A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_URI::$config is deprecated

Filename: core/URI.php

Line Number: 101

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Router::$uri is deprecated

Filename: core/Router.php

Line Number: 127

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$benchmark is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$hooks is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$config is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$log is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$utf8 is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$uri is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$exceptions is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$router is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$output is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$security is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$input is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$lang is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$load is deprecated

Filename: core/Controller.php

Line Number: 78

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$apc is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$file is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$cache is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$cacher is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$jscript is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::open($save_path, $name) should either be compatible with SessionHandlerInterface::open(string $path, string $name): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 132

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::close() should either be compatible with SessionHandlerInterface::close(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 290

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::read($session_id) should either be compatible with SessionHandlerInterface::read(string $id): string|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 164

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::write($session_id, $session_data) should either be compatible with SessionHandlerInterface::write(string $id, string $data): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 233

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::destroy($session_id) should either be compatible with SessionHandlerInterface::destroy(string $id): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 313

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::gc($maxlifetime) should either be compatible with SessionHandlerInterface::gc(int $max_lifetime): int|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 354

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 284

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_set_cookie_params(): Session cookie parameters cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 291

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 306

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 316

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 317

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 318

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 319

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 377

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: drivers/Session_files_driver.php

Line Number: 108

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_set_save_handler(): Session save handler cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 110

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_start(): Session cannot be started after headers have already been sent

Filename: Session/Session.php

Line Number: 143

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$session is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$agent is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$contentsStatus is deprecated

Filename: libraries/Common.php

Line Number: 64

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 64
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 24
Function: initContentsStatusInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$articleStatus is deprecated

Filename: libraries/Common.php

Line Number: 71

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 71
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 24
Function: initContentsStatusInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$db is deprecated

Filename: core/Loader.php

Line Number: 390

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 15
Function: database

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_DB_mysqli_driver::$failover is deprecated

Filename: database/DB_driver.php

Line Number: 371

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 15
Function: database

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents_model::$best_cnt is deprecated

Filename: ver3/Contents_model.php

Line Number: 17

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 17
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents_model::$popular_cnt is deprecated

Filename: ver3/Contents_model.php

Line Number: 18

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 18
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$member_model is deprecated

Filename: core/Loader.php

Line Number: 353

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 20
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$contents_model is deprecated

Filename: core/Loader.php

Line Number: 353

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$menuList is deprecated

Filename: libraries/Common.php

Line Number: 561

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 561
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$common is deprecated

Filename: core/Loader.php

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수학동아 - 폴리매스
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주니어 폴리매스 문제
수학 문제를 푸는 매력에 빠져 보세요!
[오일러 프로젝트] 블랙 위도우: 200만 이하 소수의 합은 얼마일까?
수학동아 2020.03.26 23:02 조회 1965
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

 

코.알.못 홍 기자의 코딩 도전기

코딩의 ‘코’자도 모르는 코.알.못. 홍 기자가 수학 문제를 코딩으로 푸는 오일러 프로젝트 문제를 하나하나 해결해 나갈 예정입니다. 오일러 프로젝트는 수학과 프로그래밍 실력을 모두 키울 수 있도록 2001년에 만든 수학 문제 웹사이트입니다. 홍 기자와 함께한다면 수학과 파이썬 모두 정복할 수 있지 않을까요?

 

 

‘어벤져스: 엔드게임’에서 생을 마감해 아쉬웠던 블랙 위도우가 영화 ‘블랙 위도우’로 돌아올 예정이죠.

그런데 표지에서 본 블랙 위도우와 다르게 제 모습은 어딘가 위축돼 보인다고요?

블랙 위도우는 어떤 전투에서도 이길 수 있을 것처럼 당당하지만 전…, 그렇지 않다고요!

과연 제가 블랙 위도우처럼 소수라는 전쟁터에서 살아남을 수 있을까요?

 

 

<오일러 프로젝트 10번 문제>

10 이하의 소수를 모두 더하면 2+3+5+7=17입니다.

200만 이하 소수의 합은 얼마일까요?

 

 

드디어 등장했습니다. 수학계의 타노스 급 문제, 소수입니다. 소수는 1과 자기 자신만을 약수로 가지는 수로 많은 수학자가 소수를 찾는 것에 집중했죠. 그중 고대 그리스의 수학자 에라토스테네스는 소수만 찾을 수 있는 '에라토스테네스의 체'를 고안해내기도 했습니다.

 

 

이번 오일러 프로젝트 10번 문제는 에라토스테네스의 체를 코딩으로 구현해 풀어볼 거예요.

200만 이하의 소수를 찾아 그 합을 구해볼까요?

 

 

파이썬 완전정복! 필수 명령어

 

1. 200만 개의 숫자를 리스트(List)로 나타내기

자동으로 순서가 있는 집합을 만드는 ‘리스트(List) 표기법’을 사용해 수를 나열합니다. 즉 대괄호([])로 리스트라는 걸 표시해 True1, True2, True3처럼 0번부터 200만 번까지 번호가 붙은 True 200만 1개를 리스트 p로 정의합니다.

 

 

2. 이중 반복문으로 합성수를 걸러 소수만 얻기

1월호 오일러 프로젝트에서 다뤘던 ‘for 문’과 ‘range 함수’를 이용해 소수만 남겨 봅시다. 0과 1은 소수도 합성수도 아니므로 True 0, True1은 소수가 아니라는 뜻의 False로 표기하고, True2에서 시작합니다. 에라토스테네스의 체에서 2의 배수부터 지웠던 것처럼, 먼저 False로 바뀌지 않은 가장 작은 i번째 True를 찾습니다.

 

 

i번째 True는 그대로 두고, i의 배수를 번호로 갖는 True를 모두 False로 바꿉니다. 즉 2i번째부터 3i, 4i 등 i 간격으로 모든 True를 False로 바꾸도록 range(시작 번호, 끝 번호+1, 간격) 형태로 코드를 입력합니다.

 

 

두 가지 반복문을 차례대로 실행하면 소수 번호에만 True로 표시됩니다.

 

 

TIP1. 파이썬은 순서를 매길 때 0번부터 시작합니다. 따라서 200만까지 다루기 위해서는 200만 1개의 True를 만들어야 합니다.

 

TIP2. 수많은 자연수에서 소수만 골라낼 때 쓰는 반복문 2개가 같은 듯 다르죠? 등호 1개(=)는 오른쪽 항의 값을 왼쪽 변수에 대입하라는 것, 등호 2개(==)는 양쪽이 같다는 뜻임을 잊지마세요! for 문과 if 문을 마치면서 마침표(:)를 넣는 것도요!

 

 

도전! 오일러 프로젝트 10번 문제 뽀개기

* 코딩 언어는 Python으로 두고 실행하세요!

 

 

#1 200만 1개의 True를 순서대로 나열한 리스트 p를 만듭니다.

#2 소수가 아닌 0과 1번의 True는 미리 False로 바꿉니다.

#3, 4, 5, 6  에라토스테네스의 체 원리로 소수 번째의 True만 남기고 모두 False로 바꿉니다.

#7 구해야 하는 소수의 합을 변수 sum으로 정의하고 초깃값으로 0을 입력합니다.

#8, 9 리스트 p에서 i번째 수가 True라면 i를 sum에 더합니다.

#10 True의 수를 모두 더한 sum을 출력합니다.

 

 

Bonus! 오일러 퀴즈

오일러 프로젝트 10번 문제를 위 코딩창에서 풀어보고, 다음 예제 문제에도 도전해 보세요!

 

1. 300만 이하 소수의 합을 구해보자.

Hint. 곳곳에 있는 ‘2000001’을 다른 숫자로 바꿔보세요!

2. 200만 이하 합성수의 합을 구해보자.

Hint. ‘if p[i] == True: sum = sum + i’의 조건을 바꿔보세요!

 

 

이번 문제를 풀 때 2를 제외한 짝수는 모두 소수가 아니니까

짝수를 빼면 더 빨리 계산 결과를 얻을 수 있지 않을까요?

아래의 계산 시간을 재는 명령어를 사용해 차이를 비교해보세요!

 

 

 

참고로 저의 최고 기록은 0.92초였답니다! (지금은 1.5초정도 나오네요. 왜 다르죠???)

저보다 더 빨리 소수의 합을 구했다면 댓글을 남겨 알려주세요!

그리고 다음 달에도 소수와 관련된 문제가 또 나올 예정이니 기대해주세요~

 

문제 찜하기 목록보기
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  •  
    폴리홀리몰리 Lv.5 2020.03.27 02:00 비밀댓글
    확인요청중
    비밀 댓글이 등록 되었습니다.
    댓글 작성하기 댓글수1
  •  
    폴리홀리몰리 Lv.5 2020.03.27 02:00

    c언어로 하니까 좀더 빨리나오는듯 하네요

    댓글 작성하기 좋아요0 댓글수3
    •  
      홍아름_기자 Lv.5 2020.03.31 23:15

       

      오우.. 파이썬보다가 C언어를 보려니 무슨 말인지 모르겠어요..ㅜㅜ

      혹시 C언어로 푸는 데 시간이 얼마나 걸렸는지 알 수 있을까요?

       

      좋아요0
    •  
      폴리홀리몰리 Lv.5 2020.04.02 00:05

      c언어로는 결과값은 실행하자마자 바로 나옵니다.

      만드는데는 오래걸리지 않았습니다.

      좋아요0
    •  
      홍아름_기자 Lv.5 2020.04.06 18:39

       

      오오 역시 파이썬 다음에 C언어를 배워봐야겠어요!

       

      좋아요0
  •  
    disciple Lv.5 2020.04.03 00:02 비밀댓글
    비밀 댓글이 등록 되었습니다.
    댓글 작성하기 댓글수1
    •  
      홍아름_기자 Lv.5 2020.04.06 18:40

       

      와~ disciple 친구! 제 최고 기록인 0.92초보다 훨씬 빠르게 했네요!

      소수를 찾을 때 2를 제외한 짝수는 확인하지 않도록 해서 그런거죠?

       

       

      좋아요0
  •  
    로보카폴리 Lv.11 2020.04.09 02:20

    #include<cstdio>
    int a[2000005]={1};
    int main(){
        int sum=2;
        for(int i=3;i<2000001;i=i+2){
            if(a[i]){
                for(int j=2*i;j<2000001;j=j+i){
                    a[j]=0;
                }
            }
        }
        for(int i=2;i<2000001;i=i+2){
            if(a[i]){
                sum+=i;
            }
        }
        printf("%d",sum);
        return 0;
    }

     

     

     

    뭐가 잘못됬나요?

    댓글 작성하기 좋아요0 댓글수2
    •  
      홍아름_기자 Lv.5 2020.04.14 17:53

       

      호...혹시... C...C언어 인가요...?

      저는 1도 모르겠어요...ㅜ^ㅜ 친구들! 도와주세요...!

       

      좋아요0
    •  
      매스파이 Lv.8 2020.05.18 00:09

      다시 확인해보니 C++이네요.

      좋아요0
  •  
    매스파이 Lv.8 2020.05.18 00:05 비밀댓글
    확인요청중
    비밀 댓글이 등록 되었습니다.
    댓글 작성하기 댓글수1
  •  
    매스파이 Lv.8 2020.05.18 00:21
    확인요청중

    0.29요!!

    댓글 작성하기 좋아요0 댓글수0
  •  
    매스파이 Lv.8 2020.05.19 22:11
    확인요청중

    0.28초요!

    댓글 작성하기 좋아요0 댓글수0
  •  
    매스파이 Lv.8 2020.05.19 22:15
    확인요청중

    0.26초요!

    댓글 작성하기 좋아요0 댓글수0
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