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{"workbook":{"problemsBrief":"{\"HYSBZ-2301\":[\"Problem b\",800,\"HAOI2011\"],\"HYSBZ-3994\":[\"约数个数和\",172,\"SDOI2015\"],\"HYSBZ-2005\":[\"能量采集\",550,\"Noi2010\"],\"HYSBZ-3930\":[\"选数\",68,\"CQOI2015\"],\"HYSBZ-2440\":[\"完全平方数\",401,\"中山市选2011\"],\"HYSBZ-2671\":[\"Calc\",13,\"\"],\"HYSBZ-2154\":[\"Crash的数字表格\",310,\"\"],\"HYSBZ-4652\":[\"循环之美\",23,\"Noi2016\"],\"HYSBZ-3309\":[\"DZY Loves Math\",70,\"\"],\"HYSBZ-3529\":[\"趣味彩票\",168,\"\\u003cp\\u003e\\u003ca href\\u003d\\\"http://www.lydsy.com/JudgeOnline/problemset.php?search\\u003d入门\\\"\\u003e入门\\u003c/a\\u003e\\u003c/p\\u003e\"],\"HYSBZ-4805\":[\"欧拉函数求和\",68,\"\\u003cp\\u003e\\u003ca href\\u003d\\\"http://www.lydsy.com/JudgeOnline/problemset.php?search\\u003dBy FancyCoder\\\"\\u003eBy FancyCoder\\u003c/a\\u003e\\u003c/p\\u003e\"],\"HYSBZ-4816\":[\"数字表格\",42,\"Sdoi2017\"],\"HYSBZ-4916\":[\"神犇和蒟蒻\",32,\"\\u003cp\\u003e\\u003ca href\\u003d\\\"http://www.lydsy.com/JudgeOnline/problemset.php?search\\u003dBy Monster_Yi\\\"\\u003eBy Monster_Yi\\u003c/a\\u003e\\u003c/p\\u003e\"],\"HDU-1695\":[\"GCD\",4761,\"\\u003cdiv class\\u003d\\\"panel_content\\\"\\u003e \\u003ca href\\u003d\\\"https://acm.hdu.edu.cn/search.php?field\\u003dproblem\\u0026amp;key\\u003d2008+%A1%B0Sunline+Cup%A1%B1+National+Invitational+Contest\\u0026amp;source\\u003d1\\u0026amp;searchmode\\u003dsource\\\"\\u003e 2008 “Sunline Cup” National Invitational Contest \\u003c/a\\u003e \\u003c/div\\u003e\"],\"HYSBZ-3944\":[\"Sum\",150,\"\"],\"UVA-11426\":[\"GCD - Extreme (II)\",4332,null],\"HYSBZ-4407\":[\"于神之怒加强版\",58,\"\\u003cp\\u003e\\u003ca href\\u003d\\\"http://www.lydsy.com/JudgeOnline/problemset.php?search\\u003d命题人:成都七中张耀楠,鸣谢excited上传。\\\"\\u003e命题人:成都七中张耀楠,鸣谢excited上传。\\u003c/a\\u003e\\u003c/p\\u003e\"],\"HYSBZ-2818\":[\"SvT\",879,\"\\u003cp\\u003e\\u003ca href\\u003d\\\"http://www.lydsy.com/JudgeOnline/problemset.php?search\\u003d后缀树\\\"\\u003e后缀树\\u003c/a\\u003e\\u003c/p\\u003e\"]}","joined":false,"groups":{}},"managingGroups":{},"author":"Enzyme125","updateTime":1556127537000,"title":"莫比乌斯反演 \u0026 狄利克雷卷积 \u0026 杜教筛","dislikeCnt":1,"content":"## 建议\n1.先学习狄利克雷卷积,在试着自己证明莫比乌斯反演(用狄利克雷卷积)。\n2.自推所有公式,用个十多页草稿纸都是很正常的\n## 学习资料\n建议学习路线: \n\n---------------\n了解狄利克雷卷积 \u003d\u003e \n知道常用数论函数的卷积结论 \u003d\u003e \n莫比乌斯反演 \u003d\u003e \n利用常用函数的卷积结论证明莫比乌斯反演(两边同时变换一下就可以了) \u003d\u003e \n利用莫比乌斯函数的性质, **做题**(经常提gcd(i,j))\u003d\u003e\n学习杜教筛并且深入了解狄利克雷卷积和积性函数之间的点积\u003d\u003e\n**初级题目可以看几道题的题解, 后面建议自推 , 看完题解自己推一次**\n\n做杜教筛的题\n做综合题.\n\n\n\n\n--------------------------\n\n狄利克雷卷积和杜教筛:[一篇Blog](https://blog.csdn.net/qq_30974369/article/details/79087445)\n莫比乌斯反演[PoPoQQQ的讲稿](https://wenku.baidu.com/view/fbec9c63ba1aa8114431d9ac.html)\n线性筛常用函数[Menci的博客](https://oi.men.ci/euler-sieve/)\n线性筛积性函数[一篇Blog](https://www.cnblogs.com/zhoushuyu/p/8275530.html)\n\n另外两篇关于数论分块的文章(初学很难弄懂n / (n / i)) \n[Candy](https://www.cnblogs.com/candy99/p/6209502.html)\n[文库](https://wenku.baidu.com/view/fbe263d384254b35eefd34eb.html)\n\n-------------------------\n\n\n## 题目\n### 莫比乌斯反演\n\n#### 初级\n[problem:HYSBZ-2671]\n[problem:UVA-11426]\n[problem:HYSBZ-2440]\n[problem:HYSBZ-2005]\n[problem:HYSBZ-2301]\n[problem:HYSBZ-2818]\n[problem:HYSBZ-2154]\n[problem:HDU-1695]\n#### 进阶\n[problem:HYSBZ-3994]\n[problem:HYSBZ-4407]\n[problem:HYSBZ-4816]\n\n[problem:HYSBZ-3309]\n#### 莫比乌斯反演结合数据结构\n\n[problem:HYSBZ-3529]\n\n\n### 杜教筛\n[problem:HYSBZ-4805]\n[problem:HYSBZ-3944]\n[problem:HYSBZ-4916]\n\n\n\n## 综合运用:\n洛谷一道题: P3768\n[problem:HYSBZ-4652]\n[problem:HYSBZ-3930]\n\n\t\t\n\t\t\n\t\t\n\t\t\n\n","threadId":31467,"likeCnt":35,"createTime":1531539339000,"isWorkbook":true,"viewCnt":3915,"openness":2,"fav":false,"id":518,"trustable":false}