{"id":1,"date":"2020-02-10T04:35:49","date_gmt":"2020-02-10T04:35:49","guid":{"rendered":"http:\/\/54.153.35.165\/feellikelearning\/?p=1"},"modified":"2020-12-18T01:18:34","modified_gmt":"2020-12-18T01:18:34","slug":"hello-world","status":"publish","type":"post","link":"https:\/\/feellikelearning.com\/index.php\/2020\/02\/10\/hello-world\/","title":{"rendered":"\u7b97\u6cd5\u7ec3\u4e60 Leetcode 222 Count Complete Tree Nodes \u89e3\u6cd5"},"content":{"rendered":"\n<p>\u9898\u76ee\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p><strong>Definition of a complete binary tree from&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/en.wikipedia.org\/wiki\/Binary_tree#Types_of_binary_trees\" target=\"_blank\">Wikipedia<\/a>:<\/strong><br>In a complete binary tree every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. It can have between 1 and 2<sup>h<\/sup>&nbsp;nodes inclusive at the last level h.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><strong>Input:<\/strong> \n    1\n   \/ \\\n  2   3\n \/ \\  \/\n4  5 6\n\n<strong>Output:<\/strong> 6<\/pre>\n\n\n\n<p>\u6700\u7b80\u5355\u7684\u505a\u6cd5\u5c31\u662f\u76f4\u63a5\u904d\u5386\u4e00\u8fb9\uff0c\u4e0d\u7ba1\u662fDFS\u8fd8\u662fBFS\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u662fO(N)\u3002\u4f46\u662f\u8fd9\u6837\u5c31\u6ca1\u5229\u7528\u5230complete binary tree\u7684\u6761\u4ef6\u3002\u4f18\u5316\u7684\u89e3\u6cd5\u5982\u679c\u6ca1\u7ec3\u8fc7\u7684\u8bdd\u5176\u5b9e\u4e0d\u592a\u597d\u60f3\u3002\u8fd9\u9898\u8981\u7684\u5176\u5b9e\u662f\u627e\u5230\u6700\u540e\u4e00\u5c42\u6709\u51e0\u4e2anode\u3002\u800c\u6bcf\u5c42\u7684node\u7684index\u5c31\u662f\u5728[2^h, 2^(h+1)-1]\u533a\u95f4\u4e4b\u5185\u3002\u5982\u679c\u6709\u4e2afunction\u53ef\u4ee5\u544a\u8bc9\u4f60\u67d0\u4e2aindex\u5728\u4e0d\u5728tree\u91cc\uff0c\u90a3\u4e48\u53ef\u4ee5\u5bf9[2^h, 2^(h+1)-1]\u505abinary search\uff0c\u627e\u5230\u5176\u4e2dindex\u6700\u5927\u5e76\u4e14\u5728tree\u91cc\u7684node\u3002Binary tree\u7684\u6700\u540e\u4e00\u5c42\u5927\u6982\u6709N\/2\u4e2anode\uff08\u6bcf\u52a0\u4e00\u5c42\uff0cnode\u6570\u91cf\u7ffb\u500d\uff01\uff09\uff0c\u90a3\u4e48\u9700\u8981\u505aO(lgN)\u6b21search\u3002<\/p>\n\n\n\n<p>\u81f3\u4e8e\u8fd9\u4e2a\u544a\u8bc9\u67d0\u4e2anode\u5728\u4e0d\u5728tree\u91cc\u7684\u51fd\u6570\u53ef\u4ee5\u8fd9\u6837\u5199\uff1a\u5199\u51e0\u4e2a\u4f8b\u5b50\u89c2\u5bdf\u4e00\u4e0b\uff0c\u5982\u679c\u4e00\u4e2anode\u7684index\u662fn, \u6bcf\u4e2anode\u7684parent\u7684index\u90fd\u662ffloor(n\/2)\u3002\u90a3\u4e48\u6211\u4eec\u5c31\u80fd\u628a\u4eceroot\u5230\u8fbe\u76ee\u6807node\u7684path\u627e\u51fa\u6765\uff0c\u6bd4\u5982\u5982\u679c\u76ee\u6807node\u662f5\uff0c\u90a3\u4e48path\u5c31\u662f[5, 2, 1]\uff0c\u5165\u80a1\u76ee\u6807\u662f8\uff0c\u90a3\u4e48path\u5c31\u662f[8, 4, 2, 1]\u3002\u7136\u540e\u4eceroot\uff0c\u4e5f\u5c31\u662f1\u53f7node\u51fa\u53d1\uff0c\u5982\u679c\u6700\u540e\u6211\u4eec\u6309\u7167\u8fd9\u4e2a\u5730\u56fe\u80fd\u8d70\u5230\u76ee\u6807\uff0c\u90a3\u4e48\u8fd9\u4e2anode\u5c31\u5728tree\u91cc\u9762\uff0c\u5426\u5219\u5c31\u4e0d\u5728\u3002\u8fd9\u4e2afunction\u9700\u8981O(lgN)\u65f6\u95f4\u548cO(lgN)\u7a7a\u95f4\u3002<\/p>\n\n\n\n<p>\u6700\u540e\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u8fd9\u6837\u8ba1\u7b97\uff0cO(lgN)\u6b21search\uff0c\u6bcf\u6b21 O(lgN)\u65f6\u95f4\uff0c\u603b\u65f6\u95f4O((lgN)^2)\u3002\u7a7a\u95f4O(lgN)\u7528\u6765\u4fdd\u5b58path\u3002<\/p>\n\n\n\n<p>\u4ee3\u7801\u5982\u4e0b<\/p>\n\n\n\n<p>C++<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>class Solution {\npublic:\n    int countNodes(TreeNode* root) {\n        if (root == NULL) {\n            return 0;\n        }\n        int h = findHeight(root);\n        int i_min = pow(2, h);\n        int i_max = pow(2, h + 1) - 1;\n        int ans = i_min;\n        while(i_min &lt;= i_max) {\n            int m = i_min + (i_max - i_min) \/ 2;\n            if (inTree(root, m)) {\n                ans = m;\n                i_min = m + 1;\n            } else{\n                i_max = m - 1;\n            }\n        }   \n        return ans;\n        \n    }\n    \n    int findHeight(TreeNode* root) {\n        int h = 0;\n        TreeNode* cur = root;\n        while (cur != NULL) {\n            cur = cur-&gt;left;\n            h += 1;\n        }\n        return h - 1;\n    }\n    \n    bool inTree(TreeNode* root, int i) {\n        if (root == NULL || i &lt; 0) {\n            return false;\n        }\n        vector&lt;int&gt; path;\n        int cur = i;\n        while (cur != 0) {\n            path.push_back(cur);\n            cur \/= 2;\n        }\n        TreeNode* curNode = root;\n        for (int j = path.size() - 2; j &gt;= 0; j--) {\n            if (path&#91;j] == path&#91;j + 1] * 2) {\n                curNode = curNode-&gt;left;\n            } else {\n                curNode = curNode-&gt;right;\n            }\n            if (curNode == NULL) {\n                return false;\n            }\n        }\n        return true;\n    }\n};<\/code><\/pre>\n\n\n\n<p><\/p>\n\n\n\n<p>Java<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>class Solution {\n    public int countNodes(TreeNode root) {\n        if (root == null) {\n            return 0;\n        }\n        int h = findHeight(root);\n        int i_min = (int)Math.pow(2, h);\n        int i_max = (int)(Math.pow(2, h + 1) - 1);\n        int ans = i_min;\n        while (i_min &lt;= i_max) {\n            int m = i_min + (i_max - i_min) \/ 2;\n            if (inTree(root, m)) {\n                ans = m;\n                i_min = m + 1;\n            } else{\n                i_max = m - 1;\n            }\n        }   \n        return ans;\n        \n    }\n    \n    public int findHeight(TreeNode root) {\n        int h = 0;\n        TreeNode cur = root;\n        while (cur != null) {\n            cur = cur.left;\n            h += 1;\n        }\n        return h - 1;\n    }\n    \n    public boolean inTree(TreeNode root, int i) {\n        if (root == null || i &lt; 0) {\n            return false;\n        }\n        List&lt;Integer&gt; path = new ArrayList&lt;&gt;();\n        int cur = i;\n        while (cur != 0) {\n            path.add(cur);\n            cur \/= 2;\n        }\n        TreeNode curNode = root;\n        for (int j = path.size() - 2; j &gt;= 0; j--) {\n            if (path.get(j) == path.get(j + 1) * 2) {\n                curNode = curNode.left;\n            } else {\n                curNode = curNode.right;\n            }\n            if (curNode == null) {\n                return false;\n            }\n        }\n        return true;\n    }\n}<\/code><\/pre>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9898\u76ee\u5982\u4e0b\uff1a Definition of a complete binary tree from&nbsp;Wikipedia:In a complete binary tree every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. It can have between 1 and&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/feellikelearning.com\/index.php\/2020\/02\/10\/hello-world\/\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":1043,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false},"categories":[1],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.10 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u7b97\u6cd5\u7ec3\u4e60 Leetcode 222 Count Complete Tree Nodes \u89e3\u6cd5 | Feel Like Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/feellikelearning.com\/index.php\/2020\/02\/10\/hello-world\/?variant=zh-hant\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u7b97\u6cd5\u7ec3\u4e60 Leetcode 222 Count Complete Tree Nodes \u89e3\u6cd5 | Feel Like Learning\" \/>\n<meta property=\"og:description\" content=\"\u9898\u76ee\u5982\u4e0b\uff1a Definition of a complete binary tree from&nbsp;Wikipedia:In a complete binary tree every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. 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