{"id":23852,"date":"2023-12-22T09:12:49","date_gmt":"2023-12-22T01:12:49","guid":{"rendered":"https:\/\/www.silicloud.com\/zh\/blog\/%e5%9c%a8%e4%ba%8c%e5%8f%89%e6%a0%91%e4%b8%ad%e8%bf%9b%e8%a1%8c%e5%b1%82%e6%ac%a1%e9%81%8d%e5%8e%86\/"},"modified":"2025-08-11T00:16:17","modified_gmt":"2025-08-10T16:16:17","slug":"%e5%9c%a8%e4%ba%8c%e5%8f%89%e6%a0%91%e4%b8%ad%e8%bf%9b%e8%a1%8c%e5%b1%82%e6%ac%a1%e9%81%8d%e5%8e%86","status":"publish","type":"post","link":"https:\/\/www.silicloud.com\/zh\/blog\/%e5%9c%a8%e4%ba%8c%e5%8f%89%e6%a0%91%e4%b8%ad%e8%bf%9b%e8%a1%8c%e5%b1%82%e6%ac%a1%e9%81%8d%e5%8e%86\/","title":{"rendered":"\u5728\u4e8c\u53c9\u6811\u4e2d\u8fdb\u884c\u5c42\u6b21\u904d\u5386"},"content":{"rendered":"<p>\u5c42\u6b21\u904d\u5386\u662f\u4e00\u79cd\u6a2a\u5411\u904d\u5386\u4e8c\u53c9\u6811\u7684\u65b9\u6cd5\u4e4b\u4e00\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u5982\u4f55\u5728C\/C++\u4e2d\u5b9e\u73b0\u8fd9\u4e2a\u7b97\u6cd5\u3002<\/p>\n<p>\u4f46\u5728\u6b64\u4e4b\u524d\uff0c\u8ba9\u6211\u4eec\u5148\u68b3\u7406\u4e00\u4e0b\u6211\u4eec\u7684\u6982\u5ff5\u3002<\/p>\n<hr>\n<\/hr>\n<h2>\u6784\u5efa\u6982\u5ff5<\/p>\n<p>\u4e8c\u53c9\u6811\u662f\u4e00\u79cd\u6570\u636e\u7ed3\u6784\uff0c\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u3002\u6700\u4e0a\u65b9\u7684\u8282\u70b9\u88ab\u79f0\u4e3a\u6839\u8282\u70b9\u3002<\/p>\n<div>\n                            <img decoding=\"async\" src=\"https:\/\/cdn.silicloud.com\/blog-img\/blog\/img\/65647b1fa4b2f92e6c72bf6d\/5-0.png\" class='post-images' alt=\"Binary Tree\" title=\"\"><\/p>\n<p>\u904d\u5386\u4e8c\u53c9\u6811\u7684\u5e38\u89c1\u65b9\u5f0f\u6709\u56db\u79cd\uff0c\u5206\u522b\u662f\uff1a<\/p>\n<ul class=\"post-ul\">\n<li>In order Traversal<\/li>\n<li>Pre Order Traversal<\/li>\n<li>Post Order Traversal<\/li>\n<li>Level Order Traversal<\/li>\n<\/ul>\n<p>\u8ba9\u6211\u4eec\u6765\u4e86\u89e3\u4e8c\u53c9\u6811\u4e2d\u7684\u5c42\u7ea7\u610f\u5473\u7740\u4ec0\u4e48\u3002<\/p>\n<p>\u4e00\u4e2a\u7ea7\u522b\u662f\u6811\u4e2d\u4e0e\u7ed9\u5b9a\u8282\u70b9\u5bf9\u5e94\u7684\u7236\u8282\u70b9\u7684\u6570\u91cf\u3002\u57fa\u672c\u4e0a\u5c31\u662f\u4ece\u8be5\u8282\u70b9\u5230\u6839\u8282\u70b9\u7684\u7956\u5148\u6570\u91cf\u3002<\/p>\n<p>\u6240\u4ee5\uff0c\u5bf9\u4e8e\u6839\u8282\u70b9\uff08\u6700\u9876\u5c42\u8282\u70b9\uff09\u800c\u8a00\uff0c\u5b83\u7684\u5c42\u7ea7\u662f0\uff0c\u56e0\u4e3a\u5b83\u6ca1\u6709\u7236\u8282\u70b9\u3002\u5982\u679c\u5b83\u6709\u5b50\u8282\u70b9\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u5c42\u7ea7\u90fd\u4f1a\u662f1\uff0c\u56e0\u4e3a\u5728\u6839\u8282\u70b9\u4e4b\u524d\u5b83\u4eec\u53ea\u6709\u4e00\u4e2a\u7956\u5148\uff0c\u5373\u6839\u8282\u70b9\u672c\u8eab\u3002<\/p>\n<div>\n                            <img decoding=\"async\" src=\"https:\/\/cdn.silicloud.com\/blog-img\/blog\/img\/65647b1fa4b2f92e6c72bf6d\/11-0.png\" class='post-images' alt=\"Binary Tree Level\" title=\"\"><\/p>\n<p>\u6211\u4eec\u8fd8\u9700\u8981\u7406\u89e3\u4e8c\u53c9\u6811\u4e2d\u7684\u9ad8\u5ea6\u6982\u5ff5\u3002\u8fd9\u5176\u5b9e\u5c31\u662f\u4ece\u6839\u8282\u70b9\u5230\u6811\u4e2d\u6700\u6df1\u8282\u70b9\u7684\u8def\u5f84\u957f\u5ea6\u3002<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9ad8\u5ea6\u5c06\u662f\u4ece\u6700\u6df1\u53f6\u8282\u70b9\uff0840\u621650\uff0c\u56e0\u4e3a\u5b83\u4eec\u5177\u6709\u6700\u5927\u5c42\u7ea7\uff09\u5230\u6839\u7684\u957f\u5ea6\u3002\u56e0\u6b64\uff0c\u6811\u7684\u9ad8\u5ea6\u4e3a2\u3002<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u638c\u63e1\u4e86\u6982\u5ff5\uff0c\u8ba9\u6211\u4eec\u6765\u4e86\u89e3\u5982\u4f55\u5b9e\u65bd\u5c42\u5e8f\u904d\u5386\u3002<\/p>\n<hr>\n<\/hr>\n<h2>\u5c42\u6b21\u904d\u5386<\/p>\n<p>\u5c42\u6b21\u904d\u5386\u662f\u4e00\u79cd\u603b\u662f\u6839\u636e\u6811\u7684\u5c42\u7ea7\u8fdb\u884c\u904d\u5386\u7684\u65b9\u6cd5\u3002<\/p>\n<p>\u6240\u4ee5\uff0c\u8fd9\u4e2a\u904d\u5386\u9996\u5148\u904d\u5386\u4e0eLevel 0\u76f8\u5bf9\u5e94\u7684\u8282\u70b9\uff0c\u7136\u540e\u662fLevel 1\uff0c\u4f9d\u6b64\u7c7b\u63a8\uff0c\u4ece\u6839\u8282\u70b9\u5f00\u59cb\u3002<\/p>\n<p>\u5728\u4e0a\u9762\u7684\u4e8c\u53c9\u6811\u4f8b\u5b50\u4e2d\uff0c\u5c42\u5e8f\u904d\u5386\u7684\u987a\u5e8f\u5c06\u4f1a\u662f\uff1a<\/p>\n<p>\uff08\u8d77\u59cb\u503c\uff0910 &#8211; > 20 -> 30 -> 40 -> 50<\/p>\n<p>\u4e3a\u4e86\u505a\u5230\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u9700\u8981\u505a\u4e24\u4ef6\u4e8b\u60c5\u3002<\/p>\n<ol>\u6211\u4eec\u9996\u5148\u5fc5\u987b\u627e\u51fa\u8fd9\u68f5\u6811\u7684\u9ad8\u5ea6\u3002<br \/>\n\u6211\u4eec\u9700\u8981\u627e\u5230\u4e00\u79cd\u65b9\u6cd5\u6765\u6253\u5370\u6bcf\u4e2a\u5c42\u7ea7\u5bf9\u5e94\u7684\u8282\u70b9\u3002<\/ol>\n<h3>\u627e\u5230\u6811\u7684\u9ad8\u5ea6<\/p>\n<p>\u9996\u5148\u6211\u4eec\u4f1a\u627e\u5230\u6811\u7684\u9ad8\u5ea6\u3002\u8981\u505a\u5230\u8fd9\u4e00\u70b9\uff0c\u903b\u8f91\u5f88\u7b80\u5355\u3002<\/p>\n<p>\u7531\u4e8e\u6811\u7684\u9ad8\u5ea6\u88ab\u5b9a\u4e49\u4e3a\u4ece\u6839\u8282\u70b9\u5230\u53f6\u5b50\u8282\u70b9\u7684\u6700\u957f\u8def\u5f84\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u9012\u5f52\u5730\u8ba1\u7b97\u5de6\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\uff0c\u5e76\u627e\u5230\u5b50\u6811\u4e2d\u7684\u6700\u5927\u9ad8\u5ea6\u3002\u6811\u7684\u9ad8\u5ea6\u5c06\u7b80\u5355\u5730\u7b49\u4e8e\u5b50\u6811\u7684\u9ad8\u5ea6\u52a01\u3002<\/p>\n<p>C-\u98ce\u683c\u7684\u4f2a\u4ee3\u7801\uff1a<\/p>\n<pre class=\"post-pre\"><code><span class=\"token comment\">\/\/ Find height of a tree, defined by the root node<\/span>\r\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">tree_height<\/span><span class=\"token punctuation\">(<\/span>Node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>root <span class=\"token operator\">==<\/span> <span class=\"token constant\">NULL<\/span><span class=\"token punctuation\">)<\/span> \r\n        <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">else<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token comment\">\/\/ Find the height of left, right subtrees<\/span>\r\n        left_height <span class=\"token operator\">=<\/span> <span class=\"token function\">tree_height<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token operator\">-&gt;<\/span>left<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n        right_height <span class=\"token operator\">=<\/span> <span class=\"token function\">tree_height<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token operator\">-&gt;<\/span>right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n        \r\n        <span class=\"token comment\">\/\/ Find max(subtree_height) + 1 to get the height of the tree<\/span>\r\n        <span class=\"token keyword\">return<\/span> <span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>left_height<span class=\"token punctuation\">,<\/span> right_height<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">+<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>\r\n<span class=\"token punctuation\">}<\/span>\r\n<\/code><\/pre>\n<h3>\u6253\u5370\u6bcf\u4e00\u7ea7\u7684\u6240\u6709\u8282\u70b9\u3002<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u6709\u4e86\u6811\u7684\u9ad8\u5ea6\uff0c\u6211\u4eec\u9700\u8981\u4e3a\u6bcf\u4e2a\u5c42\u7ea7\u6253\u5370\u8282\u70b9\u3002\u4e3a\u4e86\u505a\u5230\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u4e00\u4e2afor\u5faa\u73af\u6765\u8fed\u4ee3\u6240\u6709\u5c42\u7ea7\u76f4\u5230\u6811\u7684\u9ad8\u5ea6\uff0c\u5e76\u6253\u5370\u6bcf\u4e2a\u5c42\u7ea7\u7684\u8282\u70b9\u3002<\/p>\n<pre class=\"post-pre\"><code><span class=\"token keyword\">void<\/span> <span class=\"token function\">print_tree_level_order<\/span><span class=\"token punctuation\">(<\/span>Node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token keyword\">int<\/span> height <span class=\"token operator\">=<\/span> <span class=\"token function\">tree_height<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i<span class=\"token operator\">=<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&lt;<\/span>height<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token comment\">\/\/ Print the ith level<\/span>\r\n        <span class=\"token function\">print_level<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token punctuation\">,<\/span> i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token punctuation\">}<\/span>\r\n<span class=\"token punctuation\">}<\/span>\r\n<\/code><\/pre>\n<p>\u89c2\u5bdf\u5230\u6211\u4eec\u9700\u8981\u53e6\u4e00\u4e2a\u51fd\u6570\u6765\u6253\u5370\u6811\u7684\u7b2ci\u5c42\u3002<\/p>\n<p>\u518d\u6b21\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u7c7b\u4f3c\u7684\u903b\u8f91\u3002\u4f46\u8fd9\u6b21\uff0c\u5728\u6253\u5370\u6839\u8282\u70b9\u540e\uff0c\u6211\u4eec\u5c06\u6839\u8282\u70b9\u66f4\u6539\u4e3a\u5176\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\uff0c\u5e76\u6253\u5370\u4e24\u4e2a\u5b50\u6811\u3002<\/p>\n<p>\u76f4\u5230\u6211\u4eec\u5230\u8fbe\u53f6\u5b50\u8282\u70b9\uff0c\u4e5f\u5c31\u662f\u8f85\u52a9\u6839\u8282\u70b9\u5728\u4e0b\u4e00\u6b65\u5c06\u4e3aNULL\u7684\u65f6\u5019\uff0c\u8fd9\u5c06\u4f1a\u7ee7\u7eed\u8fdb\u884c\u3002\uff08\u56e0\u4e3a\u53f6\u5b50\u8282\u70b9\u7684\u5de6\u6307\u5411NULL\u4e14\u53f3\u6307\u5411NULL\uff09<\/p>\n<pre class=\"post-pre\"><code><span class=\"token keyword\">void<\/span> <span class=\"token function\">print_level<\/span><span class=\"token punctuation\">(<\/span>Node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> level_no<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token comment\">\/\/ Prints the nodes in the tree<\/span>\r\n    <span class=\"token comment\">\/\/ having a level = level_no<\/span>\r\n    \r\n    <span class=\"token comment\">\/\/ We have a auxiliary root node<\/span>\r\n    <span class=\"token comment\">\/\/ for printing the root of every<\/span>\r\n    <span class=\"token comment\">\/\/ sub-tree<\/span>\r\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>root<span class=\"token punctuation\">)<\/span>\r\n        <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>level_no <span class=\"token operator\">==<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token comment\">\/\/ We are at the top of a sub-tree<\/span>\r\n        <span class=\"token comment\">\/\/ So print the auxiliary root node<\/span>\r\n        <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"%d -&gt; \"<\/span><span class=\"token punctuation\">,<\/span> root<span class=\"token operator\">-&gt;<\/span>value<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token punctuation\">}<\/span>\r\n    <span class=\"token keyword\">else<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token comment\">\/\/ Make the auxiliary root node to<\/span>\r\n        <span class=\"token comment\">\/\/ be the left and right nodes for<\/span>\r\n        <span class=\"token comment\">\/\/ the sub-trees and decrease level by 1, since<\/span>\r\n        <span class=\"token comment\">\/\/ you are moving from top to bottom<\/span>\r\n        <span class=\"token function\">print_level<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token operator\">-&gt;<\/span>left<span class=\"token punctuation\">,<\/span> level_no <span class=\"token operator\">-<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n        <span class=\"token function\">print_level<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token operator\">-&gt;<\/span>right<span class=\"token punctuation\">,<\/span> level_no <span class=\"token operator\">-<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token punctuation\">}<\/span>\r\n\r\n<span class=\"token punctuation\">}<\/span>\r\n\r\n<\/code><\/pre>\n<p>\u73b0\u5728\uff0c\u6211\u4eec\u7ec8\u4e8e\u5b8c\u6210\u4e86\u5c42\u5e8f\u904d\u5386\uff01<\/p>\n<p>\u6211\u5c06\u5728\u4e0b\u9762\u63d0\u4f9b\u5b8c\u6574\u7684\u7a0b\u5e8f\uff0c\u5176\u4e2d\u8fd8\u5305\u542b\u4f7f\u7528\u63d2\u5165\u65b9\u6cd5\u6784\u5efa\u4e8c\u53c9\u6811\u7684\u90e8\u5206\u3002<\/p>\n<hr>\n<\/hr>\n<h2>\u5b8c\u6574\u7684 C\/C++ \u4ee3\u7801<\/p>\n<p>\u5c3d\u7ba1\u8fd9\u539f\u672c\u662f\u4e00\u6bb5C\u7a0b\u5e8f\uff0c\u4f46\u540c\u6837\u53ef\u4ee5\u5728C++\u4e0a\u7f16\u8bd1\u3002<\/p>\n<pre class=\"post-pre\"><code><span class=\"token comment\">\/**\r\n    Code for https:\/\/journaldev.com\r\n    File Name: level_order.c\r\n    Purpose: Find the Level Order Traversal of a Binary Tree\r\n\r\n    @author Vijay Ramachandran\r\n    @date 28\/01\/2020\r\n*\/<\/span>\r\n\r\n<span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;stdio.h&gt;<\/span><\/span>\r\n<span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;stdlib.h&gt;<\/span><\/span>\r\n\r\n<span class=\"token keyword\">typedef<\/span> <span class=\"token keyword\">struct<\/span> <span class=\"token class-name\">Node<\/span> Node<span class=\"token punctuation\">;<\/span>\r\n\r\n<span class=\"token comment\">\/\/ Define the Tree Node here<\/span>\r\n<span class=\"token keyword\">struct<\/span> <span class=\"token class-name\">Node<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token keyword\">int<\/span> value<span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token comment\">\/\/ Pointers to the left and right children<\/span>\r\n    Node<span class=\"token operator\">*<\/span> left<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">*<\/span>right<span class=\"token punctuation\">;<\/span>\r\n<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span>\r\n\r\n\r\nNode<span class=\"token operator\">*<\/span> <span class=\"token function\">init_tree<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> data<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token comment\">\/\/ Creates the tree and returns the<\/span>\r\n    <span class=\"token comment\">\/\/ root node<\/span>\r\n    Node<span class=\"token operator\">*<\/span> root <span class=\"token operator\">=<\/span> <span class=\"token punctuation\">(<\/span>Node<span class=\"token operator\">*<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token function\">malloc<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">sizeof<\/span><span class=\"token punctuation\">(<\/span>Node<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    root<span class=\"token operator\">-&gt;<\/span>left <span class=\"token operator\">=<\/span> root<span class=\"token operator\">-&gt;<\/span>right <span class=\"token operator\">=<\/span> <span class=\"token constant\">NULL<\/span><span class=\"token punctuation\">;<\/span>\r\n    root<span class=\"token operator\">-&gt;<\/span>value <span class=\"token operator\">=<\/span> data<span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">return<\/span> root<span class=\"token punctuation\">;<\/span>\r\n<span class=\"token punctuation\">}<\/span>\r\n\r\nNode<span class=\"token operator\">*<\/span> <span class=\"token function\">create_node<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> data<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token comment\">\/\/ Creates a new node<\/span>\r\n    Node<span class=\"token operator\">*<\/span> node <span class=\"token operator\">=<\/span> <span class=\"token punctuation\">(<\/span>Node<span class=\"token operator\">*<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token function\">malloc<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">sizeof<\/span><span class=\"token punctuation\">(<\/span>Node<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    node<span class=\"token operator\">-&gt;<\/span>value <span class=\"token operator\">=<\/span> data<span class=\"token punctuation\">;<\/span>\r\n    node<span class=\"token operator\">-&gt;<\/span>left <span class=\"token operator\">=<\/span> node<span class=\"token operator\">-&gt;<\/span>right <span class=\"token operator\">=<\/span> <span class=\"token constant\">NULL<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">return<\/span> node<span class=\"token punctuation\">;<\/span>\r\n<span class=\"token punctuation\">}<\/span>\r\n\r\n<span class=\"token keyword\">void<\/span> <span class=\"token function\">free_tree<\/span><span class=\"token punctuation\">(<\/span>Node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token comment\">\/\/ Deallocates memory corresponding<\/span>\r\n    <span class=\"token comment\">\/\/ to every node in the tree.<\/span>\r\n    Node<span class=\"token operator\">*<\/span> temp <span class=\"token operator\">=<\/span> root<span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>temp<span class=\"token punctuation\">)<\/span>\r\n        <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token function\">free_tree<\/span><span class=\"token punctuation\">(<\/span>temp<span class=\"token operator\">-&gt;<\/span>left<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token function\">free_tree<\/span><span class=\"token punctuation\">(<\/span>temp<span class=\"token operator\">-&gt;<\/span>right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>temp<span class=\"token operator\">-&gt;<\/span>left <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token operator\">!<\/span>temp<span class=\"token operator\">-&gt;<\/span>right<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token function\">free<\/span><span class=\"token punctuation\">(<\/span>temp<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n        <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token punctuation\">}<\/span>\r\n<span class=\"token punctuation\">}<\/span>\r\n\r\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">tree_height<\/span><span class=\"token punctuation\">(<\/span>Node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token comment\">\/\/ Get the height of the tree<\/span>\r\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>root<span class=\"token punctuation\">)<\/span>\r\n        <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">else<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token comment\">\/\/ Find the height of both subtrees<\/span>\r\n        <span class=\"token comment\">\/\/ and use the larger one<\/span>\r\n        <span class=\"token keyword\">int<\/span> left_height <span class=\"token operator\">=<\/span> <span class=\"token function\">tree_height<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token operator\">-&gt;<\/span>left<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n        <span class=\"token keyword\">int<\/span> right_height <span class=\"token operator\">=<\/span> <span class=\"token function\">tree_height<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token operator\">-&gt;<\/span>right<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>left_height <span class=\"token operator\">&gt;=<\/span> right_height<span class=\"token punctuation\">)<\/span>\r\n            <span class=\"token keyword\">return<\/span> left_height <span class=\"token operator\">+<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>\r\n        <span class=\"token keyword\">else<\/span>\r\n            <span class=\"token keyword\">return<\/span> right_height <span class=\"token operator\">+<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token punctuation\">}<\/span>\r\n<span class=\"token punctuation\">}<\/span>\r\n\r\n<span class=\"token keyword\">void<\/span> <span class=\"token function\">print_level<\/span><span class=\"token punctuation\">(<\/span>Node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> level_no<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token comment\">\/\/ Prints the nodes in the tree<\/span>\r\n    <span class=\"token comment\">\/\/ having a level = level_no<\/span>\r\n    \r\n    <span class=\"token comment\">\/\/ We have a auxiliary root node<\/span>\r\n    <span class=\"token comment\">\/\/ for printing the root of every<\/span>\r\n    <span class=\"token comment\">\/\/ subtree<\/span>\r\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>root<span class=\"token punctuation\">)<\/span>\r\n        <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>level_no <span class=\"token operator\">==<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token comment\">\/\/ We are at the top of a subtree<\/span>\r\n        <span class=\"token comment\">\/\/ So print the auxiliary root node<\/span>\r\n        <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"%d -&gt; \"<\/span><span class=\"token punctuation\">,<\/span> root<span class=\"token operator\">-&gt;<\/span>value<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token punctuation\">}<\/span>\r\n    <span class=\"token keyword\">else<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token comment\">\/\/ Make the auxiliary root node to<\/span>\r\n        <span class=\"token comment\">\/\/ be the left and right nodes for<\/span>\r\n        <span class=\"token comment\">\/\/ the subtrees and decrease level by 1, since<\/span>\r\n        <span class=\"token comment\">\/\/ you are moving from top to bottom<\/span>\r\n        <span class=\"token function\">print_level<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token operator\">-&gt;<\/span>left<span class=\"token punctuation\">,<\/span> level_no <span class=\"token operator\">-<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n        <span class=\"token function\">print_level<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token operator\">-&gt;<\/span>right<span class=\"token punctuation\">,<\/span> level_no <span class=\"token operator\">-<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token punctuation\">}<\/span>\r\n\r\n<span class=\"token punctuation\">}<\/span>\r\n\r\n<span class=\"token keyword\">void<\/span> <span class=\"token function\">print_tree_level_order<\/span><span class=\"token punctuation\">(<\/span>Node<span class=\"token operator\">*<\/span> root<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>root<span class=\"token punctuation\">)<\/span>\r\n        <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">int<\/span> height <span class=\"token operator\">=<\/span> <span class=\"token function\">tree_height<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i<span class=\"token operator\">=<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&lt;<\/span>height<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"Level %d: \"<\/span><span class=\"token punctuation\">,<\/span> i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n        <span class=\"token function\">print_level<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token punctuation\">,<\/span> i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n        <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"\\n\"<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token punctuation\">}<\/span>\r\n    <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"\\n\\n-----Complete Level Order Traversal:-----\\n\"<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i<span class=\"token operator\">=<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&lt;<\/span>height<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n        <span class=\"token function\">print_level<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token punctuation\">,<\/span> i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token punctuation\">}<\/span>\r\n    <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"\\n\"<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n<span class=\"token punctuation\">}<\/span>\r\n\r\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\r\n    <span class=\"token comment\">\/\/ Program to demonstrate Level Order Traversal<\/span>\r\n\r\n    <span class=\"token comment\">\/\/ Create the root node having a value of 10<\/span>\r\n    Node<span class=\"token operator\">*<\/span> root <span class=\"token operator\">=<\/span> <span class=\"token function\">init_tree<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    \r\n    <span class=\"token comment\">\/\/ Insert nodes onto the tree<\/span>\r\n    root<span class=\"token operator\">-&gt;<\/span>left <span class=\"token operator\">=<\/span> <span class=\"token function\">create_node<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">20<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    root<span class=\"token operator\">-&gt;<\/span>right <span class=\"token operator\">=<\/span> <span class=\"token function\">create_node<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">30<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    root<span class=\"token operator\">-&gt;<\/span>left<span class=\"token operator\">-&gt;<\/span>left <span class=\"token operator\">=<\/span> <span class=\"token function\">create_node<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">40<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    root<span class=\"token operator\">-&gt;<\/span>left<span class=\"token operator\">-&gt;<\/span>right <span class=\"token operator\">=<\/span> <span class=\"token function\">create_node<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">50<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    \r\n    <span class=\"token comment\">\/\/ Level Order Traversal<\/span>\r\n    <span class=\"token function\">print_tree_level_order<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n\r\n    <span class=\"token comment\">\/\/ Free the tree!<\/span>\r\n    <span class=\"token function\">free_tree<\/span><span class=\"token punctuation\">(<\/span>root<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\r\n    <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span>\r\n<span class=\"token punctuation\">}<\/span>\r\n\r\n<\/code><\/pre>\n<p>\u8f93\u51fa<\/p>\n<pre class=\"post-pre\"><code>Level 0: 10 -&gt; \r\nLevel 1: 20 -&gt; 30 -&gt; \r\nLevel 2: 40 -&gt; 50 -&gt; \r\n\r\n\r\n-----Complete Level Order Traversal:-----\r\n10 -&gt; 20 -&gt; 30 -&gt; 40 -&gt; 50 -&gt; \r\n<\/code><\/pre>\n<p>\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u6211\u4e3a\u6b64\u76ee\u7684\u521b\u5efa\u7684Github gist\u4e0b\u8f7d\u5b83\u3002\uff08\u8fd8\u5305\u542b\u63d2\u5165\u4ee3\u7801\u7684\u90e8\u5206\uff09<\/p>\n<hr>\n<\/hr>\n<h2>\u7ed3\u8bba<\/p>\n<p>\u5e0c\u671b\u4f60\u5bf9\u5982\u4f55\u5728C\/C++\u4e2d\u5b9e\u73b0\u5c42\u5e8f\u904d\u5386\u6709\u4e86\u66f4\u597d\u7684\u7406\u89e3\u3002\u5982\u679c\u4f60\u6709\u4efb\u4f55\u95ee\u9898\uff0c\u8bf7\u5728\u4e0b\u9762\u7684\u8bc4\u8bba\u533a\u968f\u65f6\u63d0\u95ee\uff01<\/p>\n<hr>\n<\/hr>\n","protected":false},"excerpt":{"rendered":"<p>\u5c42\u6b21\u904d\u5386\u662f\u4e00\u79cd\u6a2a\u5411\u904d\u5386\u4e8c\u53c9\u6811\u7684\u65b9\u6cd5\u4e4b\u4e00\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u5982\u4f55\u5728C\/C++\u4e2d\u5b9e\u73b0\u8fd9\u4e2a\u7b97\u6cd5\u3002 \u4f46\u5728\u6b64\u4e4b\u524d\uff0c\u8ba9\u6211 [&hellip;]<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[227],"class_list":["post-23852","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-227"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.5 (Yoast SEO v21.5) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u5728\u4e8c\u53c9\u6811\u4e2d\u8fdb\u884c\u5c42\u6b21\u904d\u5386 - Blog - Silicon Cloud<\/title>\n<meta name=\"description\" content=\"\u5173\u4e8e\u5728\u4e8c\u53c9\u6811\u4e2d\u8fdb\u884c\u5c42\u6b21\u904d\u5386\u7684\u6280\u672f\u6587\u7ae0\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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