{"id":285,"date":"2025-08-27T16:44:39","date_gmt":"2025-08-27T08:44:39","guid":{"rendered":"http:\/\/www.tgwttt.xyz\/?p=285"},"modified":"2025-11-24T16:37:49","modified_gmt":"2025-11-24T08:37:49","slug":"b%e6%a0%91","status":"publish","type":"post","link":"https:\/\/www.tgwttt.xyz\/?p=285","title":{"rendered":"b\u6811"},"content":{"rendered":"\n

\u5b8c\u6574\u4ee3\u7801:https:\/\/gitee.com\/tgwTTT\/data-structure\/tree\/master\/Btree<\/a><\/p>\n\n\n\n

B\u6811\uff08B-Tree\uff09\u662f\u4e00\u79cd\u591a\u8def\u5e73\u8861\u67e5\u627e\u6811\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u636e\u5e93\u548c\u6587\u4ef6\u7cfb\u7edf\u3002\u76f8\u6bd4\u4e8c\u53c9\u641c\u7d22\u6811\uff0cB\u6811\u6bcf\u4e2a\u8282\u70b9\u53ef\u4ee5\u5b58\u50a8\u591a\u4e2a\u5173\u952e\u5b57\u548c\u5b50\u8282\u70b9\uff0c\u6781\u5927\u5730\u964d\u4f4e\u4e86\u6811\u7684\u9ad8\u5ea6\uff0c\u63d0\u9ad8\u4e86\u67e5\u627e\u548c\u63d2\u5165\u6548\u7387\uff0c\u5c24\u5176\u9002\u5408\u78c1\u76d8\u5b58\u50a8\u573a\u666f\u3002<\/p>\n\n\n\n

\u4e00\u3001B\u6811\u7684\u7ed3\u6784<\/h2>\n\n\n\n

\u4ee5\u5982\u4e0b\u4ee3\u7801\u4e3a\u4f8b\uff0c\u5b9a\u4e49\u4e86\u4e00\u4e2a\u9636\u6570\u4e3a M \u7684 B\u6811\u8282\u70b9\uff1a<\/p>\n\n\n\n

template\nstruct BTreeNode\n{\n    K _keys[M];                \/\/ \u5b58\u50a8\u5173\u952e\u5b57\n    BTreeNode* _subs[M+1]; \/\/ \u5b58\u50a8\u5b50\u8282\u70b9\u6307\u9488\n    BTreeNode* _parent;    \/\/ \u7236\u8282\u70b9\u6307\u9488\n    size_t _n;                   \/\/ \u5f53\u524d\u5173\u952e\u5b57\u6570\u91cf\n    \/\/ \u6784\u9020\u51fd\u6570\u7565\n};<\/code><\/pre>\n\n\n\n
\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u5b58\u50a8 M \u4e2a\u5173\u952e\u5b57\u548c M+1 \u4e2a\u5b50\u8282\u70b9\u3002\u8282\u70b9\u7684\u5173\u952e\u5b57\u6709\u5e8f\u6392\u5217\uff0c\u5b50\u8282\u70b9\u6307\u5411\u5173\u952e\u5b57\u533a\u95f4<\/p>\n\n\n\n
\u7ed3\u6784\u56fe\u793a\uff08\u4ee5 M=3 \u4e3a\u4f8b\uff09<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u4e8c\u3001B\u6811\u7684\u63d2\u5165\u4e0e\u5206\u88c2\u64cd\u4f5c<\/h2>\n\n\n\n
1. \u63d2\u5165\u6d41\u7a0b<\/h3>\n\n\n\n
\u63d2\u5165\u65f6\uff0c\u9996\u5148\u67e5\u627e\u5408\u9002\u7684\u53f6\u5b50\u8282\u70b9\uff0c\u7136\u540e\u63d2\u5165\u5173\u952e\u5b57\u3002\u5982\u679c\u8282\u70b9\u672a\u6ee1\uff0c\u76f4\u63a5\u63d2\u5165\uff1b\u5982\u679c\u8282\u70b9\u5df2\u6ee1\uff0c\u5219\u9700\u8981\u5206\u88c2\u3002<\/p>\n\n\n\n
void InsertKey(Node* node, const K& key, Node* child)\n{\n    int end = node->_n - 1;\n    while (end >= 0 && key < node->_keys[end])\n    {\n        node->_keys[end + 1] = node->_keys[end];\n        node->_subs[end + 2] = node->_subs[end + 1];\n        --end;\n    }\n    node->_keys[end + 1] = key;\n    node->_subs[end + 2] = child;\n    if (child) child->_parent = node;\n    node->_n++;\n}<\/code><\/pre>\n\n\n\n
2. \u8282\u70b9\u5206\u88c2<\/h3>\n\n\n\n
\u5f53\u63d2\u5165\u540e\u8282\u70b9\u5173\u952e\u5b57\u6570\u8fbe\u5230 M\uff0c\u9700\u8981\u5206\u88c2\u8282\u70b9\uff1a<\/p>\n\n\n\n
    \n
  • \u53d6\u4e2d\u95f4\u5173\u952e\u5b57\uff08midKey\uff09\uff0c\u5c06\u5176\u63d0\u5347\u5230\u7236\u8282\u70b9\u3002<\/li>\n\n\n\n
  • \u5c06\u53f3\u534a\u90e8\u5206\u5173\u952e\u5b57\u548c\u5b50\u8282\u70b9\u5206\u88c2\u5230\u65b0\u8282\u70b9\uff08brother\uff09\u3002<\/li>\n\n\n\n
  • \u5982\u679c\u7236\u8282\u70b9\u4e5f\u6ee1\u4e86\uff0c\u7ee7\u7eed\u5411\u4e0a\u5206\u88c2\uff0c\u76f4\u5230\u6839\u8282\u70b9\u3002<\/li>\n<\/ul>\n\n\n\n
    \u4ee3\u7801\u7247\u6bb5\uff08\u5206\u88c2\u8fc7\u7a0b\uff09<\/h4>\n\n\n\n
    size_t mid = M \/ 2;\nNode* brother = new Node;\nsize_t j = 0;\nsize_t i = mid + 1;\nfor (; i <= M - 1; ++i)\n{\n    brother->_keys[j] = parent->_keys[i];\n    brother->_subs[j] = parent->_subs[i];\n    if (parent->_subs[i]) parent->_subs[i]->_parent = brother;\n    ++j;\n    parent->_keys[i] = K();\n    parent->_subs[i] = nullptr;\n}\nbrother->_subs[j] = parent->_subs[i];\nif (parent->_subs[i]) parent->_subs[i]->_parent = brother;\nparent->_subs[i] = nullptr;\n\nbrother->_n = j;\nparent->_n -= (brother->_n + 1);\n\nK midKey = parent->_keys[mid];\nparent->_keys[mid] = K();<\/code><\/pre>\n\n\n\n
    3. \u5206\u88c2\u56fe\u793a<\/h3>\n\n\n\n
    \u5047\u8bbe M=3\uff0c\u63d2\u5165\u540e\u8282\u70b9\u6ee1\u4e86\uff1a<\/p>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
    \u5982\u679c\u5206\u88c2\u7684\u662f\u6839\u8282\u70b9\uff0c\u5219\u65b0\u5efa\u4e00\u4e2a\u6839\u8282\u70b9\uff0c\u6811\u9ad8\u5ea6\u589e\u52a0\u3002<\/p>\n\n\n\n
    \u4e09\u3001B\u6811\u7684\u4e2d\u5e8f\u904d\u5386<\/h2>\n\n\n\n
    B\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u53ef\u4ee5\u6309\u987a\u5e8f\u8f93\u51fa\u6240\u6709\u5173\u952e\u5b57\uff1a<\/p>\n\n\n\n
    void _InOrder(Node* cur)
    {
    if (cur == nullptr) return;
    size_t i = 0;
    for (; i < cur->_n; ++i)
    {
    _InOrder(cur->_subs[i]);
    cout << cur->_keys[i] << \" \"; } _InOrder(cur->_subs[i]);
    }<\/p>\n\n\n\n
    \u4eca\u5929\u7684\u66f4\u65b0\u5c31\u5230\u8fd9\u91cc\uff0c\u5982\u6709\u9519\u8bef\u6b22\u8fce\u8bc4\u8bba\u533a\u6307\u51fa<\/p>\n","protected":false},"excerpt":{"rendered":"
    \u5b8c\u6574\u4ee3\u7801:https:\/\/gitee.com\/tgwTTT\/data-structure\/tree\/maste…<\/p>\n","protected":false},"author":1,"featured_media":286,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"categories":[6],"tags":[],"class_list":["post-285","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-6"],"_links":{"self":[{"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=\/wp\/v2\/posts\/285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=285"}],"version-history":[{"count":4,"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=\/wp\/v2\/posts\/285\/revisions"}],"predecessor-version":[{"id":845,"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=\/wp\/v2\/posts\/285\/revisions\/845"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=\/wp\/v2\/media\/286"}],"wp:attachment":[{"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.tgwttt.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}