{"id":38,"date":"2025-11-09T20:50:52","date_gmt":"2025-11-09T12:50:52","guid":{"rendered":"https:\/\/tblog.zeabur.app\/?p=38"},"modified":"2025-11-09T20:50:53","modified_gmt":"2025-11-09T12:50:53","slug":"%e9%a2%98%e8%a7%a3-sp10565-alicesie-alice-sieve","status":"publish","type":"post","link":"https:\/\/tblog.zeabur.app\/?p=38","title":{"rendered":"\u9898\u89e3 SP10565 ALICESIE – Alice Sieve"},"content":{"rendered":"\n

\u65b9\u6cd51\uff1a\u6a21\u62df Alice \u7b5b\u6cd5\uff08TLE\uff09<\/h3>\n\n\n\n

\u6839\u636e\u9898\u610f\u6a21\u62df\u5373\u53ef\uff08\u6ce8\u610f\uff1a\u771f\u56e0\u6570\u6307\u4e0d\u5305\u62ec $n$ \u7684\u6240\u6709 $n$\u200b \u7684\u56e0\u6570\uff09\u3002<\/p>\n\n\n\n

\u4ee3\u7801\uff1a<\/p>\n\n\n\n

#include<bits\/stdc++.h>\n#define int long long\nusing namespace std;\ninline void solve() \n{\n    int n;\n    cin>>n;\n    vector<bool>vis(n+1,false);\/\/\u771f\u56e0\u6570\n    int p=n;\n    while(p>1) \n    {\n        for(int i=1;i*i<=p;i++) \/\/\u6807\u8bb0\u771f\u56e0\u6570\n        {\n            if(p%i==0) \n            {\n                vis[i]=true;\n                if(i!=1&&i!=p\/i) \n                    vis[p\/i]=true;\n            }\n        }\n        int q=-1;\n        for(int i=p-1;i>=2;i--) \n            if(!vis[i]) \n            {\n                q=i;\/\/\u6709\u88ab\u6807\u8bb0\u7684\u6570\n                break;\n            }\n        if(q==-1)break; \n        p=q;\/\/\u6ca1\u6709\u88ab\u6807\u8bb0\u7684\u6570\n    }\n    int count=0;\/\/\u7edf\u8ba1\u6570\u91cf\n    for(int i=2;i<=n;i++) \n    {\n        if(!vis[i]) \n            count++;\n    }\n    cout<<count<<endl;\n}\nsigned main() \n{\n    int T;\n    cin>>T;\n    while(T--) \n        solve();\n    return 0;\n}<\/code><\/pre>\n\n\n\n
\u4f46\u662f\u63d0\u4ea4\u540e\u53d1\u73b0 TLE \u4e86\uff0c\u8bf4\u660e\u6709\u4e00\u5b9a\u7684\u89c4\u5f8b\u53ef\u5faa\u3002<\/p>\n\n\n\n
\u65b9\u6cd52\uff1a\u627e\u89c4\u5f8b\uff08AC\uff09<\/h3>\n\n\n\n
\u9898\u76ee\u8981\u6c42\uff1a<\/h4>\n\n\n\n
    \n
  1. \u521b\u5efa\u5e8f\u5217<\/strong>\uff1a\u4ece $n$ \u5230 $2$ \u7684\u4e25\u683c\u4e0b\u964d\u5e8f\u5217\u3002<\/li>\n\n\n\n
  2. \u521d\u59cb\u5316<\/strong>\uff1a\u4ee4 $P=n$\u3002<\/li>\n\n\n\n
  3. \u6807\u8bb0\u771f\u56e0\u6570<\/strong>\uff1a\u6807\u8bb0 $P$ \u7684\u6240\u6709\u771f\u56e0\u6570\uff08\u4e0d\u5305\u62ec $P$ \u672c\u8eab\uff09\u3002<\/li>\n\n\n\n
  4. \u5bfb\u627e\u4e0b\u4e00\u4e2a P<\/strong>\uff1a\u627e\u5230\u4ece $P-1$ \u5230 $2$ \u4e2d\u6700\u5927\u7684\u672a\u88ab\u6807\u8bb0\u7684\u6570 $q$\uff0c\u4ee4 $P = q$\u3002<\/li>\n\n\n\n
  5. \u91cd\u590d<\/strong>\uff1a\u5982\u679c $q$ \u5b58\u5728\uff0c\u91cd\u590d\u6b65\u9aa4 $3$ \u548c $4$\uff0c\u5426\u5219\u505c\u6b62\u3002<\/li>\n<\/ol>\n\n\n\n
    \u5173\u952e\uff1a<\/h4>\n\n\n\n
      \n
    1. \u6807\u8bb0\u771f\u56e0\u6570<\/strong>\uff1a\u6bcf\u6b21\u6807\u8bb0 $P$ \u7684\u771f\u56e0\u6570\u65f6 $P$ \u672c\u8eab\u4e0d\u4f1a\u88ab\u6807\u8bb0\u3002<\/li>\n\n\n\n
    2. \u5bfb\u627e\u4e0b\u4e00\u4e2a P<\/strong>\uff1a\u6bcf\u6b21\u627e\u5230\u7684 $P$ \u90fd\u662f\u5f53\u524d\u672a\u88ab\u6807\u8bb0\u7684\u6570\u4e2d\u6700\u5927\u7684\u4e00\u4e2a\u3002<\/li>\n<\/ol>\n\n\n\n
      \u7ed3\u679c\uff1a<\/h4>\n\n\n\n
        \n
      • $n$ \u4e3a\u5076\u6570\u65f6\uff1a\u6700\u540e\u4e00\u6b21\u9009 $P$ \u65f6\uff0c$P$\u200b \u6b63\u597d\u5904\u4e8e $\\frac{n-2}{2}$\u3002<\/li>\n\n\n\n
      • $n$ \u4e3a\u5947\u6570\u65f6\uff1a\u6700\u540e\u4e00\u6b21\u9009 $P$ \u65f6\uff0c$P$ \u6b63\u597d\u5904\u4e8e $\\frac{n-2}{2}-1$\u3002<\/li>\n<\/ul>\n\n\n\n
        \u6240\u4ee5\uff1a<\/h4>\n\n\n\n
        \u672a\u88ab\u6807\u8bb0\u7684\u6570\uff08\u5373\u7b54\u6848\uff09\u5219\u4e3a $\\lfloor \\frac{n+1}{2} \\rfloor$\u3002<\/p>\n\n\n\n
        \u4ee3\u7801\uff1a<\/p>\n\n\n\n
        #include<bits\/stdc++.h>\n#define int long long\nusing namespace std;\nsigned main()\n{\n    int t;\n    cin>>t;\n    while(t--)\n    {\n        int n;\n        cin>>n;\n        cout<<floor((n+1)\/2)<<endl;\n    }\n    return 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
        \u65b9\u6cd51\uff1a\u6a21\u62df Alice \u7b5b\u6cd5\uff08TLE\uff09 \u6839\u636e\u9898\u610f\u6a21\u62df\u5373\u53ef\uff08\u6ce8\u610f\uff1a\u771f\u56e0\u6570\u6307\u4e0d\u5305\u62ec $n$ \u7684\u6240\u6709 $n$\u200b \u7684 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[3],"class_list":["post-38","post","type-post","status-publish","format-standard","hentry","category-oi","tag-oi"],"featured_image_src":null,"author_info":{"display_name":"CaelumRadish_c","author_link":"https:\/\/tblog.zeabur.app\/?author=1"},"_links":{"self":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/38","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=38"}],"version-history":[{"count":1,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/38\/revisions"}],"predecessor-version":[{"id":39,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/38\/revisions\/39"}],"wp:attachment":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=38"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=38"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=38"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}