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TOC-Erik Dick - Fundametal of Turbomachinery

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C语言回文字母金字塔

水平有限,只是想记录一下,如果能帮到你,那是我的荣幸!效果: 输入行数获得对应行数的字母金字塔。代码: 总结:还是蛮有意思的,比单一符号三角形难度提高了一丢丢吧。先输出一半金字塔,然后把代码稍稍改动,并让第一次不输出,这就是上面的思路。😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁代码(可复制版):1#include<stdio.h>23main()4{5intli,i,j,k,liNum=1;charf='A',ff;6printf("请键入整数行数:");7scanf("%d",&li);8for(i=1;i<=li;i++)9{10f='A';11for(j=26;j>=i;j--)12printf("");13for(k=0;k<liNum;k++)14{15printf("%c",f);16++f;17}18ff=f-1;19for(k=1;k<liNum;k++)20{21--ff;22printf("%c",ff);23}24if(liNum<li)25liNum++;2627printf("\n");28}29}😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁😁

博客园表情符号使用

前言在使用博客园写文章时,除了文字的排版使用,还有就是表情的使用了。😘🤷‍♀️🤷‍♂️🤦‍♂️🤦‍♀️🤦‍♀️👀😊😂🤣❤😍👌😁👍🙌✌🤞😉😎🎶🎶😢💖😜👏💋🎉🌹🎂🤳🐱‍👤🐱‍🏍🐱‍💻🐱‍🐉🐱‍👓🐱‍🚀✔😃✨😆🤔🤢🎁😀😁😂🤣😄😃😅😆😉😊😋😎😍😘🥰😗😙😚☺🙂🤗🤩🤔🤨😐😑😶🙄😏😣😥😮🤐😯😪😫🥱😴😌😛😜😝🤤使用方法windows+.按住windows键加句号键即可弹出表情框。点击表情符号就行。不用区分各种排版句法。什么Markdown、Tinymce、Textbox。

HUAWEI 数通RS

📕eNSP🛫华为HCIP认证👀

日记分类

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[转载] 我的猫猫图灵完备吗? 附xkcd漫画翻译一则

作者:ChloéLourseyre编辑:PeterFordham许可:CC-BY4.0原文:https://belaycpp.com/2021/11/24/is-my-cat-turing-complete/原标题:IsmycatTuring-complete?IsmycatTuring-complete?NOVEMBER24,2021CHLOÉ`SENUA`LOURSEYREThisarticleisanadaptationofaLightningTalkIgaveatCppCon2021.Alinktothevideowillbegivenhereassoonasit’savailable.I'lltouchonalightersubjectthisweek,nonethelessquiteimportant:ismycatTuring-complete?MeetPeluchePeluche(meaning“plush”inFrench)isasmoothcatthatsomehowlivesinmyhouse.Shewillbeourtestsubjecttoday.IsPelucheTuring-complete?WhatisTuring-completenessTuring-completenessisthenotionthatifadevicecanemulateaTuringmachine,thenitcanperformanykindofcomputation1.Itmeansthatanymachinethatimplementstheeightfollowinginstructionsisacomputer(andcanthusexecuteanykindofcomputation):.and,:Inputtingandoutputtingavalue+and-:Increaseanddecreasethevaluecontainedinamemorycell2.>and<:Shiftthecurrentmemorytapeleftorright.[and]:Performingloops.So,ifPeluchecanperformtheseeightinstructions,wecanconsiderherTuring-complete.ProofoftheTuring-completenessInputandoutputFirst,ItriedtopokePelucheifIcouldgetareaction.Shelookedatme,thenjustturnedaround.Sohereitis:Ipokedher,andIgotareaction.Soshecanprocessinputsandgiveoutputs.Input/outputconfirmed!IncreaseanddecreasememoryvalueTheotherday,Icamebackfromworktothis:Kibbleseverywhere;ButthenItookacloserlookandrealizedthattheslabscouldbenumbered,likethis:Thislooksprettymuchlikeamemorytapetome!Sinceshecanspillkibblesonthetilesandtheneatthemdirectlyfromthefloor,shecanincreaseanddecreasethevaluescontainedinagivenmemorycell.Increase/decreaseconfirmed!ShiftthecurrentmemorycellleftorrightAnothertime,Iwasdoingthedishesand inadvertently spilledsomewateronPeluche.Shebegantoruneverywherearoundthekitchen,makingahugemess.Ifyoulookclose(atthetipoftheredarrow),youmaynoticethatwhilemakingthismess,shedisplacedherbowl.Displacingherbowlmeansshewillspillherkibblesinanothertile.Thiscountsasshiftingthememoryheadtoeditanothermemorycell.Shiftofthememorytapeconfirmed!PerformloopsSo,afterthismess,I(obviously)hadtocleanup.Nomorethanfiveminuteslater,Iwentbacktothekitchentothis:Yeah…shecan DEFINITELY performloops…Loopsconfirmed!WehavejustproventhatPelucheis,indeed,Turing-complete.Sonow,howcanweusehertoperformhigh-performancecomputations?Whattodowithher?NowthatI’veproventhatPelucheisTuring-complete,Icanliterallydoanythingwithher!Thus,Itriedtogivehersimplecodetoexecute3:😾😾😾😾😾😾😾😾😿🐈😾🐈😾😾🐈😾😾😾🐈😾😾😾😾🐈😾😾😾😾😾🐈😾😾😾😾😾😾🐈😾😾😾😾😾😾😾🐈😾😾😾😾😾😾😾😾🐈😾😾😾😾😾😾😾😾😾🐈😾😾😾😾😾😾😾😾😾😾🐈😾😾😾😾😾😾😾😾😾😾😾🐈😾😾😾😾😾😾😾😾😾😾😾😾🐈😾😾😾😾😾😾😾😾😾😾😾😾😾🐈😾😾😾😾😾😾😾😾😾😾😾😾😾😾🐈😾😾😾😾😾😾😾😾😾😾😾😾😾😾😾🐈😾😾😾😾😾😾😾😾😾😾😾😾😾😾😾😾😻😻😻😻😻😻😻😻😻😻😻😻😻😻😻😻🐾😸🐈🐈🐈🐈🐈🐈🐈🐈🐈🙀😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐾🐾🐾🙀😾😾😾😻😻😻😻😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐾🐾🐾🐾🙀😾😾😾😾😻😻😻😻😻😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐾🐾🐾🐾🙀😾😾😾😾😻😻😻😻😻😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐾🙀😾😻😻😻😻😻😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🙀😻😻😻😻🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐾🙀😾😻😻😻😻😻😻😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐾🙀😾😻😻😻😻😻😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈😾😾🙀🐾🐾😻😻😻😻😻😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐾🐾🐾🐾🙀😾😾😾😾😻😻😻😻😻😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐈🐾🐾🐾🐾🙀😾😾😾😾😻😻😻😻😻😻😻😻😻😻😻😻😻🐈🐈🐈🐈🐈🐈🐾🐾🙀😾😾😻😻😻😻😻😻🙀Theresultwasfinal:shewouldn’tdoathing.Thoughtheycan,maybecatsarenotdesignedtoexecutecodeafterall?About"cat-computing"Jokesaside, cat-computing isthenameIgivetothisgeneralizedpractice.Inmyexperience,ithappensquiteoftenthatwhensomeonediscoversanewfeatureofalanguage,theybegintouseiteverywhere,justbecausetheycanandtheywantto.However,justlikeyoucanexecutecodeusingacat4 butshouldn’t,it’snotbecauseyou can useafeaturethatyou should.Theyweretoobusywonderingiftheycouldtothinkaboutwhethertheyshould.DRIANMALCOLM,JURASSICPARKWrappingupCat-computingseemstobearookiemistake(anditis),buteventhemostexperienceddeveloperssometimesmakerookiemistakes(andthere’snoshameinthat).Everythreeyears,anewversionofC++ispublished.Everytime,itmakesmewanttousethenewfeaturesineverypossiblesituation.Thoughthisisagoodopportunitytobuildsomeexperiencearoundthat(oneofthebestwaystoavoidmisusesofafeatureistoperformthesemisusesonce,inmyopinion),thisisalsofavorablegroundforacquiringbadpractices.Alwaysaskyourselfifafeatureisnecessary5 beforeusingit,orelseyoumaydocat-computing.Also,cat-computingisanimalabuse,sodon’tdoit.Thanksforreadingandseeyounextweek!(Nocatswereharmedduringthewritingofthisarticle,butonewasgentlypoked.)Author: ChloéLourseyreEditor: PeterFordhamAddendumNotesThisisasimplifieddefinition,veryinaccuratebutaccurateenoughforthisexample.Ifyouwanttherealdefinition,gothere: Turingcompleteness–WikipediaIdidnotstateitexplicitly,butaTuringmachinehasa“memorytape”with“memorycells”onit.Themachineisalwayspointingtoamemorycell,whichisthementioned“current”memorycell.Youmaynotbeabletoreadthissampleofcode—thisisafancynewlanguageIdesignedcalled“braincat”.Actually,youcan’texecutecodeusingacat,Iknow,butit’sforthesakeofthemetaphorthatIassumeyoucan.Ofcourse,necessityoccurswhenthereisaknownbenefittothefeature.I’mnottalkingabout“absolutenecessity”butabout“practicalnecessity”.附"我证明了它是图灵完备的!"这种情形要么发生在一个人花了六个月让他的洗碗机能够运行马里奥的时候,要么就是在被包围的时候作者:xkcd许可:CreativeCommonsAttribution-NonCommercial2.5License.链接:https://xkcd.com/2556/

RESTful 架构详解

RESTful架构详解指路👇👇👇👇👇👇👇👇https://www.runoob.com/w3cnote/restful-architecture.html

任务计划

注:本博客五天一更2020.12.14P3715CF702FCF710FGym101480C2020.12.19P4632Gym101480CP6144CF575A2020.12.24P7154P7155P46322020.12.29P3233CF639FP4606CF1320ELOJ6184P3803P4721P4238P4245CF632EAT2064CF1096G2021.1.4P2664P2993P6329P2056P38092021.1.9P2408P4051P4248P31812021.1.14马上要qmks了,估计今天rwjh里的全部内容会原样搬到1.19CF986DCF755GCF623ECF773FCF553ECF848EP3784P4002P4463P4491UVA11107P4051P2336P3649P4341P4070P5028P4081P4094P1117P3900P4770P60952021.1.19真就CV了呗。。。其实并没有完全CV,换了一道题而已。。。CF226ECF755GCF623ECF773FCF553ECF848EP3784P4002P4463P4491UVA11107P4051P2336P3649P4341P4070P5028P4081P4094P1117P3900P4770P60952021.1.24CF226ECF553ECF848EP3784P4002P4463P4491UVA11107P2336P3649P4341P4070P5028P4081P4094P1117P3900P4770P60952021.1.27CF553ECF848EP4002P4463P4705P5320UVA11107P2336P3649P4341P4070P5028P4081P4094P1117P3900P4770P6095P71732021.2.1就nm彻底自闭了,任务计划不降反增CF553ECF848EP4002P4463P4705UVA11107P2336P3649P4341P4070P5028P4081P4094P1117P3900P4770P6095P3288P4452P3163P3171P2304P2570P3199P4074UOJ435CF506DP3396CF587FCF601E2021.2.6u1s1这当中有的题都在里面躺了五六轮了就离谱CF553ECF848EP4002P4463P4705UVA11107P2336P3649P4341P4070P5028P4081P4094P1117P3900P4770P6095P3288P4452P3163P3171P2304P2570P3199CF576ECF601E2021.2.11🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊CF553ECF848EP4002P4463P4705UOJ269UVA11107P2336P3649P4341P4070P5028P4081P4094P1117P3900P4770P6095P3288P4452P3163P3171P2304P2570P31992021.2.18🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊CF553ECF848EP4002P4463P4705UOJ269UVA11107P2336P3649P4341P4070P5028P4081P4094P1117P3900P4770P6095P3288P4452P3163P3171P2304P2570P3199CF375CAT1982CF878DCF797FCF643FCF505ECF671DCF571DCF536DCF555EP3246CF266EAT4120CF446CP5280P7334P5138CF226EP6091P4718CF587FCF1327GCF163EP55992021.2.23🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊CF553ECF848EP4002P4463P4705UOJ269P3649P5028P4094P3900P4770P6095BZOJ4310CF204ECF700EP4022CF666ECF1063FCF653FP5353P3288P4452P3163P3171P2304P2570P3199CF643FCF671DCF571DCF536DCF555EP3246CF266EAT4120CF446CP5280P7334P5138CF981FCF917ECF700DCF605DP6371CF248E2021.2.28🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊CF553ECF848EP4002P4463P4705UOJ269P3900CF1063FCF741EP5284P5353P3288P4452P3163P3171P2304P2570P3199CF671DP3246CF446CP5280P5138CF248EP4284CF1340FCF671ECF498BCF643GCF627ECF763ECF889ECF704CCF436DCF708ECF1080E2021.3.5🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊🕊CF553ECF848EP4002P4463P4705UOJ269P5284P3288P4452P3163P3171P2304P2570P3199CF671DP3246CF248EP4284CF1340FCF671ECF498BCF627ECF763ECF889ECF704CCF436DCF708ECF1080EP3688CF573ECF1476GAT1983CF833DP3576P3596P1623AT3859CF115ECF285ECF917CCF193DCF1097GCF815CCF633H2021.3.16爽CF553ECF848EP4002P4463P4705UOJ269AT3872P3288P4452P3163P3171P2304P2570P31992021.3.25CF553ECF848EP4002P4463P4705UOJ269AT3872P3645CF671DCF671ECF613ECF804DP6619P6622~~AT2377P4679AT2045P5284P5289P43822021.3.28CF671DCF671EP4382P4384P4363P4364P4365P5643P5299P5644P5206P3822P3823P3825P3826UOJ422LOJ3399UOJ345P47692021.4.18我tm也太鸽了吧。。。P5206P4426AT3945P5360CF568CP3714P3343P5279P5210P5303P5354P3242P3759P3248P5039P4452P5332P5501P53372021.6.30我giao我都多少天没有更了……P5360CF568CP3714P5279P3242P3248P5332P4708P3285CF1396DP4243P5294CF1045AP1587P3783P5344CF1415FP5450CF983ECF1010FP4076CF1045EP3302P3206P7470P7620P5446CF613ECF652FCF1089IP52062021.8.3现在五周一更还差不多(CF568CP3714P5279P3242P3248P3285CF1394DP4243CF1415FCF1045EP3302P3206P5044CF917EP5812CF500GAT2268P6774CF1408IAT2348CF720BCF1063FCF1464FCF1473GCF1392IP4458P4217CF724EP3872P4082CF1106FP4365AT4515P4177P5295P5814P2304CF598FUOJ218

JS数据类型转换完全攻略

指路👇👇👇👇👇👇👇http://c.biancheng.net/view/5477.html

问题记录:解决𝘃𝟮𝗿𝗮𝘆代理HTTP没用的问题

𝘃𝟮𝗿𝗮𝘆-参数设置-本地监听端口改成1079。看𝘃𝟮𝗿𝗮𝘆N底部状态栏,发现http代理变成1080.

mac下mysql无法使用中文问题

查询网上大部分资料是把/usr/local/mysql/support-files/目录下并没有my-default.cnf文件copy到/etc/my.cnf下,但是新版mac版mysql在/usr/local/mysql/support-files/目录下并没有my-default.cnf解决办法:1、首先关闭mysql服务(命令关闭或界面关闭自选)2、终端cd /etc3、sudovimmy.cnf4、i进入插入模式,复制下面文件拷贝进来5、esc退出编辑模式,输入:wq保存并退出6、在mysql命令模式下可以键入"status"来查看字符支持格式(1).修改前 (2).修改后附上my.cnf内容􏰀􏰁􏰂􏰃􏰄􏰅􏰆􏰇􏰈􏰉---------------------------------不包含-----------------------------------􏰊􏰋􏰌􏰍􏰎􏰏􏰐􏰑􏰒􏰓􏰔􏰕􏰖􏰁􏰗􏰘􏰙􏰚􏰛􏰑􏰜􏰝􏰞􏰟􏰁􏰠􏰡􏰢􏰁􏰣􏰟􏰇􏰤􏰥􏰋􏰙􏰀􏰁􏰂􏰃􏰄􏰅􏰆􏰇􏰈􏰉􏰊􏰋􏰌􏰍􏰎􏰏􏰐􏰑􏰒􏰓􏰔􏰕􏰖􏰁􏰗􏰘􏰙􏰚􏰛􏰑􏰜􏰝􏰞􏰟􏰁􏰠􏰡􏰢􏰁􏰣􏰟􏰇􏰤􏰥􏰊􏰋􏰌􏰍􏰎􏰏􏰐􏰑􏰒􏰓􏰔􏰕􏰖􏰁􏰗􏰘􏰙􏰚􏰛􏰑􏰜􏰝􏰞􏰟􏰁􏰠􏰡􏰢􏰁􏰣􏰟􏰇􏰤􏰊􏰋􏰌􏰍􏰎􏰏􏰐􏰑􏰒􏰓􏰔􏰕􏰖􏰁􏰗􏰘􏰙􏰚􏰛􏰑􏰜􏰝􏰞􏰟􏰁􏰠􏰡􏰢􏰁􏰣􏰟􏰇􏰤􏰥􏰋􏰙􏰊􏰋􏰌􏰍􏰎􏰏􏰐􏰑􏰒􏰓􏰔􏰕􏰖􏰁􏰗􏰘􏰙􏰚􏰛􏰑􏰜􏰝􏰞􏰟􏰁􏰠􏰡􏰢􏰁􏰣􏰟􏰇􏰤􏰥􏰋􏰙#ExampleMySQLconfigfileformediumsystems.##Thisisforasystemwithlittlememory(32M-64M)whereMySQLplays#animportantpart,orsystemsupto128MwhereMySQLisusedtogetherwith#otherprograms(suchasawebserver)##MySQLprogramslookforoptionfilesinasetof#locationswhichdependonthedeploymentplatform.#Youcancopythisoptionfiletooneofthose#locations.Forinformationabouttheselocations,see:#http://dev.mysql.com/doc/mysql/en/option-files.html##Inthisfile,youcanusealllongoptionsthataprogramsupports.#Ifyouwanttoknowwhichoptionsaprogramsupports,runtheprogram#withthe"--help"option.#ThefollowingoptionswillbepassedtoallMySQLclients[client]default-character-set=utf8#password=your_passwordport=3306socket=/tmp/mysql.sock#Herefollowsentriesforsomespecificprograms#TheMySQLserver[mysqld]character-set-server=utf8init_connect='SETNAMESutf8port=3306socket=/tmp/mysql.sockskip-external-lockingkey_buffer_size=16Mmax_allowed_packet=1Mtable_open_cache=64sort_buffer_size=512Knet_buffer_length=8Kread_buffer_size=256Kread_rnd_buffer_size=512Kmyisam_sort_buffer_size=8Mcharacter-set-server=utf8secure_file_priv=''init_connect='SETNAMESutf8'#Don'tlistenonaTCP/IPportatall.Thiscanbeasecurityenhancement,#ifallprocessesthatneedtoconnecttomysqldrunonthesamehost.#AllinteractionwithmysqldmustbemadeviaUnixsocketsornamedpipes.#NotethatusingthisoptionwithoutenablingnamedpipesonWindows#(viathe"enable-named-pipe"option)willrendermysqlduseless!##skip-networking#ReplicationMasterServer(default)#binaryloggingisrequiredforreplicationlog-bin=mysql-bin#binaryloggingformat-mixedrecommendedbinlog_format=mixed#requireduniqueidbetween1and2^32-1#defaultsto1ifmaster-hostisnotset#butwillnotfunctionasamasterifomittedserver-id=1#ReplicationSlave(commentoutmastersectiontousethis)##Toconfigurethishostasareplicationslave,youcanchoosebetween#twomethods:##1)UsetheCHANGEMASTERTOcommand(fullydescribedinourmanual)-#thesyntaxis:##CHANGEMASTERTOMASTER_HOST=<host>,MASTER_PORT=<port>,#MASTER_USER=<user>,MASTER_PASSWORD=<password>;##whereyoureplace<host>,<user>,<password>byquotedstringsand#<port>bythemaster'sportnumber(3306bydefault).##Example:##CHANGEMASTERTOMASTER_HOST='125.564.12.1',MASTER_PORT=3306,#MASTER_USER='joe',MASTER_PASSWORD='secret';##OR##2)Setthevariablesbelow.However,incaseyouchoosethismethod,then#startreplicationforthefirsttime(evenunsuccessfully,forexample#ifyoumistypedthepasswordinmaster-passwordandtheslavefailsto#connect),theslavewillcreateamaster.infofile,andanylater#changeinthisfiletothevariables'valuesbelowwillbeignoredand#overriddenbythecontentofthemaster.infofile,unlessyoushutdown#theslaveserver,deletemaster.infoandrestarttheslaverserver.#Forthatreason,youmaywanttoleavethelinesbelowuntouched#(commented)andinsteaduseCHANGEMASTERTO(seeabove)##requireduniqueidbetween2and2^32-1#(anddifferentfromthemaster)#defaultsto2ifmaster-hostisset#butwillnotfunctionasaslaveifomitted#server-id=2##Thereplicationmasterforthisslave-required#master-host=<hostname>##Theusernametheslavewilluseforauthenticationwhenconnecting#tothemaster-required#master-user=<username>##Thepasswordtheslavewillauthenticatewithwhenconnectingto#themaster-required#master-password=<password>##Theportthemasterislisteningon.#optional-defaultsto3306#master-port=<port>##binarylogging-notrequiredforslaves,butrecommended#log-bin=mysql-bin#UncommentthefollowingifyouareusingInnoDBtables#innodb_data_home_dir=/usr/local/mysql/data#innodb_data_file_path=ibdata1:10M:autoextend#innodb_log_group_home_dir=/usr/local/mysql/data#Youcanset.._buffer_pool_sizeupto50-80%#ofRAMbutbewareofsettingmemoryusagetoohigh#innodb_buffer_pool_size=16M#innodb_additional_mem_pool_size=2M#Set.._log_file_sizeto25%ofbufferpoolsize#innodb_log_file_size=5M#innodb_log_buffer_size=8M#innodb_flush_log_at_trx_commit=1#innodb_lock_wait_timeout=50[mysqldump]quickmax_allowed_packet=16M[mysql]no-auto-rehash#RemovethenextcommentcharacterifyouarenotfamiliarwithSQL#safe-updatesdefault-character-set=utf8[myisamchk]key_buffer_size=20Msort_buffer_size=20Mread_buffer=2Mwrite_buffer=2M[mysqlhotcopy]interactive-timeout---------------------------------不包含-----------------------------------

oracle 18c ORA-01078: failure in processing system parameters

SQL>startup;ORA-01078:failureinprocessingsystemparametersLRM-00109:'.../oracle/oracle/product/18/db_1/dbs/initorcl.ora'方法1:将本目录下init.ora复制一份为initorcl.ora方法2:从路径/data/oracle/oracle/admin/orcl/pfile/复制一份

Typora中的emoji表情

People😄 :smile:😆 :laughing:😫 :tired_face:😊 :blush:😃 :smiley:☺️ :relaxed:😏 :smirk:😍 :heart_eyes:😘 :kissing_heart:😚 :kissing_closed_eyes:😳 :flushed:😌 :relieved:😆 :satisfied:😁 :grin:😉 :wink:😜 :stuck_out_tongue_winking_eye:😝 :stuck_out_tongue_closed_eyes:😀 :grinning:😗 :kissing:😙 :kissing_smiling_eyes:😛 :stuck_out_tongue:😴 :sleeping:😟 :worried:😦 :frowning:😧 :anguished:😮 :open_mouth:😬 :grimacing:😕 :confused:😯 :hushed:😑 :expressionless:😒 :unamused:😅 :sweat_smile:😓 :sweat:😥 :disappointed_relieved:😩 :weary:😔 :pensive:😞 :disappointed:😖 :confounded:😨 :fearful:😰 :cold_sweat:😣 :persevere:😢 :cry:😭 :sob:😂 :joy:😲 :astonished:😱 :scream:  😠 :angry:😡 :rage:😤 :triumph:😪 :sleepy:😋 :yum:😷 :mask:😎 :sunglasses:😵 :dizzy_face:👿 :imp:😈 :smiling_imp:😐 :neutral_face:😶 :no_mouth:😇 :innocent:👽 :alien:💛 :yellow_heart:💙 :blue_heart:💜 :purple_heart:❤️ :heart:💚 :green_heart:💔 :broken_heart:💓 :heartbeat:💗 :heartpulse:💕 :two_hearts:💞 :revolving_hearts:💘 :cupid:💖 :sparkling_heart:✨ :sparkles:⭐️ :star:🌟 :star2:💫 :dizzy:💥 :boom:💥 :collision:💢 :anger:❗️ :exclamation:❓ :question:❕ :grey_exclamation:❔ :grey_question:💤 :zzz:💨 :dash:💦 :sweat_drops:🎶 :notes:🎵 :musical_note:🔥 :fire:💩 :hankey:💩 :poop:💩 :shit:👍 :+1:👍 :thumbsup:👎 :-1:👎 :thumbsdown:👌 :ok_hand:👊 :punch:👊 :facepunch:✊ :fist:✌️ :v:👋 :wave:✋ :hand:✋ :raised_hand:👐 :open_hands:☝️ :point_up:👇 :point_down:👈 :point_left:👉 :point_right:🙌 :raised_hands:🙏 :pray:👆 :point_up_2:👏 :clap:💪 :muscle:🤘 :metal:🖕 :fu:🚶 :walking:🏃 :runner:🏃 :running:👫 :couple:👪 :family:👬 :two_men_holding_hands:👭 :two_women_holding_hands:💃 :dancer:👯 :dancers:🙆 :ok_woman:🙅 :no_good:💁 :information_desk_person:🙋 :raising_hand:👰 :bride_with_veil:🙎 :person_with_pouting_face:🙍 :person_frowning:🙇 :bow::couplekiss: :couplekiss:💑 :couple_with_heart:💆 :massage:💇 :haircut:💅 :nail_care:👦 :boy:👧 :girl:👩 :woman:👨 :man:👶 :baby:👵 :older_woman:👴 :older_man:👱 :person_with_blond_hair:👲 :man_with_gua_pi_mao:👳 :man_with_turban:👷 :construction_worker:👮 :cop:👼 :angel:👸 :princess:😺 :smiley_cat:😸 :smile_cat:😻 :heart_eyes_cat:😽 :kissing_cat:😼 :smirk_cat:🙀 :scream_cat:😿 :crying_cat_face:😹 :joy_cat:😾 :pouting_cat:👹 :japanese_ogre:👺 :japanese_goblin:🙈 :see_no_evil:🙉 :hear_no_evil:🙊 :speak_no_evil:💂 :guardsman:💀 :skull:🐾 :feet:👄 :lips:💋 :kiss:💧 :droplet:👂 :ear:👀 :eyes:👃 :nose:👅 :tongue:💌 :love_letter:👤 :bust_in_silhouette:👥 :busts_in_silhouette:💬 :speech_balloon:💭 :thought_balloon:Nature☀️ :sunny:☔️ :umbrella:☁️ :cloud:❄️ :snowflake:⛄️ :snowman:⚡️ :zap:🌀 :cyclone:🌁 :foggy:🌊 :ocean:🐱 :cat:🐶 :dog:🐭 :mouse:🐹 :hamster:🐰 :rabbit:🐺 :wolf:🐸 :frog:🐯 :tiger:🐨 :koala:🐻 :bear:🐷 :pig:🐽 :pig_nose:🐮 :cow:🐗 :boar:🐵 :monkey_face:🐒 :monkey:🐴 :horse:🐎 :racehorse:🐫 :camel:🐑 :sheep:🐘 :elephant:🐼 :panda_face:🐍 :snake:🐦 :bird:🐤 :baby_chick:🐥 :hatched_chick:🐣 :hatching_chick:🐔 :chicken:🐧 :penguin:🐢 :turtle:🐛 :bug:🐝 :honeybee:🐜 :ant:🐞 :beetle:🐌 :snail:🐙 :octopus:🐠 :tropical_fish:🐟 :fish:🐳 :whale:🐋 :whale2:🐬 :dolphin:🐄 :cow2:🐏 :ram:🐀 :rat:🐃 :water_buffalo:🐅 :tiger2:🐇 :rabbit2:🐉 :dragon:🐐 :goat:🐓 :rooster:🐕 :dog2:🐖 :pig2:🐁 :mouse2:🐂 :ox:🐲 :dragon_face:🐡 :blowfish:🐊 :crocodile:🐪 :dromedary_camel:🐆 :leopard:🐈 :cat2:🐩 :poodle:🐾 :paw_prints:💐 :bouquet:🌸 :cherry_blossom:🌷 :tulip:🍀 :four_leaf_clover:🌹 :rose:🌻 :sunflower:🌺 :hibiscus:🍁 :maple_leaf:🍃 :leaves:🍂 :fallen_leaf:🌿 :herb:🍄 :mushroom:🌵 :cactus:🌴 :palm_tree:🌲 :evergreen_tree:🌳 :deciduous_tree:🌰 :chestnut:🌱 :seedling:🌼 :blossom:🌾 :ear_of_rice:🐚 :shell:🌐 :globe_with_meridians:🌞 :sun_with_face:🌝 :full_moon_with_face:🌚 :new_moon_with_face:🌑 :new_moon:🌒 :waxing_crescent_moon:🌓 :first_quarter_moon:🌔 :waxing_gibbous_moon:🌕 :full_moon:🌖 :waning_gibbous_moon:🌗 :last_quarter_moon:🌘 :waning_crescent_moon:🌜 :last_quarter_moon_with_face:🌛 :first_quarter_moon_with_face:🌔 :moon:🌍 :earth_africa:🌎 :earth_americas:🌏 :earth_asia:🌋 :volcano:🌌 :milky_way:⛅️ :partly_sunny: Object🎍 :bamboo:💝 :gift_heart:🎎 :dolls:🎒 :school_satchel:🎓 :mortar_board:🎏 :flags:🎆 :fireworks:🎇 :sparkler:🎐 :wind_chime:🎑 :rice_scene:🎃 :jack_o_lantern:👻 :ghost:🎅 :santa:🎄 :christmas_tree:🎁 :gift:🔔 :bell:🔕 :no_bell:🎋 :tanabata_tree:🎉 :tada:🎊 :confetti_ball:🎈 :balloon:🔮 :crystal_ball:💿 :cd:📀 :dvd:💾 :floppy_disk:📷 :camera:📹 :video_camera:🎥 :movie_camera:💻 :computer:📺 :tv:📱 :iphone:☎️ :phone:☎️ :telephone:📞 :telephone_receiver:📟 :pager:📠 :fax:💽 :minidisc:📼 :vhs:🔉 :sound:🔈 :speaker:🔇 :mute:📢 :loudspeaker:📣 :mega:⌛️ :hourglass:⏳ :hourglass_flowing_sand:⏰ :alarm_clock:⌚️ :watch:📻 :radio:📡 :satellite:➿ :loop:🔍 :mag:🔎 :mag_right:🔓 :unlock:🔒 :lock:🔏 :lock_with_ink_pen:🔐 :closed_lock_with_key:🔑 :key:💡 :bulb:🔦 :flashlight:🔆 :high_brightness:🔅 :low_brightness:🔌 :electric_plug:🔋 :battery:📲 :calling:✉️ :email:📫 :mailbox:📮 :postbox:🛀 :bath:🛁 :bathtub:🚿 :shower:🚽 :toilet:🔧 :wrench:🔩 :nut_and_bolt:🔨 :hammer:💺 :seat:💰 :moneybag:💴 :yen:💵 :dollar:💷 :pound:💶 :euro:💳 :credit_card:💸 :money_with_wings:📧 :e-mail:📥 :inbox_tray:📤 :outbox_tray:✉️ :envelope:📨 :incoming_envelope:📯 :postal_horn:📪 :mailbox_closed:📬 :mailbox_with_mail:📭 :mailbox_with_no_mail:🚪 :door:🚬 :smoking:💣 :bomb:🔫 :gun:🔪 :hocho:💊 :pill:💉 :syringe:📄 :page_facing_up:📃 :page_with_curl:📑 :bookmark_tabs:📊 :bar_chart:📈 :chart_with_upwards_trend:📉 :chart_with_downwards_trend:📜 :scroll:📋 :clipboard:📆 :calendar:📅 :date:📇 :card_index:📁 :file_folder:📂 :open_file_folder:✂️ :scissors:📌 :pushpin:📎 :paperclip:✒️ :black_nib:✏️ :pencil2:📏 :straight_ruler:📐 :triangular_ruler:📕 :closed_book:📗 :green_book:📘 :blue_book:📙 :orange_book:📓 :notebook:📔 :notebook_with_decorative_cover:📒 :ledger:📚 :books:🔖 :bookmark:📛 :name_badge:🔬 :microscope:🔭 :telescope:📰 :newspaper:🏈 :football:🏀 :basketball:⚽️ :soccer:⚾️ :baseball:🎾 :tennis:🎱 :8ball:🏉 :rugby_football:🎳 :bowling:⛳️ :golf:🚵 :mountain_bicyclist:🚴 :bicyclist:🏇 :horse_racing:🏂 :snowboarder:🏊 :swimmer:🏄 :surfer:🎿 :ski:♠️ :spades:♥️ :hearts:♣️ :clubs:♦️ :diamonds:💎 :gem:💍 :ring:🏆 :trophy:🎼 :musical_score:🎹 :musical_keyboard:🎻 :violin:👾 :space_invader:🎮 :video_game:🃏 :black_joker:🎴 :flower_playing_cards:🎲 :game_die:🎯 :dart:🀄️ :mahjong:🎬 :clapper:📝 :memo:📝 :pencil:📖 :book:🎨 :art:🎤 :microphone:🎧 :headphones:🎺 :trumpet:🎷 :saxophone:🎸 :guitar:👞 :shoe:👡 :sandal:👠 :high_heel:💄 :lipstick:👢 :boot:👕 :shirt:👕 :tshirt:👔 :necktie:👚 :womans_clothes:👗 :dress:🎽 :running_shirt_with_sash:👖 :jeans:👘 :kimono:👙 :bikini:🎀 :ribbon:🎩 :tophat:👑 :crown:👒 :womans_hat:👞 :mans_shoe:🌂 :closed_umbrella:💼 :briefcase:👜 :handbag:👝 :pouch:👛 :purse:👓 :eyeglasses:🎣 :fishing_pole_and_fish:☕️ :coffee:🍵 :tea:🍶 :sake:🍼 :baby_bottle:🍺 :beer:🍻 :beers:🍸 :cocktail:🍹 :tropical_drink:🍷 :wine_glass:🍴 :fork_and_knife:🍕 :pizza:🍔 :hamburger:🍟 :fries:🍗 :poultry_leg:🍖 :meat_on_bone:🍝 :spaghetti:🍛 :curry:🍤 :fried_shrimp:🍱 :bento:🍣 :sushi:🍥 :fish_cake:🍙 :rice_ball:🍘 :rice_cracker:🍚 :rice:🍜 :ramen:🍲 :stew:🍢 :oden:🍡 :dango:🥚 :egg:🍞 :bread:🍩 :doughnut:🍮 :custard:🍦 :icecream:🍨 :ice_cream:🍧 :shaved_ice:🎂 :birthday:🍰 :cake:🍪 :cookie:🍫 :chocolate_bar:🍬 :candy:🍭 :lollipop:🍯 :honey_pot:🍎 :apple:🍏 :green_apple:🍊 :tangerine:🍋 :lemon:🍒 :cherries:🍇 :grapes:🍉 :watermelon:🍓 :strawberry:🍑 :peach:🍈 :melon:🍌 :banana:🍐 :pear:🍍 :pineapple:🍠 :sweet_potato:🍆 :eggplant:🍅 :tomato:🌽 :corn:  Places🏠 :house:🏡 :house_with_garden:🏫 :school:🏢 :office:🏣 :post_office:🏥 :hospital:🏦 :bank:🏪 :convenience_store:🏩 :love_hotel:🏨 :hotel:💒 :wedding:⛪️ :church:🏬 :department_store:🏤 :european_post_office:🌇 :city_sunrise:🌆 :city_sunset:🏯 :japanese_castle:🏰 :european_castle:⛺️ :tent:🏭 :factory:🗼 :tokyo_tower:🗾 :japan:🗻 :mount_fuji:🌄 :sunrise_over_mountains:🌅 :sunrise:🌠 :stars:🗽 :statue_of_liberty:🌉 :bridge_at_night:🎠 :carousel_horse:🌈 :rainbow:🎡 :ferris_wheel:⛲️ :fountain:🎢 :roller_coaster:🚢 :ship:🚤 :speedboat:⛵️ :boat:⛵️ :sailboat:🚣 :rowboat:⚓️ :anchor:🚀 :rocket:✈️ :airplane:🚁 :helicopter:🚂 :steam_locomotive:🚊 :tram:🚞 :mountain_railway:🚲 :bike:🚡 :aerial_tramway:🚟 :suspension_railway:🚠 :mountain_cableway:🚜 :tractor:🚙 :blue_car:🚘 :oncoming_automobile:🚗 :car:🚗 :red_car:🚕 :taxi:🚖 :oncoming_taxi:🚛 :articulated_lorry:🚌 :bus:🚍 :oncoming_bus:🚨 :rotating_light:🚓 :police_car:🚔 :oncoming_police_car:🚒 :fire_engine:🚑 :ambulance:🚐 :minibus:🚚 :truck:🚋 :train:🚉 :station:🚆 :train2:🚅 :bullettrain_front:🚄 :bullettrain_side:🚈 :light_rail:🚝 :monorail:🚃 :railway_car:🚎 :trolleybus:🎫 :ticket:⛽️ :fuelpump:🚦 :vertical_traffic_light:🚥 :traffic_light:⚠️ :warning:🚧 :construction:🔰 :beginner:🏧 :atm:🎰 :slot_machine:🚏 :busstop:💈 :barber:♨️ :hotsprings:🏁 :checkered_flag:🎌 :crossed_flags:🏮 :izakaya_lantern:🗿 :moyai:🎪 :circus_tent:🎭 :performing_arts:📍 :round_pushpin:🚩 :triangular_flag_on_post:🇯🇵 :jp:🇰🇷 :kr:🇨🇳 :cn:🇺🇸 :us:🇫🇷 :fr:🇪🇸 :es:🇮🇹 :it:🇷🇺 :ru:🇬🇧 :gb:🇬🇧 :uk:🇩🇪 :de:  Symbols1️⃣ :one:2️⃣ :two:3️⃣ :three:4️⃣ :four:5️⃣ :five:6️⃣ :six:7️⃣ :seven:8️⃣ :eight:9️⃣ :nine:🔟 :keycap_ten:🔢 :1234:0️⃣ :zero:#️⃣ :hash:🔣 :symbols:◀️ :arrow_backward:⬇️ :arrow_down:▶️ :arrow_forward:⬅️ :arrow_left:🔠 :capital_abcd:🔡 :abcd:🔤 :abc:↙️ :arrow_lower_left:↘️ :arrow_lower_right:➡️ :arrow_right:⬆️ :arrow_up:↖️ :arrow_upper_left:↗️ :arrow_upper_right:⏬ :arrow_double_down:⏫ :arrow_double_up:🔽 :arrow_down_small:⤵️ :arrow_heading_down:⤴️ :arrow_heading_up:↩️:leftwards_arrow_with_hook:↪️ :arrow_right_hook:↔️ :left_right_arrow:↕️ :arrow_up_down:🔼 :arrow_up_small:🔃 :arrows_clockwise:🔄 :arrows_counterclockwise:⏪ :rewind:⏩ :fast_forward:ℹ️ :information_source:🆗 :ok:🔀 :twisted_rightwards_arrows:🔁 :repeat:🔂 :repeat_one:🆕 :new:🔝 :top:🆙 :up:🆒 :cool:🆓 :free:🆖 :ng:🎦 :cinema:🈁 :koko:📶 :signal_strength:🈹 :u5272:🈴 :u5408:🈺 :u55b6:🈯️ :u6307:🈷️ :u6708:🈶 :u6709:🈵 :u6e80:🈚️ :u7121:🈸 :u7533:🈳 :u7a7a:🈲 :u7981:🈂️ :sa:🚻 :restroom:🚹 :mens:🚺 :womens:🚼 :baby_symbol:🚭 :no_smoking:🅿️ :parking:♿️ :wheelchair:🚇 :metro:🛄 :baggage_claim:🉑 :accept:🚾 :wc:🚰 :potable_water:🚮 :put_litter_in_its_place:㊙️ :secret:㊗️ :congratulations:Ⓜ️ :m:🛂 :passport_control:🛅 :left_luggage:🛃 :customs:🉐 :ideograph_advantage:🆑 :cl:🆘 :sos:🆔 :id:🚫 :no_entry_sign:🔞 :underage:📵 :no_mobile_phones:🚯 :do_not_litter:🚱 :non-potable_water:🚳 :no_bicycles:🚷 :no_pedestrians:🚸 :children_crossing:⛔️ :no_entry:✳️ :eight_spoked_asterisk:✴️ :eight_pointed_black_star:💟 :heart_decoration:🆚 :vs:📳 :vibration_mode:📴 :mobile_phone_off:💹 :chart:💱 :currency_exchange:♈️ :aries:♉️ :taurus:♊️ :gemini:♋️ :cancer:♌️ :leo:♍️ :virgo:♎️ :libra:♏️ :scorpius:♐️ :sagittarius:♑️ :capricorn:♒️ :aquarius:♓️ :pisces:⛎ :ophiuchus:🔯 :six_pointed_star:❎:negative_squared_cross_mark:🅰️ :a:🅱️ :b:🆎 :ab:🅾️ :o2:💠:diamond_shape_with_a_dot_inside:♻️ :recycle:🔚 :end:🔛 :on:🔜 :soon:🕐 :clock1:🕜 :clock130:🕙 :clock10:🕥 :clock1030:🕚 :clock11:🕦 :clock1130:🕛 :clock12:🕧 :clock1230:🕑 :clock2:🕝 :clock230:🕒 :clock3:🕞 :clock330:🕓 :clock4:🕟 :clock430:🕔 :clock5:🕠 :clock530:🕕 :clock6:🕡 :clock630:🕖 :clock7:🕢 :clock730:🕗 :clock8:🕣 :clock830:🕘 :clock9:🕤 :clock930:💲 :heavy_dollar_sign:©️ :copyright:®️ :registered:™️ :tm:❌ :x:❗️ :heavy_exclamation_mark:‼️ :bangbang:⁉️ :interrobang:⭕️ :o:✖️ :heavy_multiplication_x:➕ :heavy_plus_sign:➖ :heavy_minus_sign:➗ :heavy_division_sign:💮 :white_flower:💯 :100:✔️ :heavy_check_mark:☑️ :ballot_box_with_check:🔘 :radio_button:🔗 :link:➰ :curly_loop:〰️ :wavy_dash:〽️ :part_alternation_mark:🔱 :trident::black_square: :black_square::white_square: :white_square:✅ :white_check_mark:🔲 :black_square_button:🔳 :white_square_button:⚫️ :black_circle:⚪️ :white_circle:🔴 :red_circle:🔵 :large_blue_circle:🔷 :large_blue_diamond:🔶 :large_orange_diamond:🔹 :small_blue_diamond:🔸 :small_orange_diamond:🔺 :small_red_triangle:🔻 :small_red_triangle_down: 

金蝶中间件上的springboot传文件问题

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【阿里云镜像】下载并安装Go环境

一、参考链接阿里巴巴开源镜像站-OPSX镜像站-阿里云开发者社区(aliyun.com)golang镜像-golang下载地址-golang安装教程-阿里巴巴开源镜像站(aliyun.com)二、Go介绍Golang(又称Go)是Google公司开发的一种静态强类型、编译型、并发型,并具有垃圾回收功能的编程语言。下载地址:https://mirrors.aliyun.com/golang/三、下载Go安装包https://mirrors.aliyun.com/golang/go1.17.4.windows-arm64.msi四、Windows系统下安装Go💖💖💖💖💖💖💖💖💖💖💖💖💖💖💖💖💖💖💖💖💚💚💚💚💚💚💚💚💚💚💚💚💚💚💚💚💚💚💚💚💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💛💙💙💙💙💙💙💙💙💙💙💙💙💙💙💙💙💙💙💙💙💜💜💜💜💜💜💜💜💜💜💜💜💜💜💜💜💜💜💜💜💥安装Go完成后,在CMD中输入go,输出如下信息,则安装成功。✅MicrosoftWindows[版本10.0.19042.1237](c)MicrosoftCorporation。保留所有权利。C:\Users\xyb>goGoisatoolformanagingGosourcecode.Usage:go<command>[arguments]Thecommandsare:bugstartabugreportbuildcompilepackagesanddependenciescleanremoveobjectfilesandcachedfilesdocshowdocumentationforpackageorsymbolenvprintGoenvironmentinformationfixupdatepackagestousenewAPIsfmtgofmt(reformat)packagesourcesgenerategenerateGofilesbyprocessingsourcegetadddependenciestocurrentmoduleandinstalltheminstallcompileandinstallpackagesanddependencieslistlistpackagesormodulesmodmodulemaintenanceruncompileandrunGoprogramtesttestpackagestoolrunspecifiedgotoolversionprintGoversionvetreportlikelymistakesinpackagesUse"gohelp<command>"formoreinformationaboutacommand.Additionalhelptopics:buildconstraintbuildconstraintsbuildmodebuildmodesccallingbetweenGoandCcachebuildandtestcachingenvironmentenvironmentvariablesfiletypefiletypesgo.modthego.modfilegopathGOPATHenvironmentvariablegopath-getlegacyGOPATHgogetgoproxymoduleproxyprotocolimportpathimportpathsyntaxmodulesmodules,moduleversions,andmoremodule-getmodule-awaregogetmodule-authmoduleauthenticationusinggo.sumpackagespackagelistsandpatternsprivateconfigurationfordownloadingnon-publiccodetestflagtestingflagstestfunctestingfunctionsvcscontrollingversioncontrolwithGOVCSUse"gohelp<topic>"formoreinformationaboutthattopic.C:\Users\xyb>输入goversion查看版本信息。C:\Users\xyb\Desktop\Go+\gop>goversiongoversiongo1.17.4windows/amd64C:\Users\xybdiy>goenvsetGO111MODULE=setGOARCH=amd64setGOBIN=setGOCACHE=C:\Users\xybdiy\AppData\Local\go-buildsetGOENV=C:\Users\xybdiy\AppData\Roaming\go\envsetGOEXE=.exesetGOEXPERIMENT=setGOFLAGS=setGOHOSTARCH=amd64setGOHOSTOS=windowssetGOINSECURE=setGOMODCACHE=C:\Users\xybdiy\go\pkg\modsetGONOPROXY=setGONOSUMDB=setGOOS=windowssetGOPATH=C:\Users\xybdiy\gosetGOPRIVATE=setGOPROXY=https://proxy.golang.org,directsetGOROOT=C:\ProgramFiles\GosetGOSUMDB=sum.golang.orgsetGOTMPDIR=setGOTOOLDIR=C:\ProgramFiles\Go\pkg\tool\windows_amd64setGOVCS=setGOVERSION=go1.17.4setGCCGO=gccgosetAR=arsetCC=gccsetCXX=g++setCGO_ENABLED=1setGOMOD=NULsetCGO_CFLAGS=-g-O2setCGO_CPPFLAGS=setCGO_CXXFLAGS=-g-O2setCGO_FFLAGS=-g-O2setCGO_LDFLAGS=-g-O2setPKG_CONFIG=pkg-configsetGOGCCFLAGS=-m64-mthreads-fmessage-length=0-fdebug-prefix-map=C:\Users\xybdiy\AppData\Local\Temp\go-build209388612=/tmp/go-build-gno-record-gcc-switchesC:\Users\xybdiy>

sourceinsight 头文件和函数注释的宏实现

*:CommentContent1:Զʾı,ΪmsgԻܴеҲܳ255ַΪУ˴Ӽȡݵİ취ǼݵǰֵĻΪûǿݣȻп󣬵ָʷdz͡CommentContentͬеϲһԸҪѡַʽ:hbuflnкs

反向求导

1.2神经网络的反向求导在上一节中,我们大致对神经网络的梯度更新有了了解,其中最核心的部分就是求出损失函数对权重 wijl">𝑤𝑙𝑖𝑗wijl 的导数。由于网上大多数资料都是生搬硬套,因此我们以计算 W1">𝑊1W1 的导数为例,对整个反向求导过程进行细致的剖析。如下图所示:其中,wjkl">𝑤𝑙𝑗𝑘wjkl 表示从第 l">𝑙l 层的第 j">𝑗j 个节点到第 l+1">𝑙+1l+1 层中的第 k">𝑘k 个节点的权重,根据前向传播的计算我们可以得到:yout&#x223C;(w113w112+w213w122)w111x1,&#x2202;yout&#x2202;w111=(w113w112+w213w122)x1;yout&#x223C;(w113w112+w213w122)w211x2,&#x2202;yout&#x2202;w211=(w113w112+w213w122)x2yout&#x223C;(w113w212+w213w222)w121x1,&#x2202;yout&#x2202;w121=(w113w212+w213w222)x1;yout&#x223C;(w113w212+w213w222)w221x1,&#x2202;yout&#x2202;w221=(w113w212+w213w222)x2yout&#x223C;(w113w312+w213w322)w131x1,&#x2202;yout&#x2202;w131=(w113w312+w213w322)x1;yout&#x223C;(w113w312+w213w322)w231x2,&#x2202;yout&#x2202;w231=(w113w312+w213w322)x2">𝑦𝑜𝑢𝑡∼(𝑤311𝑤211+𝑤321𝑤212)𝑤111𝑥1,∂𝑦𝑜𝑢𝑡∂𝑤111=(𝑤311𝑤211+𝑤321𝑤212)𝑥1;𝑦𝑜𝑢𝑡∼(𝑤311𝑤211+𝑤321𝑤212)𝑤121𝑥2,∂𝑦𝑜𝑢𝑡∂𝑤121=(𝑤311𝑤211+𝑤321𝑤212)𝑥2𝑦𝑜𝑢𝑡∼(𝑤311𝑤221+𝑤321𝑤222)𝑤112𝑥1,∂𝑦𝑜𝑢𝑡∂𝑤112=(𝑤311𝑤221+𝑤321𝑤222)𝑥1;𝑦𝑜𝑢𝑡∼(𝑤311𝑤221+𝑤321𝑤222)𝑤122𝑥1,∂𝑦𝑜𝑢𝑡∂𝑤122=(𝑤311𝑤221+𝑤321𝑤222)𝑥2𝑦𝑜𝑢𝑡∼(𝑤311𝑤231+𝑤321𝑤232)𝑤113𝑥1,∂𝑦𝑜𝑢𝑡∂𝑤113=(𝑤311𝑤231+𝑤321𝑤232)𝑥1;𝑦𝑜𝑢𝑡∼(𝑤311𝑤231+𝑤321𝑤232)𝑤123𝑥2,∂𝑦𝑜𝑢𝑡∂𝑤123=(𝑤311𝑤231+𝑤321𝑤232)𝑥2yout∼(w113w112+w213w122)w111x1,∂yout∂w111=(w113w112+w213w122)x1;yout∼(w113w112+w213w122)w211x2,∂yout∂w211=(w113w112+w213w122)x2yout∼(w113w212+w213w222)w121x1,∂yout∂w121=(w113w212+w213w222)x1;yout∼(w113w212+w213w222)w221x1,∂yout∂w221=(w113w212+w213w222)x2yout∼(w113w312+w213w322)w131x1,∂yout∂w131=(w113w312+w213w322)x1;yout∼(w113w312+w213w322)w231x2,∂yout∂w231=(w113w312+w213w322)x2用矩阵表示为:&#x2202;L&#x2202;W1=[&#x2202;yout&#x2202;w111&#x2202;yout&#x2202;w211&#x2202;yout&#x2202;w121&#x2202;yout&#x2202;w221&#x2202;yout&#x2202;w131&#x2202;yout&#x2202;w231]=([w113w112+w213w122w113w212+w213w222w113w212+w213w322]&#x2299;[x1x2])T=(W3W2&#x2299;X)T">∂𝐿∂𝑊1=⎡⎣⎢⎢⎢⎢⎢⎢⎢∂𝑦𝑜𝑢𝑡∂𝑤111∂𝑦𝑜𝑢𝑡∂𝑤112∂𝑦𝑜𝑢𝑡∂𝑤113∂𝑦𝑜𝑢𝑡∂𝑤121∂𝑦𝑜𝑢𝑡∂𝑤122∂𝑦𝑜𝑢𝑡∂𝑤123⎤⎦⎥⎥⎥⎥⎥⎥⎥=([𝑤311𝑤211+𝑤321𝑤212𝑤311𝑤221+𝑤321𝑤222𝑤311𝑤221+𝑤321𝑤232]⊙[𝑥1𝑥2])𝑇=(𝑊3𝑊2⊙𝑋)𝑇∂L∂W1=[∂yout∂w111∂yout∂w211∂yout∂w121∂yout∂w221∂yout∂w131∂yout∂w231]=([w113w112+w213w122w113w212+w213w222w113w212+w213w322]⊙[x1x2])T=(W3W2⊙X)T因此,整个反向传播的过程如下:首先计算:&#x2202;L&#x2202;W3=&#x2202;L&#x2202;yout&#x2299;(&#x2202;yout&#x2202;W3)T=&#x2202;L&#x2202;yout&#x2299;[&#x2202;yout&#x2202;w113,&#x2202;yout&#x2202;w123]T=&#x2202;L&#x2202;yout&#x2299;(Z2)T">∂𝐿∂𝑊3=∂𝐿∂𝑦𝑜𝑢𝑡⊙(∂𝑦𝑜𝑢𝑡∂𝑊3)𝑇=∂𝐿∂𝑦𝑜𝑢𝑡⊙[∂𝑦𝑜𝑢𝑡∂𝑤311,∂𝑦𝑜𝑢𝑡∂𝑤312]𝑇=∂𝐿∂𝑦𝑜𝑢𝑡⊙(𝑍2)𝑇∂L∂W3=∂L∂yout⊙(∂yout∂W3)T=∂L∂yout⊙[∂yout∂w113,∂yout∂w123]T=∂L∂yout⊙(Z2)T然后计算:&#x2202;L&#x2202;W2=&#x2202;L&#x2202;yout(&#x2202;yout&#x2202;Z2&#x2299;&#x2202;Z2&#x2202;W2)T=&#x2202;L&#x2202;yout(&#x2202;yout&#x2202;Z2&#x2299;Z1)T=&#x2202;L&#x2202;yout(W3&#x2299;Z1)T">∂𝐿∂𝑊2=∂𝐿∂𝑦𝑜𝑢𝑡(∂𝑦𝑜𝑢𝑡∂𝑍2⊙∂𝑍2∂𝑊2)𝑇=∂𝐿∂𝑦𝑜𝑢𝑡(∂𝑦𝑜𝑢𝑡∂𝑍2⊙𝑍1)𝑇=∂𝐿∂𝑦𝑜𝑢𝑡(𝑊3⊙𝑍1)𝑇∂L∂W2=∂L∂yout(∂yout∂Z2⊙∂Z2∂W2)T=∂L∂yout(∂yout∂Z2⊙Z1)T=∂L∂yout(W3⊙Z1)T最后计算:&#x2202;L&#x2202;W1=&#x2202;L&#x2202;yout(&#x2202;yout&#x2202;Z2&#x2202;Z2&#x2202;Z1&#x2299;&#x2202;Z1&#x2202;W1)T=&#x2202;L&#x2202;W1(W3W2&#x2299;X)T">∂𝐿∂𝑊1=∂𝐿∂𝑦𝑜𝑢𝑡(∂𝑦𝑜𝑢𝑡∂𝑍2∂𝑍2∂𝑍1⊙∂𝑍1∂𝑊1)𝑇=∂𝐿∂𝑊1(𝑊3𝑊2⊙𝑋)𝑇∂L∂W1=∂L∂yout(∂yout∂Z2∂Z2∂Z1⊙∂Z1∂W1)T=∂L∂W1(W3W2⊙X)T为了方便计算,反向传播通过使用计算图的形式在Tensorflow,PyTorch等深度学习框架中实现,将上述过程绘制成计算图如下:根据计算图,可以轻而易举地计算出损失函数对每个变量的导数。

吴恩达《深度学习》-课后测验-第五门课 序列模型(Sequence Models)-Week 1: Recurrent Neural Networks(第一周测验:循环神经网络)

Week1Quiz:RecurrentNeuralNetworks(第一周测验:循环神经网络)\1.Supposeyourtrainingexamplesaresentences(sequencesofwords).Whichofthefollowingreferstothejthwordintheithtrainingexample?(假设你的训练样本是句子(单词序列),下面哪个选项指的是第𝑖个训练样本中的第𝑗个词?)【】$𝑥^{(𝑖)<𝑗>}$【】\(𝑥^{<𝑖>(𝑗)}\)【】\(𝑥^{(𝑗)<𝑖>}\)【】\(𝑥^{<𝑗>(𝑖)}\)答案【★】𝑥(𝑖)<𝑗>(注:首先获取第𝑖个训练样本(用括号表示),然后到𝑗列获取单词(用括尖括号表示)。)\2.ConsiderthisRNN:Thisspecifictypeofarchitectureisappropriatewhen:(看一下下面的这个循环神经网络:在下面的条件中,满足上图中的网络结构的参数是)【】$𝑇_𝑥=𝑇_𝑦$【】$𝑇_𝑥<𝑇_𝑦$【】\(𝑇_𝑥>𝑇_𝑦\)【】$𝑇_𝑥=1$答案【★】𝑇𝑥=𝑇𝑦\3.Towhichofthesetaskswouldyouapplyamany-to-oneRNNarchitecture?(Checkallthatapply).(上图中每一个输入都与输出相匹配。这些任务中的哪一个会使用多对一的RNN体系结构?)【】Speechrecognition(inputanaudioclipandoutputatranscript)(语音识别(输入语音,输出文本)。)【】Sentimentclassification(inputapieceoftextandoutputa0/1todenotepositiveornegativesentiment)(情感分类(输入一段文字,输出0或1表示正面或者负面的情绪)。)【】Imageclassification(inputanimageandoutputalabel)(图像分类(输入一张图片,输出对应的标签)。)【】Genderrecognitionfromspeech(inputanaudioclipandoutputalabelindicatingthespeaker’sgender)(人声性别识别(输入语音,输出说话人的性别)。)答案【★】Sentimentclassification(inputapieceoftextandoutputa0/1todenotepositiveornegativesentiment)(情感分类(输入一段文字,输出0或1表示正面或者负面的情绪)。)【★】Genderrecognitionfromspeech(inputanaudioclipandoutputalabelindicatingthespeaker’sgender)(人声性别识别(输入语音,输出说话人的性别)。)\4.YouaretrainingthisRNNlanguagemodel.Atthe\(𝑡^{th}\)timestep,whatistheRNNdoing?Choosethebestanswer.(假设你现在正在训练下面这个RNN的语言模型:在𝑡时,这个RNN在做什么?)【】Estimating𝑃(\(𝑦^{<1>},𝑦^{<2>},…,𝑦^{<𝑡−1>}\))(计算𝑃(\(𝑦^{<1>},𝑦^{<2>},…,𝑦^{<𝑡−1>}\)))【】Estimating𝑃(\(𝑦^{<𝑡>}\))(计算𝑃(\(𝑦^{<𝑡>}\)))【】Estimating\(𝑃(𝑦∣𝑦^{<1>},𝑦^{<2>},…,𝑦^{<𝑡>})\)(计算\(𝑃(𝑦∣𝑦^{<1>},𝑦^{<2>},…,𝑦^{<𝑡>})\))【】Estimating\(𝑃(𝑦∣𝑦^{<1>},𝑦^{<2>},…,𝑦^{<𝑡−1>})\)(计算\(𝑃(𝑦∣𝑦^{<1>},𝑦^{<2>},…,𝑦^{<𝑡−1>})\))答案Yes,inalanguagemodelwetrytopredictthenextstepbasedontheknowledgeofallpriorsteps【★】Estimating𝑃(𝑦∣𝑦<1>,𝑦<2>,…,𝑦<𝑡>)(计算𝑃(𝑦∣𝑦<1>,𝑦<2>,…,𝑦<𝑡-1>))\5.YouhavefinishedtrainingalanguagemodelRNNandareusingittosamplerandomsentences,asfollows:Whatareyoudoingateachtimestep𝑡?(你已经完成了一个语言模型RNN的训练,并用它来对句子进行随机取样,如下图:在每个时间步𝑡都在做什么?)【】UsetheprobabilitiesoutputbytheRNNtopickthehighestprobabilitywordforthattime-stepas\(𝑦^{<𝑡>}\).(ii)Thenpasstheground-truthwordfromthetrainingsettothenexttimestep.((1)使用RNN输出的概率,选择该时间步的最高概率单词作为\(𝑦^{<𝑡>}\),(2)然后将训练集中的正确的单词传递到下一个时间步。)【】UsetheprobabilitiesoutputbytheRNNtorandomlysampleachosenwordforthattime-stepas\(𝑦^{<𝑡>}\).(ii)Thenpasstheground-truthwordfromthetrainingsettothenexttimestep.((1)使用由RNN输出的概率将该时间步的所选单词进行随机采样作为\(𝑦^{<𝑡>}\),(2)然后将训练集中的实际单词传递到下一个时间步。)【】UsetheprobabilitiesoutputbytheRNNtopickthehighestprobabilitywordforthattime-stepas\(𝑦^{<𝑡>}\).(ii)Thenpassthisselectedwordtothenexttime-step.((1)使用由RNN输出的概率来选择该时间步的最高概率词作为\(𝑦^{<𝑡>}\),(2)然后将该选择的词传递给下一个时间步。)【】UsetheprobabilitiesoutputbytheRNNtorandomlysampleachosenwordforthattime-stepas\(𝑦^{<𝑡>}\).(ii)Thenpassthisselectedwordtothenexttime-step.((1)使用RNN该时间步输出的概率对单词随机抽样的结果作为\(𝑦^{<𝑡>}\),(2)然后将此选定单词传递给下一个时间步。)答案【★】(i)UsetheprobabilitiesoutputbytheRNNtorandomlysampleachosenwordforthattime-stepas𝑦<𝑡>.(ii)Thenpassthisselectedwordtothenexttime-step.((1)使用RNN该时间步输出的概率对单词随机抽样的结果作为𝑦<𝑡>,(2)然后将此选定单词传递给下一个时间步。)\6.YouaretraininganRNN,andfindthatyourweightsandactivationsarealltakingonthevalueofNaN(“NotaNumber”).Whichoftheseisthemostlikelycauseofthisproblem?【】Vanishinggradientproblem.(梯度消失。)【】Explodinggradientproblem.(梯度爆炸。)【】ReLUactivationfunctiong(.)usedtocomputeg(z),wherezistoolarge.(ReLU函数作为激活函数𝑔(.),在计算𝑔(𝑧)时,𝑧的数值过大了。)【】Sigmoidactivationfunctiong(.)usedtocomputeg(z),wherezistoolarge.(Sigmoid函数作为激活函数𝑔(.),在计算𝑔(𝑧)时,𝑧的数值过大了。)答案【★】Explodinggradientproblem.(梯度爆炸。)7.SupposeyouaretrainingaLSTM.Youhavea10000wordvocabulary,andareusinganLSTMwith100-dimensionalactivationsa.WhatisthedimensionofΓuateachtimestep?(假设你正在训练一个LSTM网络,你有一个10,000词的词汇表,并且使用一个激活值维度为100的LSTM块,在每一个时间步中,𝛤𝑢的维度是多少?)【】1【】100【】300【】10000答案【★】100(注:𝛤𝑢的向量维度等于LSTM中隐藏单元的数量。)\8.Here’retheupdateequationsfortheGRU.AliceproposestosimplifytheGRUbyalwaysremovingthe\(𝛤_𝑢\).I.e.,setting\(𝛤_𝑢\)=1.BettyproposestosimplifytheGRUbyremovingthe\(𝛤_𝑟\).I.e.,setting\(𝛤_𝑟\)=1always.Whichofthesemodelsismorelikelytoworkwithoutvanishinggradientproblemsevenwhentrainedonverylonginputsequences?(这里有一些GRU的更新方程:爱丽丝建议通过移除\(𝛤_𝑢\)来简化GRU,即设置\(𝛤_𝑢\)=1。贝蒂提出通过移除\(𝛤_𝑟\)来简化GRU,即设置\(𝛤_𝑟\)=1。哪种模型更容易在梯度不消失问题的情况下训练,即使在很长的输入序列上也可以进行训练?)【】Alice’smodel(removing\(𝛤_𝑢\)),becauseif\(𝛤_𝑟\)≈0foratimestep,thegradientcanpropagatebackthroughthattimestepwithoutmuchdecay.(爱丽丝的模型(即移除𝛤𝑢),因为对于一个时间步而言,如果𝛤𝑟≈0,梯度可以通过时间步反向传播而不会衰减。)【】Alice’smodel(removing𝛤𝑢),becauseif𝛤𝑟≈1foratimestep,thegradientcanpropagatebackthroughthattimestepwithoutmuchdecay.(爱丽丝的模型(即移除𝛤𝑢),因为对于一个时间步而言,如果𝛤𝑟≈1,梯度可以通过时间步反向传播而不会衰减。)【】Betty’smodel(removing𝛤𝑟),becauseif𝛤u≈0foratimestep,thegradientcanpropagatebackthroughthattimestepwithoutmuchdecay.(贝蒂的模型(即移除𝛤𝑟),因为对于一个时间步而言,如果𝛤u≈0,梯度可以通过时间步反向传播而不会衰减。)【】Betty’smodel(removing𝛤𝑟),becauseif𝛤u≈1foratimestep,thegradientcanpropagatebackthroughthattimestepwithoutmuchdecay.(贝蒂的模型(即移除𝛤𝑟),因为对于一个时间步而言,如果𝛤u≈1,梯度可以通过时间步反向传播而不会衰减。)答案【★】Betty’smodel(removing𝛤𝑟),becauseif𝛤u≈0foratimestep,thegradientcanpropagatebackthroughthattimestepwithoutmuchdecay.(贝蒂的模型(即移除𝛤𝑟),因为对于一个时间步而言,如果𝛤u≈0,梯度可以通过时间步反向传播而不会衰减。)(注:要使信号反向传播而不消失,我们需要𝑐<𝑡>高度依赖于𝑐<𝑡−1>。)\9.HerearetheequationsfortheGRUandtheLSTM:Fromthese,wecanseethattheUpdateGateandForgetGateintheLSTMplayarolesimilarto_and__intheGRU.Whatshouldgointhetheblanks?(这里有一些GRU和LSTM的方程:从这些我们可以看到,在LSTM中的更新门和遗忘门在GRU中扮演类似___与___的角色,空白处应该填什么?)【】𝛤𝑢与1−𝛤𝑢(𝛤𝑢与1−𝛤𝑢)【】𝛤𝑢与𝛤𝑟(𝛤𝑢与𝛤𝑟)【】1−𝛤𝑢与𝛤𝑢(1−𝛤𝑢与𝛤𝑢)【】𝛤𝑟与𝛤𝑢(𝛤𝑟与𝛤𝑢)答案【★】𝛤𝑢与1−𝛤𝑢(𝛤𝑢与1−𝛤𝑢)\10.Youhaveapetdogwhosemoodisheavilydependentonthecurrentandpastfewdays’weather.You’vecollecteddataforthepast365daysontheweather,whichyourepresentasasequenceas\(𝑥^{<1>},…,𝑥^{<365>}\).You’vealsocollecteddataonyourdog’smood,whichyourepresentas\(𝑦^{<1>},…,𝑦^{<365>}\).You’dliketobuildamodeltomapfromx→y.ShouldyouuseaUnidirectionalRNNorBidirectionalRNNforthisproblem?(你有一只宠物狗,它的心情很大程度上取决于当前和过去几天的天气。你已经收集了过去365天的天气数据\(𝑥^{<1>},…,𝑥^{<365>}\),这些数据是一个序列,你还收集了你的狗心情的数据\(𝑦^{<1>},…,𝑦^{<365>}\),你想建立一个模型来从𝑥到𝑦进行映射,你应该使用单向RNN还是双向RNN来解决这个问题?)【】BidirectionalRNN,becausethisallowsthepredictionofmoodonday𝑡totakeintoaccountmoreinformation.(双向RNN,因为在𝑡日的情绪预测中可以考虑到更多的信息。)【】BidirectionalRNN,becausethisallowsbackpropagationtocomputemoreaccurategradients.(双向RNN,因为这允许反向传播计算中有更精确的梯度。)【】UnidirectionalRNN,becausethevalueof\(𝑦^{<𝑡>}\)dependsonlyon\(𝑥^{<1>},…,𝑥^{<𝑡>}\),butnoton\(𝑥^{<𝑡+1>},…,𝑥^{<365>}\)(单向RNN,因为\(𝑦^{<𝑡>}\)的值仅依赖于\(𝑥^{<1>},…,𝑥^{<𝑡>}\),而不依赖于\(𝑥^{<𝑡+1>},…,𝑥^{<365>}\)。)【】UnidirectionalRNN,becausethevalueof\(𝑦^{<𝑡>}\)dependsonlyon\(𝑥^{<𝑡>}\),andnototherdays’weather.(单向RNN,因为\(𝑦^{<𝑡>}\)的值只取决于\(𝑥^{<𝑡>}\),而不是其他天的天气。)答案【★】UnidirectionalRNN,becausethevalueof𝑦<𝑡>dependsonlyon𝑥<1>,…,𝑥<𝑡>,butnoton𝑥<𝑡+1>,…,𝑥<365>(单向RNN,因为𝑦<𝑡>的值仅依赖于𝑥<1>,…,𝑥<𝑡>,而不依赖于𝑥<𝑡+1>,…,𝑥<365>。)Week1CodeAssignments:✧Course5-序列模型(SequenceModels)-第一周测验-循环神经网络✦assignment1:BuildingyourRecurrentNeuralNetwork-StepbyStep)✦assignment2:Characterlevellanguagemodel-Dinosaurusland)✦assignment3:ImproviseaJazzSolowithanLSTMNetwork)

Codeforces Round #594 (Div. 2) A. Integer Points 水题

A.IntegerPointsDLSandJLSareboredwithaMathlesson.Inordertoentertainthemselves,DLStookasheetofpaperanddrew𝑛distinctlines,givenbyequations𝑦=𝑥+𝑝𝑖forsomedistinct𝑝1,𝑝2,…,𝑝𝑛.ThenJLSdrewonthesamepapersheet𝑚distinctlinesgivenbyequations𝑦=−𝑥+𝑞𝑖forsomedistinct𝑞1,𝑞2,…,𝑞𝑚.DLSandJLSareinterestedincountinghowmanylinepairshaveintegerintersectionpoints,i.e.pointswithbothcoordinatesthatareintegers.Unfortunately,thelessonwillendupsoon,soDLSandJLSareaskingforyourhelp.InputThefirstlinecontainsoneinteger𝑡(1≤𝑡≤1000),thenumberoftestcasesintheinput.Thenfollowthetestcasedescriptions.Thefirstlineofatestcasecontainsaninteger𝑛(1≤𝑛≤105),thenumberoflinesdrawnbyDLS.Thesecondlineofatestcasecontains𝑛distinctintegers𝑝𝑖(0≤𝑝𝑖≤109)describingthelinesdrawnbyDLS.Theinteger𝑝𝑖describesalinegivenbytheequation𝑦=𝑥+𝑝𝑖.Thethirdlineofatestcasecontainsaninteger𝑚(1≤𝑚≤105),thenumberoflinesdrawnbyJLS.Thefourthlineofatestcasecontains𝑚distinctintegers𝑞𝑖(0≤𝑞𝑖≤109)describingthelinesdrawnbyJLS.Theinteger𝑞𝑖describesalinegivenbytheequation𝑦=−𝑥+𝑞𝑖.Thesumofthevaluesof𝑛overalltestcasesintheinputdoesnotexceed105.Similarly,thesumofthevaluesof𝑚overalltestcasesintheinputdoesnotexceed105.Inhacksitisallowedtouseonlyonetestcaseintheinput,so𝑡=1shouldbesatisfied.OutputForeachtestcaseintheinputprintasingleinteger—thenumberoflinepairswithintegerintersectionpoints.Exampleinput3313220311111211output310NoteThepictureshowsthelinesfromthefirsttestcaseoftheexample.Blackcirclesdenoteintersectionpointswithintegercoordinates.题意一个二维平面,有两种线,一种是y=x+p[i],一种是y=-x+q[i],问你这两种直线相交后,有多少个整数交点。题解我们解出来相交点为x=(p[i]+q[i])/2,那么只要同奇偶,就是整数交点代码#include<bits/stdc++.h>usingnamespacestd;constintmaxn=100005;intp[maxn],q[maxn],n,m;voidsolve(){vector<int>cnt1(2,0),cnt2(2,0);scanf("%d",&n);for(inti=0;i<n;i++){scanf("%d",&p[i]);cnt1[p[i]%2]++;}scanf("%d",&m);for(inti=0;i<m;i++){scanf("%d",&q[i]);cnt2[q[i]%2]++;}cout<<1ll*cnt1[0]*cnt2[0]+1ll*cnt1[1]*cnt2[1]<<endl;}intmain(){intt;scanf("%d",&t);while(t--){solve();}}

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