ZTcwNjVlMzEzIiwidGFnIjoiIn0%3D; expires=Wed, 09 Apr 2025 22:49:32 GMT; Max-Age=7200; path=/; httponly; samesite=laxlaravel_session=eyJpdiI6InV3K3JzVkNUeVhVMDkrUUxleS9aREE9PSIsInZhbHVlIjoiK2VzTmpzWjdBQzA0ZEtreWNuMmxTSWtSZTAxcFQveGczZmU5aHFWdVgyMkdSSUY3cnRYVlVJQWhQemo4TERZQ29s" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjA4dUVpSmlRV0d1Z0JyNXM3L0Y2d3c9PSIsInZhbHVlIjoiTlZFZjQ1UnppUEE0ZkRKNnM3Nit0VzF6djNGaGljWEFJMzYxeWdjdHBsMktDd1l4c2tYblB3RzM1WWJ2Y1hGL2tyOTlNWndYQ0RyZW1QMUEvZjBJNHBHYkdvTkNZTHdzUDJVSHdoV2hRb0p4UmI5WHNRUC9jeEdkUmtSTi9qalgiLCJtYWMiOiI1MTQ1MjgzYzg2MGY3YjI1NWFjNzUxYmFkZTIzNWNkZjJmOGU3ZWZjMjM0ODBkYzFjZjZkNTA3NjczOThlNWZlIiwidGFnIjoiIn0%3D; expires=Wed, 09-Apr-2025 22:49:32 GMT; path=/XSRF-TOKEN=eyJpdiI6IjA4dUVpSmlRV0d1Z0JyNXM3L0Y2d3c9PSIsInZhbHVlIjoiTlZFZjQ1UnppUEE0ZkRKNnM3Nit0VzF6djNGaGljWEFJMzYxeWdjdHBsMktDd1l4c2tYblB3RzM1WWJ2Y1hGL2tyOTlNW" 1 => "laravel_session=eyJpdiI6InV3K3JzVkNUeVhVMDkrUUxleS9aREE9PSIsInZhbHVlIjoiK2VzTmpzWjdBQzA0ZEtreWNuMmxTSWtSZTAxcFQveGczZmU5aHFWdVgyMkdSSUY3cnRYVlVJQWhQemo4TERZQ29sUitjd3RSR042ZUtyRUxhM3JsYnJYMEFUTis1Z2liZDFBKzRnS0hEbzJISEhsUmtxejlhN0FWNjFyQVcxcjciLCJtYWMiOiJkZDE2MGE2MDkyZDA2NDg5YjFhNzMyYzU3ZjE2NDk3NTQ3M2E5YmM2MDkyZjVlMWRmYTIyZjQ5ZTcwNjVlMzEzIiwidGFnIjoiIn0%3D; expires=Wed, 09-Apr-2025 22:49:32 GMT; path=/; httponlylaravel_session=eyJpdiI6InV3K3JzVkNUeVhVMDkrUUxleS9aREE9PSIsInZhbHVlIjoiK2VzTmpzWjdBQzA0ZEtreWNuMmxTSWtSZTAxcFQveGczZmU5aHFWdVgyMkdSSUY3cnRYVlVJQWhQemo4TERZQ29s" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "xqoGpWCeAZNT1kbSnl02joBM9fvJ1K672vYUrCdA" "locale" => "ar" "_previous" => array:1 [ "url" => "https://www.corspedia.com/ar/%D8%A7%D9%84%D8%AF%D9%88%D8%B1%D8%A7%D8%AA/computability,-complexity-&-algorithms" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]