{"id":215,"date":"2019-03-30T17:37:24","date_gmt":"2019-03-30T09:37:24","guid":{"rendered":"http:\/\/fankasy.xyz\/?p=215"},"modified":"2019-04-11T19:23:26","modified_gmt":"2019-04-11T11:23:26","slug":"%e5%ad%a6%e4%b9%a0%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%848-avl%e6%a0%91","status":"publish","type":"post","link":"http:\/\/fankasy.xyz\/index.php\/2019\/03\/30\/%e5%ad%a6%e4%b9%a0%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%848-avl%e6%a0%91\/","title":{"rendered":"\u5b66\u4e60\u6570\u636e\u7ed3\u67848-AVL\u6811"},"content":{"rendered":"<p>\u4e8c\u53c9\u641c\u7d22\u6811\u88ab\u63d0\u51fa\u540e\u4e0d\u5c31\uff0c\u5c31\u6709\u4eba\u53d1\u73b0\u4e86\u4e00\u4e2a\u5173\u952e\u95ee\u9898\uff1a\u5f53\u6570\u636e\u65e0\u610f\u6216\u8005\u6709\u610f\u88ab\u6709\u5e8f\u8f93\u5165\u65f6\uff0c\u4e8c\u53c9\u6811\u7684\u6bcf\u4e00\u4e2a\u8282\u70b9\u90fd\u5c06\u53ea\u6709\u4e00\u4e2a\u5b69\u5b50\uff0c\u4e5f\u5c31\u662f\u4f1a\u9000\u5316\u6210\u94fe\u8868\u3002\u4e3a\u6b64\uff0cA.V.\u548cL.\u63d0\u51fa\u4e86\u4e8c\u53c9\u5e73\u8861\u6811\u7684\u6982\u5ff5\uff0c\u89e3\u51b3\u4e86\u95ee\u9898\u3002<\/p>\n<p>AVL\u6811\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u4e8c\u53c9\u6392\u5e8f\u6811\uff0c\u5b83\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a<\/p>\n<pre>1.\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u90fd\u662f\u5e73\u8861\u4e8c\u53c9\u6811\uff1b\r\n\r\n2.\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u6df1\u5ea6\uff08\u9ad8\u5ea6\uff09\u4e4b\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc71\u3002<\/pre>\n<p>\u8fd9\u6837\u53ef\u4ee5\u4fdd\u8bc1\u5728\u641c\u7d22\u5176\u4e2d\u7684\u5143\u7d20\u65f6\u6700\u5927\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u4f1a\u8d85\u8fc7log 2 N \u3002<\/p>\n<p>\u4e0b\u9762\u7ed9\u51faAVL\u6811\u7684C\u8bed\u8a00\u5b9e\u73b0\u3002<\/p>\n<p>\u9996\u5148\u662f\u6811\u8282\u70b9\u7684\u5b9a\u4e49\uff1a<\/p>\n<pre>\/\/\u4e3a\u4e86\u4fdd\u6301\u5e73\u8861\uff0c\u6bcf\u4e2a\u8282\u4f1a\u989d\u5916\u589e\u52a0\u4e00\u4e2a\u6570\u636e\u8868\u793a\u5f53\u524d\u7684\u9ad8\u5ea6\u3002\r\nstruct node\r\n{\r\n   int height;\r\n   int key;  \/\/\u8fd9\u662f\u5173\u952e\u5b57\uff0c\u5b9e\u9645\u5e94\u7528\u8fd8\u9700\u8981\u6839\u636e\u5b58\u50a8\u7684\u6570\u636e\u6765\u8ba1\u7b97\u5173\u952e\u5b57\u7684\u503c\r\n   struct node* left;\r\n   struct node* right;\r\n}AVLNode;\r\n<\/pre>\n<p>\u63a5\u4e0b\u6765\u662f\u8bbf\u95ee\u7684\u8282\u70b9<\/p>\n<pre>typedef struct\r\n{\r\n   struct node *root;\r\n}AVLTree;\r\n<\/pre>\n<p>AVL\u6811\u540c\u4e00\u822c\u7684\u4e8c\u53c9\u6811\u4e00\u6837\uff0c\u6709\u904d\u5386\uff08\u5148\u5e8f\u3001\u4e2d\u5e8f\u3001\u540e\u5e8f\uff09\uff0c\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\uff0c\u63d2\u5165\u548c\u5220\u9664\uff0c\u9500\u6bc1\u7b49\u64cd\u4f5c\uff0c\u9664\u63d2\u5165\u548c\u5220\u9664\u4ee5\u5916\u5176\u4f59\u5747\u4e0e\u4e8c\u53c9\u641c\u7d22\u6811\u76f8\u540c\uff0c\u6240\u4ee5\u8fd9\u91cc\u5c31\u53ea\u5199AVL\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u3002<\/p>\n<p>\u5728\u8fdb\u884c\u5b9e\u73b0\u4e4b\u524d\uff0c\u9700\u8981\u5148\u4e86\u89e3\u4e00\u4e0bAVL\u6811\u80fd\u591f\u5e73\u8861\u603b\u9ad8\u5ea6\u7684\u539f\u7406\u3002<strong>\u53ea\u6709\u642d\u5efa\u4e86\u8fd9\u4e9b\u65b9\u6cd5\u4e4b\u540e\u624d\u80fd\u8fdb\u884c\u8c03\u7528<\/strong>\uff08\u56fe\u7247\u8f6c\u81ea<a href=\"http:\/\/www.cnblogs.com\/bbvi\/p\/5104916.html\">\u67d0\u4e2a\u4e8c\u53c9\u6811\u751f\u6210\u5668<\/a>\uff09<\/p>\n<p>\u5728\u9762\u5bf9\u4e0d\u5e73\u8861\u7684\u6811\u65f6\uff0c\u53ef\u4ee5\u901a\u8fc7\u65cb\u8f6c\u64cd\u4f5c\u6765\u66f4\u6539\u6839\u8282\u70b9\u548c\u53f6\u5b50\u8282\u70b9\u7684\u5173\u7cfb\uff0c\u4ece\u800c\u4f7f\u8bbf\u95ee\u6839\u8282\u70b9\u65f6\uff0c\u4e8c\u53c9\u6811\u662f\u5e73\u8861\u7684\u3002<\/p>\n<p>\u6839\u636e\u4e0d\u540c\u7684\u5931\u8861\u7c7b\u578b\uff0c\u53ef\u4ee5\u5206\u4e3aLL,LR,RL,RR\u56db\u79cd\u3002\u867d\u7136\u6570\u5b66\u4e66\u955c\u50cf\u5bf9\u79f0\u7684\u95ee\u9898\u53ef\u4ee5\u5f52\u7c7b\u4e3a\u4e00\u79cd\uff0c\u4f46\u5f88\u62b1\u6b49\uff0c\u8fd9\u91cc\u4e0d\u6b22\u8fce\u6570\u5b66(\u624b\u52a8\u72d7\u5934)\u3002<\/p>\n<h2><strong>LL\u578b\uff1a<\/strong><\/h2>\n<pre>\u9488\u5bf9LL\u578b\u5931\u8861\u95ee\u9898\uff0c\u6211\u4eec\u5148\u770b\u56fe\u8bf4\u8bdd\uff1a\r\n<img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-217 size-medium\" src=\"http:\/\/fankasy.xyz\/wp-content\/uploads\/2019\/03\/bca77b0b2121fb8195b37567675b8fe-300x230.png\" alt=\"\" width=\"300\" height=\"230\" \/>\u8fd9\u91cc\u53ef\u4ee5\u770b\u51fa\uff0c1\u7684\u5b58\u5728\u9020\u6210\u4e86\u8282\u70b95\u7684\u6df1\u5ea6\u8fbe\u5230\u4e863\uff0c\u4f7f\u4e8c\u53c9\u6811\u53d1\u751f\u4e86\u5931\u8861\u3002\u5b83\u7684\u8bc6\u522b\u7279\u5f81\u662f<span style=\"color: #993366;\"><strong>\u201c\u5931\u8861\u8282\u70b9\u7684<span style=\"text-decoration: underline;\">\u5de6\u5b69\u5b50<\/span>\u7684<span style=\"text-decoration: underline;\">\u5de6\u5b69\u5b50<\/span>\u591a\u4e86\u4e00\u4e2a\u5b69\u5b50\u201d <\/strong><\/span>\u3002\r\n\u800c\u4fee\u6b63\u7b56\u7565\u7528\u81ea\u7136\u8bed\u8a00\u63cf\u8ff0\uff0c\u5c31\u662f<span style=\"color: #993366;\"><strong>\u201c\u5931\u8861\u8282\u70b9\u7684\u5de6\u5b69\u5b50\u7684\u53f3\u5b69\u5b50\u94fe\u63a5\u81f3\u5931\u8861\u8282\u70b9\uff0c\u5e76\u5c06\u8fd9\u4e2a\u5de6\u5b69\u5b50\u653e\u7f6e\u4e8e\u539f\u5931\u8861\u8282\u70b9\u539f\u672c\u7684\u4f4d\u7f6e\u201d<\/strong><\/span>\r\n\u62ff\u56fe\u91cc\u7684\u5e8f\u53f7\u6765\u8bf4\uff0c\u5c31\u662f\u5c064\u53f7\u94fe\u63a5\u81f35\u53f7\uff0c\u5e76\u628a3\u53f7\u91cd\u7f6e\u4e3a\u6839\u8282\u70b9\u3002\r\n<img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-218 size-full\" src=\"http:\/\/fankasy.xyz\/wp-content\/uploads\/2019\/03\/d91ed73f9a0aa36b3530664570735dc.png\" alt=\"\" width=\"180\" height=\"180\" srcset=\"http:\/\/fankasy.xyz\/wp-content\/uploads\/2019\/03\/d91ed73f9a0aa36b3530664570735dc.png 180w, http:\/\/fankasy.xyz\/wp-content\/uploads\/2019\/03\/d91ed73f9a0aa36b3530664570735dc-150x150.png 150w\" sizes=\"(max-width: 180px) 100vw, 180px\" \/>\r\n\u4e0b\u9762\u7ed9\u51fa\u4fee\u6b63\u7b56\u7565\u7684\u4ee3\u7801\u5b9e\u73b0\uff1a<\/pre>\n<pre><span style=\"color: #339966;\">\/*LL\u65cb\u8f6c\uff0c\r\n  \u53c2\u6570\uff1a \r\n  root \uff1a \u5931\u8861AVL\u6811\u6839\u8282\u70b9(\u4e0d\u4e00\u5b9a\u662f\u6811\u7684\u6839\u8282\u70b9)\r\n  \u8fd4\u56de\u503c \uff1a \u8c03\u6574\u540e\u7684AVL\u6811\u6839\u8282\u70b9\r\n*\/\r\n<span style=\"color: #000000;\">AVLNode* LLRotate(AVLNode* root)<\/span>\r\n<span style=\"color: #000000;\">{\r\n  AVLNode* lchild=root-&gt;left;\r\n  root-&gt;lchild=lchild-&gt;right;\r\n  lchild-&gt;right=root;\r\n\r\n  <\/span><\/span>lchild-&gt;height = max(height(lchild-&gt;left), height(root)) + 1;\r\n  root-&gt;height = max(height(root-&gt;left), height(root-&gt;right)) + 1;\r\n<span style=\"color: #008000;\">  \/\/height\u51fd\u6570\u7528\u6765\u83b7\u53d6\u8282\u70b9\u7684\u9ad8\u5ea6\uff0c\u800c+1\u662f\u56e0\u4e3a\u6211\u4eec\u521a\u628a\u4e00\u4e2a\u8282\u70b9\u65cb\u8f6c\u5230\u539froot\u7684\u5934\u4e0a<\/span>\r\n  <span style=\"color: #339966;\"><span style=\"color: #000000;\">return lchild;\r\n}<\/span>\r\n\r\n<\/span><\/pre>\n<h2>RR\u578b\uff1a<\/h2>\n<pre>\u5bf9\u4e8eRR\u578b\uff0c\u5927\u90e8\u5206\u7684\u5185\u5bb9\u548cLL\u578b\u4e00\u6837\uff0c\u66ff\u6362\u4e00\u4e9b\u5173\u952e\u5b57\u5373\u53ef\u3002\r\n<span style=\"color: #008000;\">\/*LL\u65cb\u8f6c\uff0c<\/span>\r\n<span style=\"color: #008000;\">  \u53c2\u6570\uff1a root \uff1a \u5931\u8861AVL\u6811\u6839\u8282\u70b9(\u4e0d\u4e00\u5b9a\u662f\u6811\u7684\u6839\u8282\u70b9)<\/span>\r\n<span style=\"color: #008000;\">  \u8fd4\u56de\u503c \uff1a \u8c03\u6574\u540e\u7684AVL\u6811\u6839\u8282\u70b9<\/span>\r\n<span style=\"color: #008000;\">*\/<\/span>\r\nAVLNode* RRRotate(AVLNode* root)\r\n{\r\n  AVLNode* rchild=root-&gt;right;\r\n  root-&gt;right=rchild-&gt;left;\r\n  rchild-&gt;left=root;\r\n\r\n  rchild-&gt;height = max(height(rchild-&gt;left), height(root)) + 1;\r\n  root-&gt;height = max(height(root-&gt;right), height(root-&gt;left)) + 1;\r\n \r\n  return lchild;\r\n}\r\n<\/pre>\n<h2>RL\u578b\u4e0eLR\u578b\uff1a<\/h2>\n<pre>\u8fd9\u4e9b\u95ee\u9898\u9700\u8981\u65cb\u8f6c\u4e24\u6b21\u624d\u80fd\u591f\u89e3\u51b3\uff0c\u76f8\u5bf9\u800c\u8a00\u9ebb\u70e6\u4e00\u4e9b\u3002<img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-221 size-medium\" src=\"http:\/\/fankasy.xyz\/wp-content\/uploads\/2019\/03\/2f5a5f86a7aa3289f138177b2751fbf-300x230.png\" alt=\"\" width=\"300\" height=\"230\" \/>\r\n\r\n\u5982\u4e0a\u56fe\u6240\u793a\uff0c\u5148\u5bf9\u6700\u4f4e\u5931\u8861\u6839\u7ed3\u70b9\u7684\u5de6\u5b69\u5b50\uff08\u7ed3\u70b92\uff09\u8fdb\u884cRR\u65cb\u8f6c\uff0c\u518d\u5bf9\u6700\u4f4e\u5931\u8861\u6839\u7ed3\u70b9\uff08\u7ed3\u70b95\uff09\u8fdb\u884cLL\u65cb\u8f6c\u3002\u4e0b\u56fe\u6f14\u793a\u4e86\u8c03\u6574\u8fc7\u7a0b\u3002\r\n\r\n<img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-222 size-full\" src=\"http:\/\/fankasy.xyz\/wp-content\/uploads\/2019\/03\/c6b8406170d895d1e4a09a976c1db11.png\" alt=\"\" width=\"772\" height=\"279\" srcset=\"http:\/\/fankasy.xyz\/wp-content\/uploads\/2019\/03\/c6b8406170d895d1e4a09a976c1db11.png 772w, http:\/\/fankasy.xyz\/wp-content\/uploads\/2019\/03\/c6b8406170d895d1e4a09a976c1db11-300x108.png 300w, http:\/\/fankasy.xyz\/wp-content\/uploads\/2019\/03\/c6b8406170d895d1e4a09a976c1db11-768x278.png 768w\" sizes=\"(max-width: 772px) 100vw, 772px\" \/>\u800c\u7531\u4e8e\u5df2\u7ecf\u6784\u5efa\u4e86LL\u548cRR\u65cb\u8f6c\u6240\u7528\u5230\u7684\u51fd\u6570\uff0c\u8fdb\u884c\u7b80\u5355\u62fc\u5408\u4e4b\u540e\u5c31\u53ef\u4ee5\u5f97\u5230LL\u548cLR\u7684\u4ee3\u7801\u3002\r\nAVLNode* RLRotate(AVLNode* root)\r\n{\r\n   root-&gt;left = RLRotate(root-&gt;left);    <span style=\"color: #008000;\">\/\/\u5148\u5bf9\u5de6\u5b50\u6811RR\u65cb\u8f6c<\/span>\r\n   return LLRotate(root);    <span style=\"color: #008000;\">\/\/\u518d\u5bf9\u6839\u7ed3\u70b9LL\u65cb\u8f6c<\/span>\r\n}\r\n\r\nAVLNode* LRRotate(AVLNode* root)\r\n{\r\n   root-&gt;right = LLRotate(root-&gt;right); \/\/\u5148\u5bf9\u5de6\u5b50\u6811LL\u65cb\u8f6c\r\n   return RRRotate(root); \/\/\u518d\u5bf9\u6839\u7ed3\u70b9RR\u65cb\u8f6c\r\n}\r\n<\/pre>\n<p>\u770b\u5230\u8fd9\u91cc\u5e94\u8be5\u4e5f\u7d2f\u5f97\u8981\u6b7b\u4e86\u5427&#8230;\u3002\u90a3\u4e48\u4e0b\u9762\u5c31\u8d34\u51fa\u63d2\u5165\u8282\u70b9\u7684\u4ee3\u7801\u3002\u5728\u6b64\u5904\u6307\u51fa\uff0c\u4e0e\u4e00\u822c\u7684\u4e8c\u53c9\u6811\u63d2\u5165\u4ee3\u7801\u60df\u4e00\u4e0d\u540c\u4e4b\u5904\u5728\u4e8e\u63d2\u5165\u540e\u4f1a\u68c0\u67e5\u6709\u6ca1\u6709\u51fa\u73b0\u4e0d\u5e73\u8861\u7684\u73b0\u8c61\u3002<\/p>\n<pre>AVLNode* AVLInsert(AVLNode* root, int key)\r\n{\r\n    if (root == NULL)\r\n        AVLNode root ={0,key,NULL,NULL};\r\n    else if (key &lt; root-&gt;key)    <span style=\"color: #008000;\">\/\/\u4f5c\u4e3a\u5de6\u5b50\u6811\u63d2\u5165<\/span>\r\n    {\r\n        root-&gt;left = AVLInsert(root-&gt;left, key);\r\n        if (height(root-&gt;left) - height(root-&gt;right) == 2)    <span style=\"color: #008000;\">\/\/\u63d2\u5165\u5bfc\u81f4\u4e8c\u53c9\u6811\u5931\u8861<\/span>\r\n        {\r\n            if (key &lt; root-&gt;left-&gt;key)\r\n                root = leftLeftRotate(root);\r\n            else root = leftRightRotate(root);\r\n        }\r\n    }\r\n    else if (key&gt;root-&gt;key)        <span style=\"color: #008000;\">\/\/\u4f5c\u4e3a\u53f3\u5b50\u6811\u63d2\u5165<\/span>\r\n    {\r\n        root-&gt;right = insert(root-&gt;right, key);\r\n        if (height(root-&gt;right) - height(root-&gt;left) == 2)   \r\n        {\r\n            if (key &gt; root-&gt;right-&gt;key)\r\n                root = rightRightRotate(root);\r\n            else root = rightLeftRotate(root);\r\n        }\r\n    }\r\n    root-&gt;height = max(height(root-&gt;left), height(root-&gt;right)) + 1;\r\n    return root;\r\n}\r\n\r\n<\/pre>\n<p>\u7d2f\u6b7b\u6211\u4e86,\u8fc7\u4e24\u5929\u518d\u8865\u5220\u9664\u7684\u4ee3\u7801<\/p>\n<p>4.2\uff1a\u8865\u4e2a\u9524\u5b50\uff0c\u8282\u70b9\u5220\u4e86\u518d\u68c0\u67e5\u4e00\u904d\u5e73\u8861\u6027\u5c31\u5b8c\u4e86<br \/>\n4.11\uff1a\u6211\u9519\u4e86\uff0c\u8fd9\u91cc\u5934\u597d\u591a\u4e1c\u897f<\/p>\n<h2>\u8282\u70b9\u5220\u9664<\/h2>\n<p>\u5bf9\u4e8e\u8282\u70b9\u5220\u9664\uff0c\u6709\u5f88\u591a\u79cd\u60c5\u51b5\u9700\u8981\u5206\u6790\u3002<\/p>\n<pre>0.\u6839\u8282\u70b9\r\n1.\u6ca1\u6709\u5de6\u53f3\u5b69\u5b50\r\n2.\u6709\u5de6\u53f3\u5b69\u5b50\r\n3.\u53ea\u6709\u5de6\u5b69\u5b50\r\n4.\u53ea\u6709\u53f3\u5b69\u5b50<\/pre>\n<h3>\u5220\u9664\u8282\u70b9\u6709\u4e24\u4e2a\u513f\u5b50\uff1a<\/h3>\n<p>\u4e00\u822c\u7684\u5220\u9664\u7b56\u7565\u662f\u7528\u5176\u53f3\u5b50\u6811\u7684\u6700\u5c0f\u7684\u6570\u636e\u4ee3\u66ff\u8be5\u8282\u70b9\u7684\u6570\u636e\uff0c\u5e76\u9012\u5f52\u5730\u5220\u9664\u90a3\u4e2a\u53f3\u5b50\u6811\u7684\u6700\u5c0f\u8282\u70b9\u3002\u5982\u679c\u5220\u9664\u8282\u70b92\uff0c\u90a3\u4e48\u5148\u7528\u5176\u53f3\u5b50\u6811\u7684\u6700\u5c0f\u6570\u636e\u8282\u70b93\u4ee3\u66ff\u8be5\u8282\u70b9\u7684\u6570\u636e\uff0c\u7136\u540e\u518d\u9012\u5f52\u5730\u5220\u9664\u8282\u70b93\u3002\u6570\u636e\u7ed3\u6784\u7684\u5404\u4e2a\u6570\u636e\u8282\u70b9\u4ec5\u6570\u503c\u4e0d\u540c\uff0c\u4fee\u6539\u6570\u636e\u5176\u5b9e\u5c31\u662f\u4fee\u6539\u6570\u636e\u8282\u70b9\u3002<\/p>\n<pre><span style=\"color: #339966;\">\/*<\/span>\r\n<span style=\"color: #339966;\">*              6                             6                       6<\/span>\r\n<span style=\"color: #339966;\">*             \/ \\                           \/ \\                     \/ \\ <\/span>\r\n<span style=\"color: #339966;\">*            2   8                         3   8                   3   8<\/span>\r\n<span style=\"color: #339966;\">*           \/ \\   \\        --&gt;            \/ \\   \\        --&gt;      \/ \\   \\<\/span>\r\n<span style=\"color: #339966;\">*          1   4   10                    1   4   10              1   4   10<\/span>\r\n<span style=\"color: #339966;\">*             \/                             \/<\/span>\r\n<span style=\"color: #339966;\">*            3                             3<\/span>\r\n<span style=\"color: #339966;\">*\/<\/span><\/pre>\n<p align=\"left\">\u6839\u636e\u4e8c\u53c9\u67e5\u627e\u6811\u7684\u7279\u6027\uff0c\u53f3\u5b50\u6811\u7684\u6700\u5c0f\u6570\u636e\u8282\u70b9\u5927\u4e8e\u8be5\u8282\u70b9\u7684\u6240\u6709\u5de6\u5b50\u6811\u8282\u70b9\uff0c\u5c0f\u4e8e\u8be5\u8282\u70b9\u7684\u53f3\u5b50\u6811\u8282\u70b9\u5f53\u4e2d\u9664\u4e86\u6700\u5c0f\u8282\u70b9\u7684\u6240\u6709\u8282\u70b9\uff0c\u8fd9\u6837\u7528\u8fd9\u4e2a\u53f3\u5b50\u6811\u6700\u5c0f\u6570\u636e\u8282\u70b9\u4ee3\u66ff\u8be5\u8282\u70b9\uff0c\u90a3\u4e48\u64cd\u4f5c\u4e4b\u540e\u7684\u8fd8\u662f\u4e8c\u53c9\u67e5\u627e\u6811\u3002<\/p>\n<h3 align=\"left\">\u5220\u9664\u8282\u70b9\u53ea\u6709\u5de6\u5b69\u5b50\uff1a<\/h3>\n<p>\u5206\u4e24\u79cd\u60c5\u51b5<\/p>\n<p>1.\u5de6\u5b69\u5b50\u662f\u53f6\u5b50\u8282\u70b9<\/p>\n<p>\u8fd9\u79cd\u60c5\u51b5\u5f88\u597d\u529e\uff0c\u7528\u5de6\u5b69\u5b50\u7684\u503c\u66ff\u6362\u5f53\u524d\u8282\u70b9\uff0c\u968f\u540e\u5220\u9664\u5de6\u5b69\u5b50\u8282\u70b9\u3002<\/p>\n<p>2.\u5de6\u5b69\u5b50\u4e0d\u662f\u53f6\u5b50\u8282\u70b9<\/p>\n<p>\u6b64\u65f6\u9700\u8981\u627e\u5230\u5de6\u5b69\u5b50\u7684\u6240\u6709\u5b50\u8282\u70b9\u4e2d\uff0c\u6700\u5927\u7684\u503c\u3002\u539f\u56e0\u540c\u4e0a\u3002\u968f\u540e\u518d\u4ee5\u8fd9\u4e2a\u6b21\u5927\u7684\u8282\u70b9\u9012\u5f52\u8fdb\u884c\u5220\u9664\u3002<\/p>\n<pre>\/*\r\n*             6                             4                       4                 4\r\n*            \/                             \/                       \/                 \/\r\n*           2                             2                       2                 2\r\n*          \/ \\            --&gt;            \/ \\            --&gt;      \/ \\     --&gt;       \/ \\\r\n*         1   4                         1   4                   1   3             1   3\r\n*            \/                             \/                       \/\r\n*           3                             3                       3\r\n*\/\r\n\r\n<\/pre>\n<h3>\u5220\u9664\u8282\u70b9\u53ea\u6709\u53f3\u5b69\u5b50\uff1a<\/h3>\n<p>\u540c\u4e0a\uff0c\u5982\u679c\u53ea\u6709\u4e00\u4e2a\u53f3\u5b69\u5b50\uff0c\u66ff\u6362\u5e76\u5220\u9664\u5373\u53ef\u3002<\/p>\n<p>\u82e5\u4e0d\u662f\uff0c\u627e\u5230\u53f3\u5b69\u5b50\u7684\u5b50\u8282\u70b9\u91cc\u6700\u5c0f\u7684\u66ff\u6362\uff0c\u7136\u540e\u9012\u5f52\u5220\u9664&#8230;<\/p>\n<pre>\/*\r\n*              6                             6                       6                 \r\n*             \/                             \/                       \/                 \r\n*            2                             3                       3                  \r\n*             \\            --&gt;              \\            --&gt;        \\     \r\n*              4                             4                       4            \r\n*             \/                             \/                        \r\n*            3                             3                        \r\n*\/\r\n\r\n<\/pre>\n<p>\u4ece\u4e0a\u9762\u5206\u6790\u53ef\u4ee5\u770b\u51fa\uff0c\u5220\u9664\u64cd\u4f5c\u662f\u7528\u6811\u4e2d\u7684\u67d0\u4e2a\u6570\u636e\u4ee3\u66ff\u5220\u9664\u8282\u70b9\u952e\u503c\uff0c\u5b9e\u9645\u4e0a\u5220\u9664\u7684\u90fd\u662f\u53f6\u5b50\u8282\u70b9\uff0c\u636e\u6b64\u6211\u4eec\u53ef\u4ee5\u628a\u6240\u6709\u60c5\u51b5\u7528\u4e00\u4e2a\u7a0b\u5e8f\u89e3\u51b3\u3002<\/p>\n<h3>\u5220\u9664\u4ee3\u7801:<\/h3>\n<pre>AVLNode* AVLdel(AVLNode* root, int key)\r\n{\r\n   if(root==NULL)\r\n        return NULL;\r\n   \r\n   else if(root-&gt;key &gt; key)\/\/\u5728\u5de6\u5b50\u6811\u4e2d\r\n      {\r\n        root-&gt;lchild = AVLdel(root-&gt;lchild, key); \r\n        if (height(root-&gt;left) - height(root-&gt;right) == 2) \/\/\u63d2\u5165\u5bfc\u81f4\u4e8c\u53c9\u6811\u5931\u8861\r\n            { \r\n              if (key &lt; root-&gt;left-&gt;key) \r\n                 root = leftLeftRotate(root); \r\n              else root = leftRightRotate(root); \r\n            }\r\n      }\r\n   else if(root-&gt;key &lt; key)\/\/\u5728\u53f3\u5b50\u6811\u4e2d\r\n      {\r\n        root-&gt;lchild = AVLdel(root-&gt;rchild, key); \r\n        if (height(root-&gt;left) - height(root-&gt;right) == 2) \/\/\u63d2\u5165\u5bfc\u81f4\u4e8c\u53c9\u6811\u5931\u8861\r\n            { \r\n              if (key &lt; root-&gt;left-&gt;key) \r\n                 root = leftLeftRotate(root); \r\n              else root = leftRightRotate(root); \r\n            }\r\n      }\r\n   \r\n   else if(root-&gt;key == key)\r\n     {\r\n         if(root-&gt;lchild &amp;&amp; root-&gt;rchild)\/\/\u5de6\u53f3\u5b69\u5b50\u90fd\u5b58\u5728\r\n           {\r\n              if (HEIGHT(root->lchild) > HEIGHT(root->rchild))\r\n              {\r\n                \/\/ \u5982\u679croot\u7684\u5de6\u5b50\u6811\u6bd4\u53f3\u5b50\u6811\u9ad8\uff1b\r\n                \/\/ \u5219(01)\u627e\u51faroot\u7684\u5de6\u5b50\u6811\u4e2d\u7684\u6700\u5927\u8282\u70b9\r\n                \/\/   AVLMax\u51fd\u6570\u5c31\u662f\u5e72\u8fd9\u4e2a\u7684\uff0c\u522b\u95ee\u600e\u4e48\u5e72\r\n                \/\/   (02)\u5c06\u8be5\u6700\u5927\u8282\u70b9\u7684\u503c\u8d4b\u503c\u7ed9root\u3002\r\n                \/\/   (03)\u5220\u9664\u8be5\u6700\u5927\u8282\u70b9\u3002\r\n                \/\/ \u8fd9\u7c7b\u4f3c\u4e8e\u7528\"root\u7684\u5de6\u5b50\u6811\u4e2d\u6700\u5927\u8282\u70b9\"\u505a\"root\"\u7684\u66ff\u8eab\uff1b\r\n                \/\/ \u91c7\u7528\u8fd9\u79cd\u65b9\u5f0f\u7684\u597d\u5904\u662f\uff1a\u5220\u9664\"root\u7684\u5de6\u5b50\u6811\u4e2d\u6700\u5927\u8282\u70b9\"\u4e4b\u540e\uff0cAVL\u6811\u4ecd\u7136\u662f\u5e73\u8861\u7684\u3002\r\n                AVLNode *max = AVLMax(root->lchild);\r\n                root->key = max->key;\r\n                root->lchild = AVLdel(root->lchild, max);\r\n              }\r\n              else\r\n              {\r\n                \/\/ \u5982\u679croot\u7684\u5de6\u5b50\u6811\u4e0d\u6bd4\u53f3\u5b50\u6811\u9ad8(\u5373\u5b83\u4eec\u76f8\u7b49\uff0c\u6216\u53f3\u5b50\u6811\u6bd4\u5de6\u5b50\u6811\u9ad81)\r\n                \/\/ \u5219(01)\u627e\u51faroot\u7684\u53f3\u5b50\u6811\u4e2d\u7684\u6700\u5c0f\u8282\u70b9\r\n                \/\/   (02)\u5c06\u8be5\u6700\u5c0f\u8282\u70b9\u7684\u503c\u8d4b\u503c\u7ed9root\u3002\r\n                \/\/   (03)\u5220\u9664\u8be5\u6700\u5c0f\u8282\u70b9\u3002\r\n                \/\/ \u8fd9\u7c7b\u4f3c\u4e8e\u7528\"root\u7684\u53f3\u5b50\u6811\u4e2d\u6700\u5c0f\u8282\u70b9\"\u505a\"root\"\u7684\u66ff\u8eab\uff1b\r\n                \/\/ \u91c7\u7528\u8fd9\u79cd\u65b9\u5f0f\u7684\u597d\u5904\u662f\uff1a\u5220\u9664\"root\u7684\u53f3\u5b50\u6811\u4e2d\u6700\u5c0f\u8282\u70b9\"\u4e4b\u540e\uff0cAVL\u6811\u4ecd\u7136\u662f\u5e73\u8861\u7684\u3002\r\n                AVLNode *min = AVLMin(root->rchild);\r\n                root->key = min->key;\r\n                root->rchild = AVLdel(root->rchild, min);\r\n              }\r\n     }\r\n   else \/\/\u90fd\u4e0d\u662f\uff0c\u90a3\u6ca1\u6709\u8fd9\u4e2a\u8282\u70b9\uff0c\u628a\u7528\u6237\u9a82\u4e00\u987f\r\n      {\r\n          AVLNode *tmp = root;\r\n          root = root->lchild ? root->lchild : root->rchild;\r\n          free(tmp);\r\n      }\r\n\r\n  return root;\r\n\r\n}<\/pre>\n<p>\u53c2\u8003\u6587\u732e\uff1ahttps:\/\/www.cnblogs.com\/skywang12345\/p\/3576969.html<br \/>\n<del datetime=\"2019-04-11T11:20:30+00:00\">\u9690\u5f62\u773c\u955c\u662f\u4f1f\u5927\u7684\u53d1\u660e<\/del><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e8c\u53c9\u641c\u7d22\u6811\u88ab\u63d0\u51fa\u540e\u4e0d\u5c31\uff0c\u5c31\u6709\u4eba\u53d1\u73b0\u4e86\u4e00\u4e2a\u5173\u952e\u95ee\u9898\uff1a\u5f53\u6570\u636e\u65e0\u610f\u6216\u8005\u6709\u610f\u88ab\u6709\u5e8f\u8f93\u5165\u65f6\uff0c\u4e8c\u53c9\u6811\u7684\u6bcf\u4e00\u4e2a\u8282\u70b9\u90fd\u5c06\u53ea\u6709\u4e00 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[5,10],"tags":[],"_links":{"self":[{"href":"http:\/\/fankasy.xyz\/index.php\/wp-json\/wp\/v2\/posts\/215"}],"collection":[{"href":"http:\/\/fankasy.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/fankasy.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/fankasy.xyz\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"http:\/\/fankasy.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=215"}],"version-history":[{"count":0,"href":"http:\/\/fankasy.xyz\/index.php\/wp-json\/wp\/v2\/posts\/215\/revisions"}],"wp:attachment":[{"href":"http:\/\/fankasy.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=215"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/fankasy.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=215"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/fankasy.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}