{"id":199642,"date":"2025-05-06T09:30:34","date_gmt":"2025-05-06T01:30:34","guid":{"rendered":"https:\/\/server.hk\/cnblog\/199642\/"},"modified":"2025-05-06T09:30:34","modified_gmt":"2025-05-06T01:30:34","slug":"%e8%af%a6%e8%a7%a3b%e6%a0%91%e5%88%a0%e9%99%a4%e6%93%8d%e4%bd%9c%ef%bc%9a%e4%bd%bf%e7%94%a8python%e5%ae%9e%e7%8e%b0%e7%9a%84b%e6%a0%91%e5%88%a0%e9%99%a4%e6%93%8d%e4%bd%9c%e5%9b%be%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/server.hk\/cnblog\/199642\/","title":{"rendered":"\u8be6\u89e3B\u6811\u5220\u9664\u64cd\u4f5c\uff1a\u4f7f\u7528Python\u5b9e\u73b0\u7684B\u6811\u5220\u9664\u64cd\u4f5c\u56fe\u89e3"},"content":{"rendered":"<p><b><\/b> <\/p>\n<h1>\u8be6\u89e3B\u6811\u5220\u9664\u64cd\u4f5c\uff1a\u4f7f\u7528Python\u5b9e\u73b0\u7684B\u6811\u5220\u9664\u64cd\u4f5c\u56fe\u89e3<\/h1>\n<p>\u5927\u5bb6\u597d\uff0c\u6211\u4eec\u53c8\u89c1\u9762\u4e86\u554a~\u672c\u6587\u7684\u5185\u5bb9\u4e2d\u5c06\u4f1a\u6d89\u53ca\u5230\u7b49\u7b49\u3002\u5982\u679c\u4f60\u6b63\u5728\u5b66\u4e60\u76f8\u5173\u77e5\u8bc6\uff0c\u6b22\u8fce\u5173\u6ce8\u6211\uff0c\u4ee5\u540e\u4f1a\u7ed9\u5927\u5bb6\u5e26\u6765\u66f4\u591a\u76f8\u5173\u6587\u7ae0\uff0c\u5e0c\u671b\u6211\u4eec\u80fd\u4e00\u8d77\u8fdb\u6b65\uff01\u4e0b\u9762\u5c31\u5f00\u59cb\u672c\u6587\u7684\u6b63\u5f0f\u5185\u5bb9~<\/p>\n<p>B\u6811\u5220\u9664\u64cd\u4f5c\u9700\u8981\u8003\u8651\u8282\u70b9\u6240\u5728\u4f4d\u7f6e\u548c\u5e73\u8861\uff0c\u5e76\u4e14\u5f88\u6709\u53ef\u80fd\u4f1a\u53d1\u751f\u4e0b\u6ea2\u7684\u60c5\u51b5\u3002\u5f53\u4e00\u4e2a\u8282\u70b9\u5305\u542b\u7684\u5b50\u8282\u70b9\u6570\u91cf\u5c11\u4e8e\u5b83\u5e94\u8be5\u6301\u6709\u7684\u6700\u5c0f\u6570\u91cf\u65f6\uff0c\u5c31\u4f1a\u53d1\u751f\u4e0b\u6ea2\u3002<\/p>\n<h3>\u56fe\u6587\u5c55\u793aB\u6811\u5220\u9664\u64cd\u4f5c\u539f\u7406<\/h3>\n<p>\u5728\u4e0d\u5f71\u54cd\u5e73\u8861\u60c5\u51b5\u4e0b\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.17golang.com\/uploads\/20240126\/170624772265b3462a641dd.jpg\" class=\"aligncenter\"> <\/p>\n<p>\u4e0b\u6ea2\u60c5\u51b5\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.17golang.com\/uploads\/20240126\/170624772265b3462a67cd8.jpg\" class=\"aligncenter\"> <\/p>\n<p>\u5220\u9664\u5185\u90e8\u8282\u70b9\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.17golang.com\/uploads\/20240126\/170624772265b3462a69652.jpg\" class=\"aligncenter\"> <\/p>\n<h3>Python\u5b9e\u73b0B\u6811\u5220\u9664\u64cd\u4f5c<\/h3>\n<pre># B\u6811\u8282\u70b9\r\nclass BTreeNode:\r\n    def __init__(self, leaf=False):\r\n        self.leaf = leaf\r\n        self.keys = []\r\n        self.child = []\r\n\r\nclass BTree:\r\n    def __init__(self, t):\r\n        self.root = BTreeNode(True)\r\n        self.t = t\r\n\r\n    # \u63d2\u5165\u5143\u7d20\r\n    def insert(self, k):\r\n        root = self.root\r\n        if len(root.keys) == (2 * self.t) - 1:\r\n            temp = BTreeNode()\r\n            self.root = temp\r\n            temp.child.insert(0, root)\r\n            self.split_child(temp, 0)\r\n            self.insert_non_full(temp, k)\r\n        else:\r\n            self.insert_non_full(root, k)\r\n\r\n    def insert_non_full(self, x, k):\r\n        i = len(x.keys) - 1\r\n        if x.leaf:\r\n            x.keys.append((None, None))\r\n            while i &gt;= 0 and k[0] &lt; x.keys[i][0]:\r\n                x.keys[i + 1] = x.keys[i]\r\n                i -= 1\r\n            x.keys[i + 1] = k\r\n        else:\r\n            while i &gt;= 0 and k[0] &lt; x.keys[i][0]:\r\n                i -= 1\r\n            i += 1\r\n            if len(x.child[i].keys) == (2 * self.t) - 1:\r\n                self.split_child(x, i)\r\n                if k[0] &gt; x.keys[i][0]:\r\n                    i += 1\r\n            self.insert_non_full(x.child[i], k)\r\n\r\n    # \u5206\u5f00\u5b50\u8282\u70b9\r\n    def split_child(self, x, i):\r\n        t = self.t\r\n        y = x.child[i]\r\n        z = BTreeNode(y.leaf)\r\n        x.child.insert(i + 1, z)\r\n        x.keys.insert(i, y.keys[t - 1])\r\n        z.keys = y.keys[t: (2 * t) - 1]\r\n        y.keys = y.keys[0: t - 1]\r\n        if not y.leaf:\r\n            z.child = y.child[t: 2 * t]\r\n            y.child = y.child[0: t - 1]\r\n\r\n    # \u5220\u9664\u8282\u70b9\r\n    def delete(self, x, k):\r\n        t = self.t\r\n        i = 0\r\n        while i &lt; len(x.keys) and k[0] &gt; x.keys[i][0]:\r\n            i += 1\r\n        if x.leaf:\r\n            if i &lt; len(x.keys) and x.keys[i][0] == k[0]:\r\n                x.keys.pop(i)\r\n                return\r\n            return\r\n\r\n        if i &lt; len(x.keys) and x.keys[i][0] == k[0]:\r\n            return self.delete_internal_node(x, k, i)\r\n        elif len(x.child[i].keys) &gt;= t:\r\n            self.delete(x.child[i], k)\r\n        else:\r\n            if i != 0 and i + 2 &lt; len(x.child):\r\n                if len(x.child[i - 1].keys) &gt;= t:\r\n                    self.delete_sibling(x, i, i - 1)\r\n                elif len(x.child[i + 1].keys) &gt;= t:\r\n                    self.delete_sibling(x, i, i + 1)\r\n                else:\r\n                    self.delete_merge(x, i, i + 1)\r\n            elif i == 0:\r\n                if len(x.child[i + 1].keys) &gt;= t:\r\n                    self.delete_sibling(x, i, i + 1)\r\n                else:\r\n                    self.delete_merge(x, i, i + 1)\r\n            elif i + 1 == len(x.child):\r\n                if len(x.child[i - 1].keys) &gt;= t:\r\n                    self.delete_sibling(x, i, i - 1)\r\n                else:\r\n                    self.delete_merge(x, i, i - 1)\r\n            self.delete(x.child[i], k)\r\n\r\n    # \u5220\u9664\u8282\u70b9\r\n    def delete_internal_node(self, x, k, i):\r\n        t = self.t\r\n        if x.leaf:\r\n            if x.keys[i][0] == k[0]:\r\n                x.keys.pop(i)\r\n                return\r\n            return\r\n\r\n        if len(x.child[i].keys) &gt;= t:\r\n            x.keys[i] = self.delete_predecessor(x.child[i])\r\n            return\r\n        elif len(x.child[i + 1].keys) &gt;= t:\r\n            x.keys[i] = self.delete_successor(x.child[i + 1])\r\n            return\r\n        else:\r\n            self.delete_merge(x, i, i + 1)\r\n            self.delete_internal_node(x.child[i], k, self.t - 1)\r\n\r\n    # \u5220\u9664\u524d\u8282\u70b9\r\n    def delete_predecessor(self, x):\r\n        if x.leaf:\r\n            return x.pop()\r\n        n = len(x.keys) - 1\r\n        if len(x.child[n].keys) &gt;= self.t:\r\n            self.delete_sibling(x, n + 1, n)\r\n        else:\r\n            self.delete_merge(x, n, n + 1)\r\n        self.delete_predecessor(x.child[n])\r\n\r\n    # \u5220\u9664\u7ee7\u4efb\u8282\u70b9\r\n    def delete_successor(self, x):\r\n        if x.leaf:\r\n            return x.keys.pop(0)\r\n        if len(x.child[1].keys) &gt;= self.t:\r\n            self.delete_sibling(x, 0, 1)\r\n        else:\r\n            self.delete_merge(x, 0, 1)\r\n        self.delete_successor(x.child[0])\r\n\r\n    def delete_merge(self, x, i, j):\r\n        cnode = x.child[i]\r\n\r\n        if j &gt; i:\r\n            rsnode = x.child[j]\r\n            cnode.keys.append(x.keys[i])\r\n            for k in range(len(rsnode.keys)):\r\n                cnode.keys.append(rsnode.keys[k])\r\n                if len(rsnode.child) &gt; 0:\r\n                    cnode.child.append(rsnode.child[k])\r\n            if len(rsnode.child) &gt; 0:\r\n                cnode.child.append(rsnode.child.pop())\r\n            new = cnode\r\n            x.keys.pop(i)\r\n            x.child.pop(j)\r\n        else:\r\n            lsnode = x.child[j]\r\n            lsnode.keys.append(x.keys[j])\r\n            for i in range(len(cnode.keys)):\r\n                lsnode.keys.append(cnode.keys[i])\r\n                if len(lsnode.child) &gt; 0:\r\n                    lsnode.child.append(cnode.child[i])\r\n            if len(lsnode.child) &gt; 0:\r\n                lsnode.child.append(cnode.child.pop())\r\n            new = lsnode\r\n            x.keys.pop(j)\r\n            x.child.pop(i)\r\n\r\n        if x == self.root and len(x.keys) == 0:\r\n            self.root = new\r\n\r\n    # \u5220\u9664\u540c\u4e00\u7ea7\u7684\u5176\u4ed6\u5b50\u8282\u70b9\r\n    def delete_sibling(self, x, i, j):\r\n        cnode = x.child[i]\r\n        if i &lt; j:\r\n            rsnode = x.child[j]\r\n            cnode.keys.append(x.keys[i])\r\n            x.keys[i] = rsnode.keys[0]\r\n            if len(rsnode.child) &gt; 0:\r\n                cnode.child.append(rsnode.child[0])\r\n                rsnode.child.pop(0)\r\n            rsnode.keys.pop(0)\r\n        else:\r\n            lsnode = x.child[j]\r\n            cnode.keys.insert(0, x.keys[i - 1])\r\n            x.keys[i - 1] = lsnode.keys.pop()\r\n            if len(lsnode.child) &gt; 0:\r\n                cnode.child.insert(0, lsnode.child.pop())\r\n\r\n    # \u8f93\u51faB\u6811\r\n    def print_tree(self, x, l=0):\r\n        print(\"Level \", l, \" \", len(x.keys), end=\":\")\r\n        for i in x.keys:\r\n            print(i, end=\" \")\r\n        print()\r\n        l += 1\r\n        if len(x.child) &gt; 0:\r\n            for i in x.child:\r\n                self.print_tree(i, l)\r\n\r\nB = BTree(3)\r\n\r\nfor i in range(10):\r\n    B.insert((i, 2 * i))\r\n\r\nB.print_tree(B.root)\r\nB.delete(B.root, (8,))\r\nprint(\"\\n\")\r\nB.print_tree(B.root)<\/pre>\n<p>\u5230\u8fd9\u91cc\uff0c\u6211\u4eec\u4e5f\u5c31\u8bb2\u5b8c\u4e86\u300a\u8be6\u89e3B\u6811\u5220\u9664\u64cd\u4f5c\uff1a\u4f7f\u7528Python\u5b9e\u73b0\u7684B\u6811\u5220\u9664\u64cd\u4f5c\u56fe\u89e3\u300b\u7684\u5185\u5bb9\u4e86\u3002\u4e2a\u4eba\u8ba4\u4e3a\uff0c\u57fa\u7840\u77e5\u8bc6\u7684\u5b66\u4e60\u548c\u5de9\u56fa\uff0c\u662f\u4e3a\u4e86\u66f4\u597d\u7684\u5c06\u5176\u8fd0\u7528\u5230\u9879\u76ee\u4e2d\uff0c\u6b22\u8fce\u5173\u6ce8\u4e3b\u673a\u5b9d\u8d1d\u516c\u4f17\u53f7\uff0c\u5e26\u4f60\u4e86\u89e3\u66f4\u591a\u5173\u4e8eB\u6811\u7684\u6982\u5ff5\u7684\u77e5\u8bc6\u70b9\uff01<\/p>\n<p> \u7248\u672c\u58f0\u660e \u672c\u6587\u8f6c\u8f7d\u4e8e\uff1a\u7f51\u6613\u4f0f\u7fb2 \u5982\u6709\u4fb5\u72af\uff0c\u8bf7\u8054\u7cfb \u5220\u9664 <\/p>\n<dl>\n<dt>\n <\/dt>\n<\/dl>\n","protected":false},"excerpt":{"rendered":"<p>\u8be6\u89e3B\u6811\u5220\u9664\u64cd\u4f5c\uff1a\u4f7f\u7528Pytho&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[101],"tags":[],"class_list":["post-199642","post","type-post","status-publish","format-standard","hentry","category-database"],"_links":{"self":[{"href":"https:\/\/server.hk\/cnblog\/wp-json\/wp\/v2\/posts\/199642","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/server.hk\/cnblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/server.hk\/cnblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/server.hk\/cnblog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/server.hk\/cnblog\/wp-json\/wp\/v2\/comments?post=199642"}],"version-history":[{"count":0,"href":"https:\/\/server.hk\/cnblog\/wp-json\/wp\/v2\/posts\/199642\/revisions"}],"wp:attachment":[{"href":"https:\/\/server.hk\/cnblog\/wp-json\/wp\/v2\/media?parent=199642"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/server.hk\/cnblog\/wp-json\/wp\/v2\/categories?post=199642"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/server.hk\/cnblog\/wp-json\/wp\/v2\/tags?post=199642"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}