{"id":24,"date":"2025-11-09T20:40:14","date_gmt":"2025-11-09T12:40:14","guid":{"rendered":"https:\/\/tblog.zeabur.app\/?p=24"},"modified":"2025-11-09T20:54:33","modified_gmt":"2025-11-09T12:54:33","slug":"%e9%a2%98%e8%a7%a3-luogu-p1168-%e4%b8%ad%e4%bd%8d%e6%95%b0-pbds-tree-%e7%94%a8%e6%b3%95%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/tblog.zeabur.app\/?p=24","title":{"rendered":"\u9898\u89e3 Luogu P1168 \u4e2d\u4f4d\u6570\/pbds tree \u7528\u6cd5\u8be6\u89e3"},"content":{"rendered":"\n

\u5728\u653e\u4ee3\u7801\u4e4b\u524d\uff0c\u5148\u4ecb\u7ecd\u4e00\u4e2a\u5e93\u2014\u2014 pbds\uff08Policy-Based Data Structures\uff09\uff0c\u8fd9\u662f\u4e00\u4e2a GNU C++ STL \u7684\u6269\u5c55\u5e93\uff0c\u63d0\u4f9b\u4e86\u589e\u5f3a\u7248\u6570\u636e\u7ed3\u6784\uff0c\u5305\u62ec\u4f18\u5148\u961f\u5217\uff0c\u5e73\u8861\u6811\u3002<\/p>\n\n\n\n

\u5728 pbds \u5e93\u4e2d\uff0c\u6709\u4e00\u4e2a\u5bb9\u5668\uff0c\u53eb tree<\/code>\uff0c\u662f\u4e00\u79cd\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811<\/strong>\uff0c\u53ef\u4ee5\u652f\u6301\u6309\u6392\u540d<\/strong>\u8bbf\u95ee\u5143\u7d20\u3002<\/p>\n\n\n\n

tree \u5bb9\u5668<\/h2>\n\n\n\n

\u5b9a\u4e49<\/h3>\n\n\n\n
template<\n    typename Key,                           \/\/ \u5143\u7d20\u7c7b\u578b\n    typename Mapped,                        \/\/ \u6620\u5c04\u503c\u7c7b\u578b (\u76f8\u5f53\u4e8e map \u7684\u6620\u5c04\u503c)\uff0c\u6a21\u62df set \u65f6\u65e0\u9700\u8be5\u9879\uff0c\u8bbe\u4e3a null_type\u5373\u53ef\n    typename Cmp_Fn,                        \/\/ \u6bd4\u8f83\u51fd\u6570\uff0c\u4f8b\u5982 less<Key> \u7b49\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528\u81ea\u5b9a\u4e49\u6bd4\u8f83\u51fd\u6570\n    typename Tag,                           \/\/ \u6811\u7c7b\u578b rb_tree_tag\uff08\u7ea2\u9ed1\u6811\uff0c\u9ed8\u8ba4\u662f\u8fd9\u4e2a\uff09 \/ splay_tree_tag\n    template<typename Const_Node_Iterator,\n             typename Node_Iterator,\n             typename Cmp_Fn_,\n             typename Allocator_>class Node_Update \/\/ \u8282\u70b9\u66f4\u65b0\u7b56\u7565\uff0c\u4f8b\u5982 tree_order_statistics_node_update\n>class tree;<\/code><\/pre>\n\n\n\n
\u4f7f\u7528\u524d\u63d0<\/h3>\n\n\n\n
    \n
  • \u9700\u8981\u5305\u542b<ext\/pb_ds\/assoc_container.hpp><\/code>\uff0c<ext\/pb_ds\/tree_policy.hpp><\/code> \u5934\u6587\u4ef6\uff08\u6ce8\u610f\uff0c\u4e07\u80fd\u5934\u6587\u4ef6\u4e2d\u4e00\u822c\u4e0d\u542b\u8fd9\u4e24\u4e2a\u5934\u6587\u4ef6\uff09\u3002<\/li>\n\n\n\n
  • \u4f7f\u7528 find_by_order<\/code> \u6216 order_of_key<\/code> \u51fd\u6570\u65f6\uff0c\u5fc5\u987b\u4f7f\u7528 tree_order_statistics_node_update<\/code> \u7b56\u7565\u3002<\/li>\n\n\n\n
  • \u9ed8\u8ba4\u53bb\u91cd\uff0c\u91cd\u590d\u5143\u7d20\u9700\u7528 pair \u5904\u7406\u3002<\/li>\n<\/ul>\n\n\n\n
    \u6838\u5fc3\u529f\u80fd\/\u51fd\u6570<\/h3>\n\n\n\n
    \u529f\u80fd<\/th>\u51fd\u6570<\/th>\u8bf4\u660e<\/th>\u8fd4\u56de\u503c\/\u7c7b\u578b<\/th>\u65f6\u95f4\u590d\u6742\u5ea6 *<\/th><\/tr><\/thead>
    \u63d2\u5165\u5143\u7d20<\/td>insert(x)<\/code><\/td>\u63d2\u5165\u5143\u7d20 x\uff08\u552f\u4e00\uff09<\/td>void<\/td>O(log n)<\/td><\/tr>
    \u5220\u9664\u5143\u7d20<\/td>erase(x)<\/code><\/td>\u5220\u9664\u503c\u7b49\u4e8e x \u7684\u5143\u7d20<\/td>void<\/td>O(log n)<\/td><\/tr>
    \u67e5\u627e\u5143\u7d20<\/td>find(x)<\/code><\/td>\u8fd4\u56de\u8fed\u4ee3\u5668<\/td>iterator<\/td>O(log n)<\/td><\/tr>
    \u67e5\u627e\u7b2c k \u5c0f<\/td>find_by_order(k)<\/code><\/td>\u8fd4\u56de\u7b2c k \u5c0f\u5143\u7d20\uff0c0-index<\/td>iterator<\/td>O(log n)<\/td><\/tr>
    \u67e5\u8be2\u6392\u540d<\/td>order_of_key(x)<\/code><\/td>\u8fd4\u56de\u4e25\u683c\u5c0f\u4e8e x \u7684\u5143\u7d20\u6570\u91cf<\/td>int<\/td>O(log n)<\/td><\/tr>
    \u5927\u5c0f<\/td>size()<\/code><\/td>\u5f53\u524d\u5143\u7d20\u4e2a\u6570<\/td>int<\/td>O(1)<\/td><\/tr>
    \u662f\u5426\u4e3a\u7a7a<\/td>empty()<\/code><\/td>\u68c0\u67e5\u662f\u5426\u4e3a\u7a7a<\/td>bool<\/td>O(1)<\/td><\/tr>
    \u6e05\u7a7a<\/td>clear()<\/code><\/td>\u5220\u9664\u6240\u6709\u5143\u7d20<\/td>void<\/td>O(n)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
    *\uff1a\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u5728 rb_tree_tag<\/code> \u7684\u57fa\u7840\u4e0a\u8ba1\u7b97\u7684\u3002<\/p>\n\n\n\n
    \u300e\u9898\u89e3\u300fP1168\u4e2d\u4f4d\u6570<\/h2>\n\n\n\n
    \u9898\u76ee\u5927\u610f<\/h3>\n\n\n\n
    \u9898\u76ee\u7b49\u4ef7\u4e8e\uff1a\u52a8\u6001\u7ef4\u62a4\u524di\u4e2a\u5143\u7d20\u7684\u6709\u5e8f\u5e8f\u5217\uff0c\u5feb\u901f\u53d6\u7b2ck\u5c0f\u5143\u7d20\u3002<\/p>\n\n\n\n
      \n
    • \u4e2d\u4f4d\u6570\u7684\u4e0b\u6807 $\\displaystyle k=\\frac{i}{2}$ (1-indexed)\u3002<\/li>\n\n\n\n
    • \u8f93\u5165 $N \\le 1 0^{5}$\uff0c\u5143\u7d20\u8303\u56f4 $0 \\le A_{i}\\le 1 0^{9}$\u3002<\/li>\n<\/ul>\n\n\n\n
      \u4ee3\u7801\u5b9e\u73b0<\/h3>\n\n\n\n
      #include<bits\/stdc++.h>\n#include<ext\/pb_ds\/assoc_container.hpp>\n#include<ext\/pb_ds\/tree_policy.hpp>\n#define int long long\nusing namespace std;\nusing namespace __gnu_pbds;\/\/\u4f7f\u7528 __gnu_pbds \u547d\u540d\u7a7a\u95f4\ntree<pair<int,int>,null_type,less<pair<int,int>>,rb_tree_tag,tree_order_statistics_node_update>s;\/\/\u5b9a\u4e49\u4e00\u68f5\u5e73\u8861\u6811\nsigned main() \n{\n    int n;\n    cin>>n;\n    for (int i=1;i<=n;i++) \n    {\n        int x;\n        cin>>x;\n        s.insert({x,i});\/\/\u5c06\u6bcf\u4e00\u4e2a\u503c\u63d2\u5165\u6811\u4e2d\uff0ci \u907f\u514d\u91cd\u590d\n        if(i%2==1) \/\/\u5982\u679c\u662f\u5947\u6570\u9879\n        {\n            cout<<s.find_by_order(i\/2)->first<<\"\\n\";\/\/\u8f93\u51fa\u6392\u540d\u4e3a i\/2 \u7684\u9879\u7684\u503c\uff0c\u5373\u524d 1~i \u4f4d\u7684\u4e2d\u4f4d\u6570\n        }\n    }\n    return 0;\n}<\/code><\/pre>\n\n\n\n
      \u65f6\u95f4\u590d\u6742\u5ea6<\/h3>\n\n\n\n
      $\\mathcal{O}(n \\log n)$\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
      \u5728\u653e\u4ee3\u7801\u4e4b\u524d\uff0c\u5148\u4ecb\u7ecd\u4e00\u4e2a\u5e93\u2014\u2014 pbds\uff08Policy-Based Data Structures\uff09\uff0c\u8fd9\u662f\u4e00\u4e2a […]<\/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-24","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\/24","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=24"}],"version-history":[{"count":1,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/24\/revisions"}],"predecessor-version":[{"id":25,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/24\/revisions\/25"}],"wp:attachment":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}