[{"data":1,"prerenderedAt":1598},["ShallowReactive",2],{"blog-taxonomies":3,"blog-stats":507,"post-2025\u002F2025-12-25-关于动态规划(背包问题为例)":1083},[4,11,16,21,25,29,36,39,44,47,52,58,63,66,71,76,80,84,87,93,96,101,105,110,113,117,122,127,132,136,141,143,146,151,155,157,162,165,169,173,176,179,183,186,190,193,197,200,205,208,211,214,219,222,228,234,237,239,245,249,253,256,260,266,271,276,281,283,287,290,293,298,301,304,306,308,311,314,316,318,321,327,332,337,342,347,352,354,356,358,361,365,367,369,371,374,376,378,381,386,390,393,396,400,404,407,411,413,415,417,421,423,425,428,431,433,435,437,439,441,443,446,448,450,454,456,459,461,463,465,467,469,471,473,477,483,486,488,491,493,495,497,499,501,503,505],{"category":5,"tags":6},"笔记",[7,8,9,10],"QQ","插件","LiteLoader","美化",{"category":12,"tags":13},"其他",[14,15,10],"博客","IP签名",{"category":17,"tags":18},"杂谈",[19,20],"互联网","观点",{"category":5,"tags":22},[14,23,24],"GitHub","数据可视化",{"category":5,"tags":26},[14,27,28],"访问统计","不蒜子",{"category":30,"tags":31},"工具",[32,33,34,35],"Python","爬虫","选课脚本","广州大学",{"category":5,"tags":37},[38,5],"数学分析",{"category":40,"tags":41},"算法",[42,40,43],"数据结构","线性表",{"category":40,"tags":45},[42,46],"复习",{"category":5,"tags":48},[49,50,51],"高等代数","线性代数","知识点",{"category":5,"tags":53},[14,54,55,56,57],"Typora","PicGo","图床","Markdown",{"category":30,"tags":59},[60,61,62],"Jupyter","工具配置","中文",{"category":30,"tags":64},[65,61,10],"VSCode",{"category":30,"tags":67},[68,69,70,35],"路由器","OpenWrt","校园网",{"category":12,"tags":72},[73,74,75],"网络协议","Wireshark","DEVP2P",{"category":5,"tags":77},[73,74,78,79],"Lua","解码器",{"category":5,"tags":81},[82,5,83],"常微分方程","数学",{"category":5,"tags":85},[86,5,83],"概率论",{"category":30,"tags":88},[89,90,91,92],"Docker","WSL","Windows","磁盘清理",{"category":30,"tags":94},[32,33,95,35],"课程表",{"category":5,"tags":97},[14,98,99,100],"Hexo","Gitalk","评论系统",{"category":5,"tags":102},[14,103,98,104],"Obsidian","写作工具",{"category":12,"tags":106},[107,108,109],"课题研究","泊松分布","参数估计",{"category":12,"tags":111},[107,108,109,112],"组会",{"category":12,"tags":114},[109,115,108,116],"IM模型","统计学",{"category":17,"tags":118},[119,120,121],"软考","网络规划","信息系统项目管理",{"category":30,"tags":123},[124,125,126],"Arch Linux","AppImage","Linux",{"category":5,"tags":128},[129,130,131],"编程语言","计算机科学","内存管理",{"category":5,"tags":133},[134,135],"Canvas","前端",{"category":5,"tags":137},[14,138,139,140],"GitHub Actions","Vite","部署",{"category":5,"tags":142},[135],{"category":5,"tags":144},[135,145],"系统设计",{"category":5,"tags":147},[135,148,149,150],"安全","XSS","CSRF",{"category":152,"tags":153},"项目",[134,154],"PixiJS",{"category":152,"tags":156},null,{"category":40,"tags":158},[42,159,160,161],"栈","队列","JavaScript",{"category":40,"tags":163},[42,164,161],"哈希表",{"category":5,"tags":166},[167,161,168],"ES6","Set",{"category":40,"tags":170},[40,171,172],"动态规划","背包问题",{"category":40,"tags":174},[40,175],"滑动窗口",{"category":40,"tags":177},[42,178,161],"链表",{"category":40,"tags":180},[40,181,161,182],"ACM","面试",{"category":40,"tags":184},[40,161,185],"数据类型转换",{"category":40,"tags":187},[42,188,178,189],"顺序表","TypeScript",{"category":5,"tags":191},[135,154,134,192],"渲染",{"category":5,"tags":194},[135,195,134,196],"富文本编辑","wangEditor",{"category":40,"tags":198},[199,40,178],"力扣",{"category":5,"tags":201},[202,203,204,91],"DNS","加密","网络安全",{"category":5,"tags":206},[135,207],"Axios",{"category":5,"tags":209},[135,207,189,210],"接口封装",{"category":5,"tags":212},[135,213,145],"JWT",{"category":152,"tags":215},[134,216,217,154,218],"画布","React","项目开发",{"category":17,"tags":220},[221],"日志",{"category":5,"tags":223},[224,225,226,227],"Neo4j","图数据库","中心度分析","PageRank",{"category":12,"tags":229},[230,231,232,233],"论文","机器学习","随机森林","保险欺诈",{"category":5,"tags":235},[236],"人工智能",{"category":5,"tags":238},[231,40,32],{"category":12,"tags":240},[241,242,243,244],"共识算法","最长链","区块链","算法设计",{"category":5,"tags":246},[161,247,248,135],"闭包","作用域",{"category":5,"tags":250},[14,138,251,252],"RSS","自动化",{"category":30,"tags":254},[89,90,91,255],"安装",{"category":30,"tags":257},[258,91,259],"MSYS2","开发环境",{"category":5,"tags":261},[262,263,264,265],"团队协作","Git","Commit规范","代码审查",{"category":30,"tags":267},[268,269,270],"oh-my-posh","终端美化","CLI",{"category":5,"tags":272},[273,274,275],"上下文工程","Agent","RAG",{"category":5,"tags":277},[278,279,280],"前端工程化","技术选型","工程基建",{"category":5,"tags":282},[275],{"category":5,"tags":284},[285,286],"SDD","规格驱动开发",{"category":5,"tags":288},[289],"neovim",{"category":5,"tags":291},[292],"技术写作",{"category":5,"tags":294},[295,32,296,89,297],"FastAPI","后端","工程实践",{"category":152,"tags":299},[274,300],"Harness Engineering",{"category":5,"tags":302},[303],"RFC",{"category":152,"tags":305},[274,300,275],{"category":152,"tags":307},[274],{"category":40,"tags":309},[199,40,161,310],"两数之和",{"category":40,"tags":312},[199,40,161,313],"双指针",{"category":40,"tags":315},[199,40,161,178],{"category":40,"tags":317},[199,40,161,175],{"category":40,"tags":319},[199,40,161,320],"回溯",{"category":5,"tags":322},[323,324,325,326],"分布式处理与计算","Spark","Scala","RDD",{"category":5,"tags":328},[323,329,330,331],"线性回归","逻辑回归","监督学习",{"category":5,"tags":333},[323,334,335,336],"数值优化","牛顿法","收敛性",{"category":5,"tags":338},[323,339,340,341],"PCA","数据降维","正则化",{"category":5,"tags":343},[323,344,345,346],"聚类","层次聚类","K-Means",{"category":5,"tags":348},[323,349,350,351],"随机模拟","统计推断","EM算法",{"category":5,"tags":353},[24],{"category":5,"tags":355},[24],{"category":5,"tags":357},[24],{"category":40,"tags":359},[42,360],"图论",{"category":40,"tags":362},[42,363,364],"树","二叉树",{"category":40,"tags":366},[42,160],{"category":40,"tags":368},[42],{"category":40,"tags":370},[42,159],{"category":40,"tags":372},[42,40,373],"复杂度分析",{"category":40,"tags":375},[42,43,178],{"category":40,"tags":377},[42,43,188],{"category":40,"tags":379},[42,380],"基础概念",{"category":17,"tags":382},[383,384,385],"随记","照片","高中",{"category":17,"tags":387},[383,388,389],"团建","战地",{"category":17,"tags":391},[383,392],"生活",{"category":17,"tags":394},[383,395],"文学",{"category":17,"tags":397},[383,398,399],"SCP","模因",{"category":17,"tags":401},[383,402,403],"画集","艺术",{"category":17,"tags":405},[14,406,383],"写作",{"category":17,"tags":408},[383,409,410],"音乐","摇滚",{"category":17,"tags":412},[383,392],{"category":17,"tags":414},[383,409],{"category":17,"tags":416},[383,35,392],{"category":17,"tags":418},[383,419,420],"同人","手书",{"category":17,"tags":422},[383,392],{"category":17,"tags":424},[383,392],{"category":17,"tags":426},[383,427],"植物",{"category":17,"tags":429},[383,430],"读书",{"category":17,"tags":432},[383,392],{"category":17,"tags":434},[383,392],{"category":17,"tags":436},[383,392],{"category":17,"tags":438},[383,392],{"category":17,"tags":440},[383,392],{"category":17,"tags":442},[383,392],{"category":17,"tags":444},[14,445,383],"一周年",{"category":17,"tags":447},[383,392],{"category":17,"tags":449},[383,392],{"category":17,"tags":451},[35,452,453],"开源组织","SITE-193",{"category":17,"tags":455},[383,392],{"category":17,"tags":457},[383,458],"年末",{"category":17,"tags":460},[383,392],{"category":17,"tags":462},[383,392],{"category":17,"tags":464},[14,17],{"category":17,"tags":466},[383,392],{"category":17,"tags":468},[383,392],{"category":17,"tags":470},[383,392],{"category":17,"tags":472},[383,392],{"category":17,"tags":474},[383,475,476],"游戏","Control",{"category":30,"tags":478},[479,480,481,482],"Quadim","图像处理","四叉树","Rust",{"category":17,"tags":484},[14,485],"上线纪念",{"category":17,"tags":487},[383,395],{"category":30,"tags":489},[203,490],"测试",{"category":17,"tags":492},[383],{"category":17,"tags":494},[383,392],{"category":17,"tags":496},[383],{"category":5,"tags":498},[40],{"category":5,"tags":500},[40],{"category":5,"tags":502},[40],{"category":5,"tags":504},[40],{"category":5,"tags":506},[40],[508,512,516,520,524,528,532,536,540,544,548,552,556,560,564,568,572,576,579,583,587,590,594,598,602,606,610,614,618,622,626,630,634,638,642,646,650,654,658,662,666,670,674,678,682,686,690,694,698,702,706,710,714,718,722,726,730,734,738,742,746,750,754,758,762,766,770,774,778,782,786,790,794,798,801,805,809,813,817,821,825,829,833,837,841,845,849,853,857,861,865,869,873,877,881,885,889,893,897,901,904,907,911,915,919,923,927,930,934,938,942,946,950,954,957,961,965,969,973,977,981,984,988,992,996,1000,1004,1007,1011,1015,1019,1023,1027,1031,1035,1039,1043,1047,1051,1055,1059,1063,1067,1071,1075,1079],{"path":509,"words":510,"published":511,"date":156},"\u002Fposts\u002F2024\u002F2024-06-25-liteloaderqqnt",1296,"2024-06-25 11:03:08",{"path":513,"words":514,"published":515,"date":156},"\u002Fposts\u002F2024\u002F2024-06-26-ip签名",0,"2024-06-26 22:53:53",{"path":517,"words":518,"published":519,"date":156},"\u002Fposts\u002F2024\u002F2024-06-29-何加盐中文互联网正在加速崩塌",4853,"2024-06-29 00:47:13",{"path":521,"words":522,"published":523,"date":156},"\u002Fposts\u002F2024\u002F2024-07-12-github-chart",270,"2024-07-12 20:02:50",{"path":525,"words":526,"published":527,"date":156},"\u002Fposts\u002F2024\u002F2024-07-14-访客数统计",192,"2024-07-24 01:34:28",{"path":529,"words":530,"published":531,"date":156},"\u002Fposts\u002F2024\u002F2024-07-26-广大选课脚本",110,"2024-07-26 01:34:28",{"path":533,"words":534,"published":535,"date":156},"\u002Fposts\u002F2024\u002F2024-07-26-数学分析笔记其二",14,"2024-07-26 23:54:02",{"path":537,"words":538,"published":539,"date":156},"\u002Fposts\u002F2024\u002F2024-07-26-数据结构复习其二",12856,"2024-07-26 02:48:08",{"path":541,"words":542,"published":543,"date":156},"\u002Fposts\u002F2024\u002F2024-07-26-数据结构复习相关",32856,"2024-07-26 02:24:14",{"path":545,"words":546,"published":547,"date":156},"\u002Fposts\u002F2024\u002F2024-07-26-线性代数与空间解析几何知识点全汇总",6110,"2024-07-26 03:27:55",{"path":549,"words":550,"published":551,"date":156},"\u002Fposts\u002F2024\u002F2024-07-31-typora-picgo-兰空图床打造markdown写作环境",311,"2024-07-31 12:56:23",{"path":553,"words":554,"published":555,"date":156},"\u002Fposts\u002F2024\u002F2024-09-02-jupyter配置中文",441,"2024-09-02 23:49:05",{"path":557,"words":558,"published":559,"date":156},"\u002Fposts\u002F2024\u002F2024-09-02-自定义vscode背景图片",100,"2024-09-02 23:39:00",{"path":561,"words":562,"published":563,"date":156},"\u002Fposts\u002F2024\u002F2024-09-03-制作gzhu校园网路由器",1423,"2024-09-03 23:43:18",{"path":565,"words":566,"published":567,"date":156},"\u002Fposts\u002F2024\u002F2024-09-26-09-25-2024",136,"2024-09-26 00:49:26",{"path":569,"words":570,"published":571,"date":156},"\u002Fposts\u002F2024\u002F2024-11-04-创建一个网络包解码器分析devp2p协议",1943,"2024-11-04 16:45:19",{"path":573,"words":574,"published":575,"date":156},"\u002Fposts\u002F2024\u002F2025-03-09-2024一些笔记常微分",16,"2024-12-09 22:51:00",{"path":577,"words":574,"published":578,"date":156},"\u002Fposts\u002F2024\u002F2025-03-09-2024一些笔记概率论","2025-03-09 22:51:00",{"path":580,"words":581,"published":582,"date":156},"\u002Fposts\u002F2025\u002F2025-03-01-windows下释放docker占用的wsl空间",164,"2025-03-01 13:54:15",{"path":584,"words":585,"published":586,"date":156},"\u002Fposts\u002F2025\u002F2025-03-01-爬虫实战-爬取广州大学课程表",774,"2025-03-01 14:55:48",{"path":588,"words":530,"published":589,"date":156},"\u002Fposts\u002F2025\u002F2025-04-03-hexo集成gitalk的问题","2025-04-03 14:26:34",{"path":591,"words":592,"published":593,"date":156},"\u002Fposts\u002F2025\u002F2025-09-22-记一次配置obsidian配合hexo写博客",92,"2025-09-22 16:47:52",{"path":595,"words":596,"published":597,"date":156},"\u002Fposts\u002F2025\u002F2025-10-24-10-20课题",204,"2025-10-24 08:15:01",{"path":599,"words":600,"published":601,"date":156},"\u002Fposts\u002F2025\u002F2025-11-02-组会朝花夕拾",501,"2025-11-02 18:56:59",{"path":603,"words":604,"published":605,"date":156},"\u002Fposts\u002F2025\u002F2025-11-05-基于随机加权推断模型im的参数估计算法",481,"2025-11-05 20:51:41",{"path":607,"words":608,"published":609,"date":156},"\u002Fposts\u002F2025\u002F2025-11-09-关于软考高项网规",884,"2025-11-09 19:54:52",{"path":611,"words":612,"published":613,"date":156},"\u002Fposts\u002F2025\u002F2025-11-17-arch-linux运行appimage相关",365,"2025-11-17 09:59:59",{"path":615,"words":616,"published":617,"date":156},"\u002Fposts\u002F2025\u002F2025-11-19-相关概念",2058,"2025-11-19 11:06:20",{"path":619,"words":620,"published":621,"date":156},"\u002Fposts\u002F2025\u002F2025-11-21-web可视化实践canvas",6393,"2025-11-21 14:50:48",{"path":623,"words":624,"published":625,"date":156},"\u002Fposts\u002F2025\u002F2025-11-22-使用-github-actions-自动部署基于vite的项目到-github-pages",272,"2025-11-23 01:59:24",{"path":627,"words":628,"published":629,"date":156},"\u002Fposts\u002F2025\u002F2025-11-22-关于前端包管理器npmpnpmyarn和bun",4890,"2025-11-22 21:21:15",{"path":631,"words":632,"published":633,"date":156},"\u002Fposts\u002F2025\u002F2025-11-23-undo-redo-机制具体实现",7839,"2025-11-23 19:15:00",{"path":635,"words":636,"published":637,"date":156},"\u002Fposts\u002F2025\u002F2025-11-27-前端安全-关于xss与crsf",1866,"2025-11-28 02:05:25",{"path":639,"words":640,"published":641,"date":156},"\u002Fposts\u002F2025\u002F2025-12-05-现代协同-2d-画布编辑器pixijs-v8",4285,"2025-12-05 02:00:16",{"path":643,"words":644,"published":645,"date":156},"\u002Fposts\u002F2025\u002F2025-12-07-杂谈-课题组系统设计",3710,"2025-12-07 21:09:33",{"path":647,"words":648,"published":649,"date":156},"\u002Fposts\u002F2025\u002F2025-12-25-javascript中的数组方法与栈stack和队列queue的实现",474,"2025-11-29 16:58:15",{"path":651,"words":652,"published":653,"date":156},"\u002Fposts\u002F2025\u002F2025-12-25-关于javascript-实现哈希表",189,"2025-11-27 11:31:39",{"path":655,"words":656,"published":657,"date":156},"\u002Fposts\u002F2025\u002F2025-12-25-关于javascript的set方法",332,"2025-12-25 15:26:18",{"path":659,"words":660,"published":661,"date":156},"\u002Fposts\u002F2025\u002F2025-12-25-关于动态规划(背包问题为例)",1238,"2025-11-17 18:24:04",{"path":663,"words":664,"published":665,"date":156},"\u002Fposts\u002F2025\u002F2025-12-25-关于滑动窗口",712,"2025-11-20 15:04:40",{"path":667,"words":668,"published":669,"date":156},"\u002Fposts\u002F2025\u002F2025-12-25-关于链表(javascript)",500,"2025-11-25 13:00:48",{"path":671,"words":672,"published":673,"date":156},"\u002Fposts\u002F2025\u002F2025-12-25-面试算法acm模式构建构建输入输出模板",2051,"2025-12-25 23:09:45",{"path":675,"words":676,"published":677,"date":156},"\u002Fposts\u002F2025\u002F2025-12-26-javascript-数字数组字符串的处理",483,"2025-12-26 11:20:25",{"path":679,"words":680,"published":681,"date":156},"\u002Fposts\u002F2025\u002F2025-12-26-javascripttypescript-的顺序表链表实现",446,"2025-12-26 12:16:12",{"path":683,"words":684,"published":685,"date":156},"\u002Fposts\u002F2025\u002F2025-12-27-前端画布设计vol-1-实现基础yuan素渲染和状态控制",2136,"2025-12-28 01:23:08",{"path":687,"words":688,"published":689,"date":156},"\u002Fposts\u002F2025\u002F2025-12-27-前端画布设计vol-2-实现富文本编辑",1838,"2025-12-28 02:58:47",{"path":691,"words":692,"published":693,"date":156},"\u002Fposts\u002F2025\u002F2025-12-27-算法刷题-关于链表操作",2135,"2025-12-27 16:12:42",{"path":695,"words":696,"published":697,"date":156},"\u002Fposts\u002F2025\u002F2025-12-27-配置dnscrypt-proxy实现加密dns服务windows",1899,"2025-11-15 01:06:37",{"path":699,"words":700,"published":701,"date":156},"\u002Fposts\u002F2025\u002F2025-12-28-前端-关于网络请求xhrajaxfetchaxios",7788,"2025-10-28 15:48:46",{"path":703,"words":704,"published":705,"date":156},"\u002Fposts\u002F2025\u002F2025-12-28-前端-接口封装与请求规范axios为例",2373,"2025-12-29 01:01:18",{"path":707,"words":708,"published":709,"date":156},"\u002Fposts\u002F2025\u002F2025-12-28-前端-身份验证管理-基于-jwt-token-的实现",2709,"2025-11-23 22:04:41",{"path":711,"words":712,"published":713,"date":156},"\u002Fposts\u002F2025\u002F2025-12-29-记canvas画布项目开发",6254,"2025-12-29 04:52:15",{"path":715,"words":716,"published":717,"date":156},"\u002Fposts\u002F2025\u002Fabout-site",116,"2025-03-31 16:44:24",{"path":719,"words":720,"published":721,"date":156},"\u002Fposts\u002F2025\u002F使用neo4j图数据科学库gds进行中心度分析",143,"2025-04-02 23:37:24",{"path":723,"words":724,"published":725,"date":156},"\u002Fposts\u002F2026\u002F2026-01-03-论文实训草稿",10445,"2026-01-03 14:10:49",{"path":727,"words":728,"published":729,"date":156},"\u002Fposts\u002F2026\u002F2026-01-06-人工智能导论",11461,"2026-01-07 03:25:49",{"path":731,"words":732,"published":733,"date":156},"\u002Fposts\u002F2026\u002F2026-01-07-机器学习相关算法",82,"2026-01-08 02:28:13",{"path":735,"words":736,"published":737,"date":156},"\u002Fposts\u002F2026\u002F2026-01-16-关于低复杂度最长链共识算法设计",4466,"2026-01-16 10:33:23",{"path":739,"words":740,"published":741,"date":156},"\u002Fposts\u002F2026\u002F2026-01-19-杂记2026-01-19",5754,"2026-01-20 01:03:26",{"path":743,"words":744,"published":745,"date":156},"\u002Fposts\u002F2026\u002F2026-01-22-github-action-自动同步博客到-github-主页",1069,"2026-01-22 16:31:47",{"path":747,"words":748,"published":749,"date":156},"\u002Fposts\u002F2026\u002F2026-03-01-windows-wsl安装docker",257,"2026-03-01 20:55:31",{"path":751,"words":752,"published":753,"date":156},"\u002Fposts\u002F2026\u002F2026-03-14-关于-msys2",701,"2026-03-15 03:05:04",{"path":755,"words":756,"published":757,"date":156},"\u002Fposts\u002F2026\u002F2026-03-28-团队项目协作规范随记",2419,"2026-03-29 05:33:50",{"path":759,"words":760,"published":761,"date":156},"\u002Fposts\u002F2026\u002F2026-03-29-oh-my-posh配置分享",104,"2026-03-29 16:34:43",{"path":763,"words":764,"published":765,"date":156},"\u002Fposts\u002F2026\u002F2026-06-13-从上下文工程到-agent-harness-engineering",8840,"2026-06-13 21:06:20",{"path":767,"words":768,"published":769,"date":156},"\u002Fposts\u002F2026\u002F2026-07-13-简谈前端基建质量标准与ai友好建设",3814,"2026-07-13 21:06:20",{"path":771,"words":772,"published":773,"date":156},"\u002Fposts\u002F2026\u002F2026-07-15-agentic-rag-系统实践",13357,"2026-07-15 21:06:20",{"path":775,"words":776,"published":777,"date":156},"\u002Fposts\u002F2026\u002F2026-07-18-简谈sdd规范驱动开发-copy",4476,"2026-07-18 11:06:20",{"path":779,"words":780,"published":781,"date":156},"\u002Fposts\u002F2026\u002F2026-07-20-个人neovim配置分享",366,"2026-07-22 13:46:50",{"path":783,"words":784,"published":785,"date":156},"\u002Fposts\u002F2026\u002F2026-07-20-关于技术写作-设计文档",6763,"2026-07-20 13:46:50",{"path":787,"words":788,"published":789,"date":156},"\u002Fposts\u002F2026\u002F2026-07-29-fastapi-工程实践随记",3417,"2026-07-29 04:58:34",{"path":791,"words":792,"published":793,"date":156},"\u002Fposts\u002Frfc_agentic_project\u002F2026-06-19-rfc-liskin_code_agent",3563,"2026-06-19 15:18:20",{"path":795,"words":796,"published":797,"date":156},"\u002Fposts\u002Frfc_agentic_project\u002F2026-07-25-rfc-glushkov_ogas",13461,"2026-07-28 23:46:50",{"path":799,"words":800,"published":793,"date":156},"\u002Fposts\u002Frfc_agentic_project\u002F2026-08-03-adr-ogas-arkhiv",2698,{"path":802,"words":803,"published":804,"date":156},"\u002Fposts\u002Frfc_agentic_project\u002Frag\u002F2026-08-12-arkhiv_rag-vol-1",4366,"2026-08-12 15:18:20",{"path":806,"words":807,"published":808,"date":156},"\u002Fposts\u002Fleetcode\u002F2025-12-25-力扣百题速练javascripttypescriptvol-1",3108,"2025-12-25 13:57:08",{"path":810,"words":811,"published":812,"date":156},"\u002Fposts\u002Fleetcode\u002F2025-12-26-力扣百题速练javascripttypescriptvol-2",3185,"2025-12-26 13:57:08",{"path":814,"words":815,"published":816,"date":156},"\u002Fposts\u002Fleetcode\u002F2025-12-28-力扣百题速练javascripttypescriptvol-3",2533,"2025-12-29 02:15:44",{"path":818,"words":819,"published":820,"date":156},"\u002Fposts\u002Fleetcode\u002F2026-01-17-力扣百题速练javascripttypescriptvol-4",3024,"2026-01-17 22:53:01",{"path":822,"words":823,"published":824,"date":156},"\u002Fposts\u002Fleetcode\u002F2026-01-19-力扣百题速练javascripttypescriptvol-5",293,"2026-01-19 15:15:12",{"path":826,"words":827,"published":828,"date":156},"\u002Fposts\u002F分布式处理与计算\u002F分布式处理与计算spark系统与scala语言",4320,"2026-07-06 14:10:49",{"path":830,"words":831,"published":832,"date":156},"\u002Fposts\u002F分布式处理与计算\u002F分布式处理与计算分类与回归分析",2081,"2026-07-07 12:40:29",{"path":834,"words":835,"published":836,"date":156},"\u002Fposts\u002F分布式处理与计算\u002F分布式处理与计算数值优化方法",2182,"2026-07-07 13:50:29",{"path":838,"words":839,"published":840,"date":156},"\u002Fposts\u002F分布式处理与计算\u002F分布式处理与计算数据降维",1583,"2026-07-07 21:50:29",{"path":842,"words":843,"published":844,"date":156},"\u002Fposts\u002F分布式处理与计算\u002F分布式处理与计算聚类分析",1882,"2026-07-07 16:50:29",{"path":846,"words":847,"published":848,"date":156},"\u002Fposts\u002F分布式处理与计算\u002F分布式处理与计算随机模拟与统计推断",2433,"2026-07-06 22:40:29",{"path":850,"words":851,"published":852,"date":156},"\u002Fposts\u002F数据可视化\u002F2026-06-14-数据可视化-基本图像",10011,"2026-06-14 20:18:20",{"path":854,"words":855,"published":856,"date":156},"\u002Fposts\u002F数据可视化\u002F2026-06-14-数据可视化-概论",10030,"2026-06-14 15:18:20",{"path":858,"words":859,"published":860,"date":156},"\u002Fposts\u002F数据可视化\u002F2026-06-15-数据可视化-可视化库",2032,"2026-06-15 20:18:20",{"path":862,"words":863,"published":864,"date":156},"\u002Fposts\u002F数据结构\u002F2025-09-29-数据结构-图",5451,"2025-04-15 20:48:06",{"path":866,"words":867,"published":868,"date":156},"\u002Fposts\u002F数据结构\u002F2025-09-29-数据结构-树",4211,"2025-04-30 02:19:06",{"path":870,"words":871,"published":872,"date":156},"\u002Fposts\u002F数据结构\u002F2025-09-29-数据结构-队列",921,"2025-04-11 15:30:08",{"path":874,"words":875,"published":876,"date":156},"\u002Fposts\u002F数据结构\u002F关于数据结构的一些想法",456,"2025-04-04 19:13:49",{"path":878,"words":879,"published":880,"date":156},"\u002Fposts\u002F数据结构\u002F数据结构-栈",920,"2025-04-18 00:17:37",{"path":882,"words":883,"published":884,"date":156},"\u002Fposts\u002F数据结构\u002F数据结构-算法复杂度",2153,"2025-04-05 16:09:55",{"path":886,"words":887,"published":888,"date":156},"\u002Fposts\u002F数据结构\u002F数据结构-线性表链表",4572,"2025-04-06 00:24:40",{"path":890,"words":891,"published":892,"date":156},"\u002Fposts\u002F数据结构\u002F数据结构-线性表顺序表",4191,"2025-04-05 22:09:59",{"path":894,"words":895,"published":896,"date":156},"\u002Fposts\u002F数据结构\u002F数据结构-绪论",2881,"2025-04-05 11:31:22",{"path":898,"words":899,"published":156,"date":900},"\u002Fposts\u002F杂记\u002F2023-12-26-2023年12月26日",7,"2023-12-26 23:51:33",{"path":902,"words":899,"published":156,"date":903},"\u002Fposts\u002F杂记\u002F2024-01-01-2024团建","2024-01-01 01:51:27",{"path":905,"words":581,"published":156,"date":906},"\u002Fposts\u002F杂记\u002F2024-01-09-随记","2024-01-09 20:50:35",{"path":908,"words":909,"published":156,"date":910},"\u002Fposts\u002F杂记\u002F2024-03-12-花名",5275,"2024-03-12 16:04:23",{"path":912,"words":913,"published":156,"date":914},"\u002Fposts\u002F杂记\u002F2024-04-15-逆模因",1353,"2024-04-15 00:26:16",{"path":916,"words":917,"published":156,"date":918},"\u002Fposts\u002F杂记\u002F2024-05-03-艺作",27,"2024-05-03 00:01:00",{"path":920,"words":921,"published":156,"date":922},"\u002Fposts\u002F杂记\u002F2024-05-21-关于博客",1720,"2024-02-21 23:21:11",{"path":924,"words":925,"published":156,"date":926},"\u002Fposts\u002F杂记\u002F2024-06-20-dnvrc维克多崔专访-2023",2036,"2024-06-20 00:28:39",{"path":928,"words":760,"published":156,"date":929},"\u002Fposts\u002F杂记\u002F2024-06-25-6月25日随记","2024-06-25 12:46:36",{"path":931,"words":932,"published":156,"date":933},"\u002Fposts\u002F杂记\u002F2024-06-25-歌名-想見星星",148,"2024-06-25 22:47:59",{"path":935,"words":936,"published":156,"date":937},"\u002Fposts\u002F杂记\u002F2024-07-11-桂花岗",6,"2024-07-11 00:28:17",{"path":939,"words":940,"published":156,"date":941},"\u002Fposts\u002F杂记\u002F2024-07-15-rolling-bocci",9,"2024-07-15 21:25:56",{"path":943,"words":944,"published":156,"date":945},"\u002Fposts\u002F杂记\u002F2024-07-22-七月九日",34,"2024-07-09 17:54:23",{"path":947,"words":948,"published":156,"date":949},"\u002Fposts\u002F杂记\u002F2024-07-22-六月随记",1052,"2024-07-22 01:03:19",{"path":951,"words":952,"published":156,"date":953},"\u002Fposts\u002F杂记\u002F2024-07-22-石菖蒲",41,"2024-07-10 01:26:05",{"path":955,"words":514,"published":156,"date":956},"\u002Fposts\u002F杂记\u002F2024-07-23-新书","2024-07-23 01:05:49",{"path":958,"words":959,"published":156,"date":960},"\u002Fposts\u002F杂记\u002F2024-07-29-年前",74,"2024-07-29 23:59:07",{"path":962,"words":963,"published":156,"date":964},"\u002Fposts\u002F杂记\u002F2024-07-30-周边",138,"2024-07-30 02:03:23",{"path":966,"words":967,"published":156,"date":968},"\u002Fposts\u002F杂记\u002F2024-07-31-2024-7-31日",185,"2024-07-31 01:21:52",{"path":970,"words":971,"published":156,"date":972},"\u002Fposts\u002F杂记\u002F2024-08-02-八月",1710,"2024-08-30 00:31:02",{"path":974,"words":975,"published":156,"date":976},"\u002Fposts\u002F杂记\u002F2024-09-01-九月",1484,"2024-09-26 16:30:15",{"path":978,"words":979,"published":156,"date":980},"\u002Fposts\u002F杂记\u002F2024-09-08-2024年9月8日",97,"2024-09-08 13:59:36",{"path":982,"words":514,"published":156,"date":983},"\u002Fposts\u002F杂记\u002F2024-09-19-博客站的一周年","2024-09-18 23:36:24",{"path":985,"words":986,"published":156,"date":987},"\u002Fposts\u002F杂记\u002F2024-10-03-十月",1028,"2024-10-31 23:54:27",{"path":989,"words":990,"published":156,"date":991},"\u002Fposts\u002F杂记\u002F2024-11-04-十一月",2134,"2024-11-30 00:04:39",{"path":993,"words":994,"published":156,"date":995},"\u002Fposts\u002F杂记\u002F2024-11-10-gzhu-site-193",80,"2024-11-10 19:19:12",{"path":997,"words":998,"published":156,"date":999},"\u002Fposts\u002F杂记\u002F2024-12-01-十二月",455,"2024-12-30 23:13:47",{"path":1001,"words":1002,"published":156,"date":1003},"\u002Fposts\u002F杂记\u002F2024-12-21-年末",23,"2024-12-21 23:21:49",{"path":1005,"words":522,"published":156,"date":1006},"\u002Fposts\u002F杂记\u002F2025-01-30-一月","2025-01-30 23:44:41",{"path":1008,"words":1009,"published":156,"date":1010},"\u002Fposts\u002F杂记\u002F2025-03-01-二月",224,"2025-02-28 00:11:08",{"path":1012,"words":1013,"published":156,"date":1014},"\u002Fposts\u002F杂记\u002F2025-03-01-博客杂谈",344,"2025-03-01 16:03:18",{"path":1016,"words":1017,"published":156,"date":1018},"\u002Fposts\u002F杂记\u002F2025-03-05-三月",2090,"2025-03-05 19:17:28",{"path":1020,"words":1021,"published":156,"date":1022},"\u002Fposts\u002F杂记\u002F2025-07-10-七月",361,"2025-07-10 22:04:32",{"path":1024,"words":1025,"published":156,"date":1026},"\u002Fposts\u002F杂记\u002F2025-09-21-九月",781,"2025-09-21 20:53:37",{"path":1028,"words":1029,"published":156,"date":1030},"\u002Fposts\u002F杂记\u002F2025-10-09-十月",591,"2025-10-09 00:35:07",{"path":1032,"words":1033,"published":156,"date":1034},"\u002Fposts\u002F杂记\u002Fcontrol",13,"2023-09-25 13:03:59",{"path":1036,"words":1037,"published":156,"date":1038},"\u002Fposts\u002F杂记\u002Fquadim四叉树图像处理",1094,"2023-10-21 11:27:06",{"path":1040,"words":1041,"published":156,"date":1042},"\u002Fposts\u002F杂记\u002Fsuccess",24,"2023-09-22 15:59:07",{"path":1044,"words":1045,"published":156,"date":1046},"\u002Fposts\u002F杂记\u002F三光年",295,"2023-11-18 04:18:40",{"path":1048,"words":1049,"published":156,"date":1050},"\u002Fposts\u002F杂记\u002F加密测试",961,"2023-11-21 14:24:01",{"path":1052,"words":1053,"published":156,"date":1054},"\u002Fposts\u002F杂记\u002F啊啊啊啊啊啊啊",54,"2023-09-20 17:29:33",{"path":1056,"words":1057,"published":156,"date":1058},"\u002Fposts\u002F杂记\u002F杂谈",124,"2023-09-25 23:11:32",{"path":1060,"words":1061,"published":156,"date":1062},"\u002Fposts\u002F杂记\u002F艹",25,"2023-10-21 17:40:43",{"path":1064,"words":1065,"published":1066,"date":156},"\u002Fposts\u002F神经网络\u002F神经网络与深度学习卷积神经网络",3168,"2026-06-07 11:23:08",{"path":1068,"words":1069,"published":1070,"date":156},"\u002Fposts\u002F神经网络\u002F神经网络与深度学习循环神经网络",2348,"2026-06-07 11:33:08",{"path":1072,"words":1073,"published":1074,"date":156},"\u002Fposts\u002F神经网络\u002F神经网络与深度学习改进学习方法",3360,"2026-06-07 10:13:08",{"path":1076,"words":1077,"published":1078,"date":156},"\u002Fposts\u002F神经网络\u002F神经网络与深度学习深度生成模型",2727,"2026-06-07 11:43:08",{"path":1080,"words":1081,"published":1082,"date":156},"\u002Fposts\u002F神经网络\u002F神经网络与深度学习神经网络基础",3205,"2026-06-07 10:03:08",{"id":1084,"title":1085,"abbrlink":1086,"body":1087,"category":40,"cover":156,"date":156,"description":1115,"extension":1589,"mathjax":1590,"meta":1591,"navigation":1590,"path":659,"published":661,"readingMinutes":1562,"seo":1594,"stem":1595,"sticky":156,"swiper_index":156,"tags":1596,"updated":156,"words":660,"__hash__":1597},"posts\u002Fposts\u002F2025\u002F2025-12-25-关于动态规划(背包问题为例).md","2025-11-17-关于动态规划(背包问题为例)","24254",{"type":1088,"value":1089,"toc":1561},"minimark",[1090,1094,1107,1110,1117,1122,1126,1140,1143,1157,1161,1164,1169,1174,1177,1235,1238,1249,1253,1262,1266,1274,1280,1284,1305,1308,1316,1322,1326,1344,1346,1351,1357,1364,1368,1371,1379,1385,1391,1396,1398,1406,1410,1416,1419,1422,1426,1441,1444,1502,1506,1509,1514,1522,1526,1532,1535,1541],[1091,1092,1093],"h3",{"id":1093},"动态规划介绍",[1095,1096,1097,1098,1102,1103,1106],"p",{},"动态规划（Dynamic Programming，简称 DP）是一种算法设计范式，用于解决具有",[1099,1100,1101],"strong",{},"重叠子问题","和",[1099,1104,1105],{},"最优子结构","性质的优化问题。它通过将原问题分解为若干子问题，先解决子问题并保存结果（通常使用表格或数组），从而避免重复计算，最终构建出原问题的解。",[1095,1108,1109],{},"动态规划的核心思想源于数学中的贝尔曼最优性原理：最优策略的子策略总是最优的。与分治法不同，动态规划适用于子问题重叠的情况，能将指数级时间复杂度优化至多项式级。",[1095,1111,1112],{},[1113,1114],"img",{"alt":1115,"src":1116},"","https:\u002F\u002Fmedia.geeksforgeeks.org\u002Fwp-content\u002Fuploads\u002F20220914114911\u002FDynamicProgramming1.jpg",[1095,1118,1119],{},[1113,1120],{"alt":1115,"src":1121},"https:\u002F\u002Fdeen3evddmddt.cloudfront.net\u002Fuploads\u002Fcontent-images\u002Fdynamic-programming.webp",[1123,1124,1125],"h4",{"id":1125},"动态规划的适用条件",[1127,1128,1129,1135],"ul",{},[1130,1131,1132,1134],"li",{},[1099,1133,1105],{},"：原问题的最优解可由子问题的最优解组合得出。",[1130,1136,1137,1139],{},[1099,1138,1101],{},"：子问题在递归求解中会被多次计算。",[1123,1141,1142],{"id":1142},"实现方式",[1127,1144,1145,1151],{},[1130,1146,1147,1150],{},[1099,1148,1149],{},"自底向上（表格填充）","：使用循环从小型子问题开始填充 DP 表格，直至原问题（常见于背包问题）。",[1130,1152,1153,1156],{},[1099,1154,1155],{},"自顶向下（记忆化递归）","：递归求解并使用备忘录存储已计算子问题结果。",[1091,1158,1160],{"id":1159},"以-01-背包问题为例","以 0\u002F1 背包问题为例",[1095,1162,1163],{},"0\u002F1 背包问题（0\u002F1 Knapsack Problem）是动态规划的经典应用：给定 n 个物品，每个物品有重量 w_i 和价值 v_i，以及一个容量为 W 的背包。每个物品只能选择取或不取（0\u002F1），求背包中物品的最大总价值。",[1095,1165,1166],{},[1113,1167],{"alt":1115,"src":1168},"https:\u002F\u002Fmedia.geeksforgeeks.org\u002Fwp-content\u002Fuploads\u002F20240805101207\u002FRecursion-Tree-for-01-KnapSack.png",[1095,1170,1171],{},[1113,1172],{"alt":1115,"src":1173},"https:\u002F\u002Fmedia.geeksforgeeks.org\u002Fwp-content\u002Fuploads\u002F20250312122610325590\u002FRecursion-tree-for-01-Knapsack-3-1.webp",[1123,1175,1176],{"id":1176},"问题分析",[1127,1178,1179,1185,1196,1222],{},[1130,1180,1181,1184],{},[1099,1182,1183],{},"子问题","：考虑前 i 个物品和容量为 j 的背包的最大价值。",[1130,1186,1187,1190,1191,1195],{},[1099,1188,1189],{},"状态定义","：",[1192,1193,1194],"code",{},"dp[i][j]"," 表示前 i 个物品在容量 j 下的最大价值。",[1130,1197,1198,1201,1202],{},[1099,1199,1200],{},"状态转移方程","：\n",[1127,1203,1204,1210,1216],{},[1130,1205,1206,1207],{},"不取第 i 个物品：",[1192,1208,1209],{},"dp[i][j] = dp[i-1][j]",[1130,1211,1212,1213],{},"取第 i 个物品（若 j ≥ w_i）：",[1192,1214,1215],{},"dp[i][j] = dp[i-1][j - w_i] + v_i",[1130,1217,1218,1221],{},[1192,1219,1220],{},"dp[i][j] = max","(以上两种情况)",[1130,1223,1224,1190,1227,1230,1231,1234],{},[1099,1225,1226],{},"边界",[1192,1228,1229],{},"dp[0][j] = 0","（无物品），",[1192,1232,1233],{},"dp[i][0] = 0","（容量为 0）",[1123,1236,1237],{"id":1237},"示例",[1095,1239,1240,1241,1244,1245,1248],{},"假设物品：重量",[1192,1242,1243],{}," [1, 3, 4]","，价值",[1192,1246,1247],{},"[15, 20, 30]","，背包容量 W = 4。\nDP 表格填充过程如下所示：",[1123,1250,1252],{"id":1251},"初始状态i0无物品","初始状态（i=0，无物品）",[1254,1255,1260],"pre",{"className":1256,"code":1258,"language":1259},[1257],"language-text","容量 w:   0    1    2    3    4\n物品 i\n0        [0]  [0]  [0]  [0]  [0]\n","text",[1192,1261,1258],{"__ignoreMap":1115},[1123,1263,1265],{"id":1264},"考虑第-1-个物品重量-1价值-15","考虑第 1 个物品（重量 1，价值 15）",[1127,1267,1268,1271],{},[1130,1269,1270],{},"对于 w \u003C 1：无法放入，只能取上一行值（0）。",[1130,1272,1273],{},"对于 w ≥ 1：max(不放入: 0, 放入: 0 + 15) = 15。",[1254,1275,1278],{"className":1276,"code":1277,"language":1259},[1257],"容量 w:   0    1    2    3    4\n物品 i\n0        [0]  [0]  [0]  [0]  [0]\n1        [0] [15] [15] [15] [15]\n",[1192,1279,1277],{"__ignoreMap":1115},[1123,1281,1283],{"id":1282},"考虑第-2-个物品重量-3价值-20","考虑第 2 个物品（重量 3，价值 20）",[1127,1285,1286],{},[1130,1287,1288,1289],{},"对于每个 w：\n",[1127,1290,1291,1294],{},[1130,1292,1293],{},"如果 w \u003C 3：无法放入，取上一行值。",[1130,1295,1296,1297,1300,1301,1304],{},"如果 w ≥ 3：max(不放入: ",[1192,1298,1299],{},"dp[1][w]",", 放入: ",[1192,1302,1303],{},"dp[1][w-3] + 20",")。",[1095,1306,1307],{},"计算示例：",[1127,1309,1310,1313],{},[1130,1311,1312],{},"w=3：max(15, 15 + 20) = 35",[1130,1314,1315],{},"w=4：max(15, 15 + 20) = 35",[1254,1317,1320],{"className":1318,"code":1319,"language":1259},[1257],"容量 w:   0    1    2    3    4\n物品 i\n0        [0]  [0]  [0]  [0]  [0]\n1        [0] [15] [15] [15] [15]\n2        [0] [15] [15] [35] [35]\n",[1192,1321,1319],{"__ignoreMap":1115},[1123,1323,1325],{"id":1324},"考虑第-3-个物品重量-4价值-30","考虑第 3 个物品（重量 4，价值 30）",[1127,1327,1328],{},[1130,1329,1288,1330],{},[1127,1331,1332,1335],{},[1130,1333,1334],{},"如果 w \u003C 4：无法放入，取上一行值。",[1130,1336,1337,1338,1300,1341,1304],{},"如果 w ≥ 4：max(不放入: ",[1192,1339,1340],{},"dp[2][w]",[1192,1342,1343],{},"dp[2][w-4] + 30",[1095,1345,1307],{},[1127,1347,1348],{},[1130,1349,1350],{},"w=4：max(35, 0 + 30) = 35（不放入更好）",[1254,1352,1355],{"className":1353,"code":1354,"language":1259},[1257],"容量 w:   0    1    2    3    4\n物品 i\n0        [0]  [0]  [0]  [0]  [0]\n1        [0] [15] [15] [15] [15]\n2        [0] [15] [15] [35] [35]\n3        [0] [15] [15] [35] [35]\n",[1192,1356,1354],{"__ignoreMap":1115},[1095,1358,1359,1360,1363],{},"最终结果：",[1192,1361,1362],{},"dp[3][4] = 35","（选择第 1 和第 2 个物品：重量 1+3=4，价值 15+20=35）。",[1123,1365,1367],{"id":1366},"一维-dp-优化过程简要文本模拟","一维 DP 优化过程简要文本模拟",[1095,1369,1370],{},"一维数组从后向前更新（避免覆盖）：",[1095,1372,1373,1374,1378],{},"初始 dp: ",[1375,1376,1377],"span",{},"0, 0, 0, 0, 0","（容量 0 到 4）",[1095,1380,1381,1382],{},"第 1 个物品后： ",[1375,1383,1384],{},"0, 15, 15, 15, 15",[1095,1386,1387,1388],{},"第 2 个物品后： ",[1375,1389,1390],{},"0, 15, 15, 35, 35",[1095,1392,1393,1394],{},"第 3 个物品后： ",[1375,1395,1390],{},[1123,1397,373],{"id":373},[1127,1399,1400,1403],{},[1130,1401,1402],{},"时间复杂度：O(n × capacity)",[1130,1404,1405],{},"空间复杂度：二维 O(n × capacity)，一维 O(capacity)",[1123,1407,1409],{"id":1408},"伪代码自底向上","伪代码（自底向上）",[1254,1411,1414],{"className":1412,"code":1413,"language":1259},[1257],"dp = 二维数组 (n+1) x (W+1)，初始化为 0\n\nfor i = 1 to n:\n    for j = 1 to W:\n        if w[i-1] > j:\n            dp[i][j] = dp[i-1][j]\n        else:\n            dp[i][j] = max(dp[i-1][j], dp[i-1][j - w[i-1]] + v[i-1])\n\n返回 dp[n][W]\n",[1192,1415,1413],{"__ignoreMap":1115},[1095,1417,1418],{},"时间复杂度 O(nW)，空间复杂度 O(nW)（可优化至 O(W) 使用一维数组）",[1095,1420,1421],{},"动态规划通过系统地记录子问题解，避免了暴力递归的冗余计算，在组合优化、序列问题等领域广泛应用。理解背包问题有助于掌握 DP 的状态设计与转移核心。",[1091,1423,1425],{"id":1424},"_01-背包问题的-typescript-实现详解","0\u002F1 背包问题的 TypeScript 实现详解",[1095,1427,1428,1429,1432,1433,1436,1437,1440],{},"0\u002F1 背包问题（0\u002F1 Knapsack Problem）是动态规划的经典示例。给定 n 个物品，每个物品具有重量 ",[1192,1430,1431],{},"weights[i]"," 和价值 ",[1192,1434,1435],{},"values[i]","，以及一个背包容量 ",[1192,1438,1439],{},"capacity","。每个物品只能选择放入或不放入（不可重复），目标是求背包内物品的最大总价值。",[1123,1442,1443],{"id":1443},"动态规划状态定义与转移",[1127,1445,1446,1455,1483,1494],{},[1130,1447,1448,1190,1451,1454],{},[1099,1449,1450],{},"状态",[1192,1452,1453],{},"dp[i][w]"," 表示考虑前 i 个物品（索引 0 到 i-1），背包容量为 w 时的最大价值。",[1130,1456,1457,1201,1460],{},[1099,1458,1459],{},"转移方程",[1127,1461,1462,1468,1478],{},[1130,1463,1464,1465],{},"如果不放入第 i 个物品：",[1192,1466,1467],{},"dp[i][w] = dp[i-1][w]",[1130,1469,1470,1471,1474,1475],{},"如果放入第 i 个物品（前提 ",[1192,1472,1473],{},"w ≥ weights[i-1]","）：",[1192,1476,1477],{},"dp[i][w] = dp[i-1][w - weights[i-1]] + values[i-1]",[1130,1479,1480],{},[1192,1481,1482],{},"dp[i][w] = Math.max(不放入, 放入)",[1130,1484,1485,1190,1488,1230,1491,1493],{},[1099,1486,1487],{},"初始条件",[1192,1489,1490],{},"dp[0][w] = 0",[1192,1492,1233],{},"（容量为 0）。",[1130,1495,1496,1190,1499],{},[1099,1497,1498],{},"结果",[1192,1500,1501],{},"dp[n][capacity]",[1123,1503,1505],{"id":1504},"typescript-实现","TypeScript 实现",[1095,1507,1508],{},"以下提供两种实现：标准二维 DP 和空间优化的一维 DP（推荐，后者空间复杂度 O(capacity)）",[1510,1511,1513],"h5",{"id":1512},"_1-二维-dp-实现","1. 二维 DP 实现",[1254,1515,1520],{"className":1516,"code":1518,"language":1519,"meta":1115},[1517],"language-typescript","function knapsack01(weights: number[], values: number[], capacity: number): number {\n    const n = weights.length;\n    \u002F\u002F 创建 (n+1) x (capacity+1) 的二维数组，初始化为 0\n    const dp: number[][] = Array.from({ length: n + 1 }, () => Array(capacity + 1).fill(0));\n\n    for (let i = 1; i \u003C= n; i++) {\n        for (let w = 1; w \u003C= capacity; w++) {\n            if (weights[i - 1] > w) {\n                \u002F\u002F 重量超出，无法放入\n                dp[i][w] = dp[i - 1][w];\n            } else {\n                \u002F\u002F 取最大值\n                dp[i][w] = Math.max(\n                    dp[i - 1][w],                              \u002F\u002F 不放入\n                    dp[i - 1][w - weights[i - 1]] + values[i - 1]  \u002F\u002F 放入\n                );\n            }\n        }\n    }\n\n    return dp[n][capacity];\n}\n","typescript",[1192,1521,1518],{"__ignoreMap":1115},[1510,1523,1525],{"id":1524},"_2-一维-dp-实现空间优化使用滚动数组","2. 一维 DP 实现（空间优化，使用滚动数组）",[1254,1527,1530],{"className":1528,"code":1529,"language":1519,"meta":1115},[1517],"function knapsack01Optimized(weights: number[], values: number[], capacity: number): number {\n    const n = weights.length;\n    \u002F\u002F 一维数组，dp[w] 表示容量 w 时的最大价值\n    const dp: number[] = Array(capacity + 1).fill(0);\n\n    for (let i = 0; i \u003C n; i++) {\n        \u002F\u002F 从后向前遍历（防止覆盖前状态）\n        for (let w = capacity; w >= weights[i]; w--) {\n            dp[w] = Math.max(dp[w], dp[w - weights[i]] + values[i]);\n        }\n    }\n\n    return dp[capacity];\n}\n",[1192,1531,1529],{"__ignoreMap":1115},[1123,1533,1237],{"id":1534},"示例-1",[1254,1536,1539],{"className":1537,"code":1538,"language":1519,"meta":1115},[1517],"const weights = [1, 3, 4];\nconst values = [15, 20, 30];\nconst capacity = 4;\n\nconsole.log(knapsack01Optimized(weights, values, capacity));  \u002F\u002F 输出 35（放入重量 1 和 3 的物品）\n",[1192,1540,1538],{"__ignoreMap":1115},[1127,1542,1543,1546,1552,1558],{},[1130,1544,1545],{},"物品数量 n = 3",[1130,1547,1548,1549],{},"重量 weights = ",[1375,1550,1551],{},"1, 3, 4",[1130,1553,1554,1555],{},"价值 values = ",[1375,1556,1557],{},"15, 20, 30",[1130,1559,1560],{},"背包容量 capacity = 4",{"title":1115,"searchDepth":1562,"depth":1562,"links":1563},4,[1564,1569,1580],{"id":1093,"depth":1565,"text":1093,"children":1566},3,[1567,1568],{"id":1125,"depth":1562,"text":1125},{"id":1142,"depth":1562,"text":1142},{"id":1159,"depth":1565,"text":1160,"children":1570},[1571,1572,1573,1574,1575,1576,1577,1578,1579],{"id":1176,"depth":1562,"text":1176},{"id":1237,"depth":1562,"text":1237},{"id":1251,"depth":1562,"text":1252},{"id":1264,"depth":1562,"text":1265},{"id":1282,"depth":1562,"text":1283},{"id":1324,"depth":1562,"text":1325},{"id":1366,"depth":1562,"text":1367},{"id":373,"depth":1562,"text":373},{"id":1408,"depth":1562,"text":1409},{"id":1424,"depth":1565,"text":1425,"children":1581},[1582,1583,1588],{"id":1443,"depth":1562,"text":1443},{"id":1504,"depth":1562,"text":1505,"children":1584},[1585,1587],{"id":1512,"depth":1586,"text":1513},5,{"id":1524,"depth":1586,"text":1525},{"id":1534,"depth":1562,"text":1237},"md",true,{"uuid":1592,"slots":1593},"d6c224c0-e17b-11f0-84d6-53c7df0c5471",{},{"title":1085,"description":1115},"posts\u002F2025\u002F2025-12-25-关于动态规划(背包问题为例)",[40,171,172],"qm_q4IZr2mnl2jlhYs6jk11slk-AqxHhMZtQfCCMBPE",1790443287901]