{"id":462,"date":"2025-10-29T14:10:33","date_gmt":"2025-10-29T06:10:33","guid":{"rendered":"https:\/\/heyingnian.com\/?p=462"},"modified":"2025-10-29T14:11:01","modified_gmt":"2025-10-29T06:11:01","slug":"leetcode-124","status":"publish","type":"post","link":"https:\/\/heyingnian.com\/index.php\/2025\/10\/29\/leetcode-124\/","title":{"rendered":"\u4e8c\u53c9\u6811\u4e2d\u7684\u6700\u5927\u8def\u5f84\u548c"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\ud83d\udd17 \u4e8c\u53c9\u6811\u4e2d\u7684\u6700\u5927\u8def\u5f84\u548c<\/h1>\n\n\n\n<p><strong>\u9898\u76ee\u6765\u6e90<\/strong>\uff1a<a target=\"_blank\" rel=\"noreferrer noopener\"><a href=\"https:\/\/leetcode.cn\/problems\/binary-tree-maximum-path-sum\/description\/?envType=study-plan-v2&amp;envId=top-100-liked\" target=\"_blank\" rel=\"noopener\">124. \u4e8c\u53c9\u6811\u4e2d\u7684\u6700\u5927\u8def\u5f84\u548c &#8211; \u529b\u6263\uff08LeetCode\uff09<\/a><\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udccc \u9898\u76ee\u63cf\u8ff0<\/h2>\n\n\n\n<p><strong>\u8def\u5f84<\/strong>\u88ab\u5b9a\u4e49\u4e3a\u4e00\u6761\u8282\u70b9\u5e8f\u5217\uff0c\u5e8f\u5217\u4e2d\u6bcf\u5bf9\u76f8\u90bb\u8282\u70b9\u4e4b\u95f4\u90fd\u5b58\u5728\u4e00\u6761\u8fb9\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u540c\u4e00\u4e2a\u8282\u70b9\u5728\u4e00\u6761\u8def\u5f84\u4e2d\u00a0<strong>\u81f3\u591a\u51fa\u73b0\u4e00\u6b21<\/strong>\uff1b<\/li>\n\n\n\n<li>\u8def\u5f84\u00a0<strong>\u81f3\u5c11\u5305\u542b\u4e00\u4e2a\u8282\u70b9<\/strong>\uff1b<\/li>\n\n\n\n<li>\u8def\u5f84\u00a0<strong>\u4e0d\u4e00\u5b9a\u7ecf\u8fc7\u6839\u8282\u70b9<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u8def\u5f84\u548c<\/strong> \u662f\u8def\u5f84\u4e2d\u5404\u8282\u70b9\u503c\u7684\u603b\u548c\u3002<\/p>\n\n\n\n<p>\u7ed9\u5b9a\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9 <code>root<\/code>\uff0c\u8fd4\u56de\u5176 <strong>\u6700\u5927\u8def\u5f84\u548c<\/strong>\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u2705 \u793a\u4f8b\u89e3\u6790<\/h2>\n\n\n\n<p><strong>\u793a\u4f8b 1\uff1a<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/heyingnian.com\/wp-content\/uploads\/2025\/10\/image-15.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"322\" height=\"182\" data-original=\"https:\/\/heyingnian.com\/wp-content\/uploads\/2025\/10\/image-15.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-463\"  sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/div><\/figure>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>\u8f93\u5165\uff1aroot = [1,2,3]<br>\u8f93\u51fa\uff1a6<br>\u89e3\u91ca\uff1a\u6700\u4f18\u8def\u5f84\u662f 2 \u2192 1 \u2192 3\uff0c\u8def\u5f84\u548c\u4e3a 2 + 1 + 3 = 6\u3002<\/code><\/pre>\n\n\n\n<p><strong>\u793a\u4f8b 2\uff1a<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/heyingnian.com\/wp-content\/uploads\/2025\/10\/image-16.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"431\" height=\"302\" data-original=\"https:\/\/heyingnian.com\/wp-content\/uploads\/2025\/10\/image-16.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-464\"  sizes=\"auto, (max-width: 431px) 100vw, 431px\" \/><\/div><\/figure>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>\u8f93\u5165\uff1aroot = [-10,9,20,null,null,15,7]<br>\u8f93\u51fa\uff1a42<br>\u89e3\u91ca\uff1a\u6700\u4f18\u8def\u5f84\u662f 15 \u2192 20 \u2192 7\uff0c\u8def\u5f84\u548c\u4e3a 15 + 20 + 7 = 42\u3002<\/code><\/pre>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u6ce8\u610f\uff1a\u8def\u5f84\u4e0d\u80fd\u201c\u6298\u8fd4\u201d\u4e24\u6b21\uff08\u5982 15 \u2192 20 \u2192 9\uff09\uff0c\u56e0\u4e3a\u90a3\u6837\u4f1a\u5bfc\u81f4 20 \u88ab\u8bbf\u95ee\u4e24\u6b21\uff0c\u8fdd\u53cd\u201c\u6bcf\u4e2a\u8282\u70b9\u81f3\u591a\u51fa\u73b0\u4e00\u6b21\u201d\u7684\u89c4\u5219\u3002<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u26a0\ufe0f \u63d0\u793a<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8282\u70b9\u6570\u76ee\u8303\u56f4\uff1a<code>[1, 3 \u00d7 10\u2074]<\/code><\/li>\n\n\n\n<li><code>Node.val<\/code>\u00a0\u8303\u56f4\uff1a<code>[-1000, 1000]<\/code><\/li>\n\n\n\n<li>\u8282\u70b9\u503c\u53ef\u4e3a\u8d1f\u6570\uff0c<strong>\u4e0d\u80fd\u7b80\u5355\u8df3\u8fc7\u8d1f\u503c\u5b50\u6811<\/strong>\uff0c\u9700\u52a8\u6001\u5224\u65ad\u662f\u5426\u201c\u820d\u5f03\u201d\u5b50\u8def\u5f84\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udca1 \u89e3\u6cd5\uff1a\u9012\u5f52 + \u8d2a\u5fc3\u526a\u679d \u2014\u2014 O(n) \u65f6\u95f4\uff0cO(h) \u7a7a\u95f4<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>class Solution {\n    int maxSum = Integer.MIN_VALUE;\n\n    public int maxPathSum(TreeNode root) {\n        dfs(root);\n        return maxSum;\n    }\n\n    \/\/ \u8fd4\u56de\uff1a\u4ee5\u5f53\u524d\u8282\u70b9\u4e3a\u8d77\u70b9\uff0c\u5411\u4e0b\u5ef6\u4f38\u7684\u6700\u5927\u5355\u8fb9\u8def\u5f84\u548c\uff08\u53ef\u4e0d\u9009\u5b50\u6811\uff09\n    private int dfs(TreeNode node) {\n        if (node == null) {\n            return 0;\n        }\n\n        \/\/ \u9012\u5f52\u8ba1\u7b97\u5de6\u53f3\u5b50\u6811\u7684\u6700\u5927\u8d21\u732e\u503c\uff08\u8d1f\u6570\u5219\u820d\u5f03\uff0c\u7528 0 \u4ee3\u66ff\uff09\n        int leftGain = Math.max(0, dfs(node.left));\n        int rightGain = Math.max(0, dfs(node.right));\n\n        \/\/ \u8ba1\u7b97\u201c\u7ecf\u8fc7\u5f53\u524d\u8282\u70b9\u201d\u7684\u5b8c\u6574\u8def\u5f84\u548c\uff08\u5de6 \u2190 \u5f53\u524d \u2192 \u53f3\uff09\n        int currentPathSum = node.val + leftGain + rightGain;\n\n        \/\/ \u66f4\u65b0\u5168\u5c40\u6700\u5927\u8def\u5f84\u548c\n        maxSum = Math.max(maxSum, currentPathSum);\n\n        \/\/ \u8fd4\u56de\u5f53\u524d\u8282\u70b9\u80fd\u5411\u4e0a\u63d0\u4f9b\u7684\u6700\u5927\u5355\u8fb9\u8def\u5f84\u548c\uff08\u53ea\u80fd\u9009\u4e00\u8fb9\uff09\n        return node.val + Math.max(leftGain, rightGain);\n    }\n}<\/code><\/pre>\n\n\n\n<p>\u2705 <strong>\u5173\u952e\u70b9<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8def\u5f84\u53ea\u80fd\u201c\u62d0\u4e00\u6b21\u5f2f\u201d<\/strong>\uff1a\u5373\u5f62\u5982\u00a0<code>\u5de6\u5b50\u6811 \u2190 \u6839 \u2192 \u53f3\u5b50\u6811<\/code>\uff0c\u4e0d\u80fd\u7ee7\u7eed\u5411\u4e0a\u518d\u62d0\uff1b<\/li>\n\n\n\n<li><strong>\u5355\u8fb9\u8def\u5f84 vs \u5b8c\u6574\u8def\u5f84<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li><code>dfs<\/code>\u00a0\u8fd4\u56de\u7684\u662f<strong>\u5355\u8fb9\u8def\u5f84<\/strong>\uff08\u7528\u4e8e\u7236\u8282\u70b9\u6784\u5efa\u8def\u5f84\uff09\uff1b<\/li>\n\n\n\n<li>\u5168\u5c40\u00a0<code>maxSum<\/code>\u00a0\u8bb0\u5f55\u7684\u662f<strong>\u5b8c\u6574\u8def\u5f84<\/strong>\uff08\u53ef\u80fd\u5305\u542b\u5de6\u53f3\u5b50\u6811\uff09\uff1b<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u8d1f\u8d21\u732e\u526a\u679d<\/strong>\uff1a\u82e5\u5b50\u6811\u8d21\u732e\u4e3a\u8d1f\uff0c\u5219\u7528\u00a0<code>0<\/code>\u00a0\u4ee3\u66ff\uff08\u76f8\u5f53\u4e8e\u4e0d\u9009\u8be5\u5b50\u6811\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udcca \u590d\u6742\u5ea6\u5206\u6790<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u65f6\u95f4\u590d\u6742\u5ea6<\/strong>\uff1a<code>O(n)<\/code><br>\u6bcf\u4e2a\u8282\u70b9\u88ab\u8bbf\u95ee\u4e00\u6b21\uff0c\u6bcf\u6b21\u64cd\u4f5c <code>O(1)<\/code>\u3002<\/li>\n\n\n\n<li><strong>\u7a7a\u95f4\u590d\u6742\u5ea6<\/strong>\uff1a<code>O(h)<\/code>\n<ul class=\"wp-block-list\">\n<li>\u9012\u5f52\u6808\u6df1\u5ea6\u4e3a\u6811\u9ad8\u00a0<code>h<\/code>\uff1b<\/li>\n\n\n\n<li>\u6700\u574f\u60c5\u51b5\uff08\u94fe\u8868\uff09\uff1a<code>O(n)<\/code>\uff1b<\/li>\n\n\n\n<li>\u6700\u597d\u60c5\u51b5\uff08\u5e73\u8861\u6811\uff09\uff1a<code>O(log n)<\/code>\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\udde9 \u89e3\u9898\u601d\u8def<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e3a\u4ec0\u4e48\u4e0d\u80fd\u76f4\u63a5\u8fd4\u56de\u5de6\u53f3\u5b50\u6811\u6700\u5927\u503c\u4e4b\u548c\uff1f<\/h3>\n\n\n\n<p>\u56e0\u4e3a<strong>\u8def\u5f84\u4e0d\u80fd\u5206\u53c9<\/strong>\uff01<br>\u5f53\u5411\u4e0a\u4f20\u9012\u65f6\uff0c\u7236\u8282\u70b9\u53ea\u80fd\u9009\u62e9<strong>\u5de6\u6216\u53f3\u5176\u4e2d\u4e00\u6761\u8def\u5f84<\/strong>\u7ee7\u7eed\u5ef6\u4f38\uff0c\u4e0d\u80fd\u540c\u65f6\u9009\u4e24\u8fb9\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\ud83c\udf30 \u4e3e\u4f8b\uff1a<br>\u5bf9\u4e8e\u8282\u70b9 <code>20<\/code>\uff08\u793a\u4f8b2\uff09\uff0c\u5176\u5de6\u53f3\u5b50\u6811\u8d21\u732e\u5206\u522b\u4e3a <code>15<\/code> \u548c <code>7<\/code>\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5b83\u80fd\u8d21\u732e\u7ed9\u7236\u8282\u70b9\u00a0<code>(-10)<\/code>\u00a0\u7684\u6700\u5927\u5355\u8fb9\u8def\u5f84\u662f\u00a0<code>20 + max(15,7) = 35<\/code>\uff1b<\/li>\n\n\n\n<li>\u4f46\u5b83\u81ea\u5df1\u5185\u90e8\u7684\u5b8c\u6574\u8def\u5f84\u53ef\u4ee5\u662f\u00a0<code>15 + 20 + 7 = 42<\/code>\uff0c\u8fd9\u5c31\u662f\u7b54\u6848\u3002<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b97\u6cd5\u6838\u5fc3\uff1a\u4e24\u79cd\u8def\u5f84\u89d2\u8272<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u89d2\u8272<\/th><th>\u8bf4\u660e<\/th><th>\u7528\u9014<\/th><\/tr><\/thead><tbody><tr><td><strong>\u5b8c\u6574\u8def\u5f84<\/strong><\/td><td>\u7ecf\u8fc7\u5f53\u524d\u8282\u70b9\uff0c\u53ef\u5305\u542b\u5de6\u53f3\u5b50\u6811<\/td><td>\u7528\u4e8e\u66f4\u65b0\u5168\u5c40\u6700\u5927\u503c&nbsp;<code>maxSum<\/code><\/td><\/tr><tr><td><strong>\u5355\u8fb9\u8def\u5f84<\/strong><\/td><td>\u4ece\u5f53\u524d\u8282\u70b9\u5411\u4e0b\u5ef6\u4f38\uff0c\u53ea\u80fd\u9009\u5de6\u6216\u53f3<\/td><td>\u7528\u4e8e\u8fd4\u56de\u7ed9\u7236\u8282\u70b9\uff0c\u6784\u5efa\u66f4\u957f\u8def\u5f84<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e3a\u4ec0\u4e48\u521d\u59cb\u5316&nbsp;<code>maxSum = Integer.MIN_VALUE<\/code>\uff1f<\/h3>\n\n\n\n<p>\u56e0\u4e3a\u8282\u70b9\u503c\u53ef\u80fd\u5168\u4e3a\u8d1f\u6570\uff08\u5982 <code>[-3, -2, -1]<\/code>\uff09\uff0c\u6b64\u65f6\u6700\u5927\u8def\u5f84\u548c\u5c31\u662f\u6700\u5927\u7684\u90a3\u4e2a\u8d1f\u6570\uff08<code>-1<\/code>\uff09\uff0c\u4e0d\u80fd\u521d\u59cb\u5316\u4e3a <code>0<\/code>\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd17 \u4e8c\u53c9\u6811\u4e2d\u7684\u6700\u5927\u8def\u5f84\u548c \u9898\u76ee\u6765\u6e90\uff1a124. \u4e8c\u53c9\u6811\u4e2d\u7684\u6700\u5927\u8def\u5f84\u548c &#8211; \u529b\u6263\uff08LeetCode\uff09  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[39,12],"tags":[57,58,14],"class_list":["post-462","post","type-post","status-publish","format-standard","hentry","category-binary_tree","category-algorithm","tag-binary_tree","tag-dfs","tag-algorithm"],"_links":{"self":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/462","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/comments?post=462"}],"version-history":[{"count":1,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/462\/revisions"}],"predecessor-version":[{"id":465,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/462\/revisions\/465"}],"wp:attachment":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/media?parent=462"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/categories?post=462"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/tags?post=462"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}