{"id":433,"date":"2025-10-14T19:20:00","date_gmt":"2025-10-14T11:20:00","guid":{"rendered":"https:\/\/heyingnian.com\/?p=433"},"modified":"2025-10-14T19:20:26","modified_gmt":"2025-10-14T11:20:26","slug":"leetcode-230","status":"publish","type":"post","link":"https:\/\/heyingnian.com\/index.php\/2025\/10\/14\/leetcode-230\/","title":{"rendered":"\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u7b2c k \u5c0f\u7684\u5143\u7d20"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\ud83d\udd17 \u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u7b2c k \u5c0f\u7684\u5143\u7d20<\/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\/kth-smallest-element-in-a-bst\/description\/?envType=study-plan-v2&amp;envId=top-100-liked\" target=\"_blank\" rel=\"noopener\">230. \u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u7b2c K \u5c0f\u7684\u5143\u7d20 &#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>\u7ed9\u5b9a\u4e00\u4e2a\u4e8c\u53c9\u641c\u7d22\u6811\uff08BST\uff09\u7684\u6839\u8282\u70b9 <code>root<\/code>\uff0c\u548c\u4e00\u4e2a\u6574\u6570 <code>k<\/code>\uff0c\u8bf7\u4f60\u8bbe\u8ba1\u4e00\u4e2a\u7b97\u6cd5\u67e5\u627e\u5176\u4e2d<strong>\u7b2c <code>k<\/code> \u5c0f\u7684\u5143\u7d20<\/strong>\uff08\u4ece 1 \u5f00\u59cb\u8ba1\u6570\uff09\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-4.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"212\" height=\"301\" data-original=\"https:\/\/heyingnian.com\/wp-content\/uploads\/2025\/10\/image-4.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-434\"\/><\/div><\/figure>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>\u8f93\u5165\uff1aroot = [3,1,4,null,2], k = 1<br>\u8f93\u51fa\uff1a1<\/code><\/pre>\n\n\n\n<p>\u89e3\u91ca\uff1a\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217\u4e3a <code>[1, 2, 3, 4]<\/code>\uff0c\u7b2c 1 \u5c0f\u7684\u5143\u7d20\u662f <code>1<\/code>\u3002<\/p>\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-5.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"382\" height=\"302\" data-original=\"https:\/\/heyingnian.com\/wp-content\/uploads\/2025\/10\/image-5.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-435\"  sizes=\"auto, (max-width: 382px) 100vw, 382px\" \/><\/div><\/figure>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>\u8f93\u5165\uff1aroot = [5,3,6,2,4,null,null,1], k = 3<br>\u8f93\u51fa\uff1a3<\/code><\/pre>\n\n\n\n<p>\u89e3\u91ca\uff1a\u4e2d\u5e8f\u904d\u5386\u5e8f\u5217\u4e3a <code>[1, 2, 3, 4, 5, 6]<\/code>\uff0c\u7b2c 3 \u5c0f\u7684\u5143\u7d20\u662f <code>3<\/code>\u3002<\/p>\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>\u6811\u4e2d\u7684\u8282\u70b9\u6570\u4e3a\u00a0<code>n<\/code>\u3002<\/li>\n\n\n\n<li><code>1 &lt;= k &lt;= n &lt;= 10\u2074<\/code><\/li>\n\n\n\n<li><code>0 &lt;= Node.val &lt;= 10\u2074<\/code><\/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\u4e2d\u5e8f\u904d\u5386\uff08DFS \u9012\u5f52\uff09\u2014\u2014 O(H + k) \u65f6\u95f4\uff0cO(H) \u7a7a\u95f4<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>class Solution {\n    private int count = 0;       \n    private int kthSmallest = 0;  \n\n    public int kthSmallest(TreeNode root, int k) {\n        inorderTraversal(root, k);\n        return kthSmallest;\n    }\n\n    private void inorderTraversal(TreeNode node, int k) {\n        \/\/ \u63d0\u524d\u7ec8\u6b62\uff1a\u8282\u70b9\u4e3a\u7a7a\uff0c\u6216\u5df2\u627e\u5230\u7ed3\u679c\uff08\u53ef\u4f18\u5316\u4e3a count >= k\uff09\n        if (node == null || count >= k) {\n            return;\n        }\n\n        \/\/ \u904d\u5386\u5de6\u5b50\u6811\n        inorderTraversal(node.left, k);\n\n        \/\/ \u8bbf\u95ee\u5f53\u524d\u8282\u70b9\n        count++;\n        if (count == k) {\n            kthSmallest = node.val;\n            return; \/\/ \u627e\u5230\u540e\u7acb\u5373\u8fd4\u56de\uff0c\u907f\u514d\u65e0\u6548\u904d\u5386\n        }\n\n        \/\/ \u904d\u5386\u53f3\u5b50\u6811\n        inorderTraversal(node.right, k);\n    }\n}<\/code><\/pre>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u2705 <strong>\u4f18\u5316\u8bf4\u660e<\/strong>\uff1a\u5c06\u7ec8\u6b62\u6761\u4ef6\u4ece <code>count &gt; k<\/code> \u6539\u4e3a <code>count &gt;= k<\/code>\uff0c\u5e76\u5728\u627e\u5230\u7ed3\u679c\u540e <code>return<\/code>\uff0c\u53ef\u63d0\u524d\u7ed3\u675f\u9012\u5f52\uff0c\u63d0\u5347\u6548\u7387\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\">\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(H + k)<\/code><br>\u5176\u4e2d <code>H<\/code> \u662f\u6811\u7684\u9ad8\u5ea6\u3002\u6700\u574f\u60c5\u51b5\u4e0b\u9700\u904d\u5386 <code>k<\/code> \u4e2a\u8282\u70b9\uff08\u5982\u5de6\u504f\u6811\uff09\uff0c\u800c\u5230\u8fbe\u7b2c\u4e00\u4e2a\u53f6\u5b50\u9700 <code>H<\/code> \u6b65\u3002\n<ul class=\"wp-block-list\">\n<li>\u5e73\u8861 BST\uff1a<code>H = O(log n)<\/code>\u00a0\u2192 \u603b\u65f6\u95f4\u00a0<code>O(log n + k)<\/code><\/li>\n\n\n\n<li>\u9000\u5316\u4e3a\u94fe\u8868\uff1a<code>H = O(n)<\/code>\u00a0\u2192 \u6700\u574f\u00a0<code>O(n)<\/code><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7a7a\u95f4\u590d\u6742\u5ea6<\/strong>\uff1a<code>O(H)<\/code><br>\u9012\u5f52\u8c03\u7528\u6808\u7684\u6df1\u5ea6\u7b49\u4e8e\u6811\u7684\u9ad8\u5ea6 <code>H<\/code>\u3002\n<ul class=\"wp-block-list\">\n<li>\u5e73\u8861\u6811\uff1a<code>O(log n)<\/code><\/li>\n\n\n\n<li>\u94fe\u8868\uff1a<code>O(n)<\/code><\/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\">\u6838\u5fc3\u6027\u8d28\uff1a<strong>\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u662f\u5347\u5e8f\u5e8f\u5217<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e2d\u5e8f\u904d\u5386\u987a\u5e8f\uff1a<strong>\u5de6\u5b50\u6811 \u2192 \u6839\u8282\u70b9 \u2192 \u53f3\u5b50\u6811<\/strong><\/li>\n\n\n\n<li>\u5bf9 BST \u800c\u8a00\uff0c\u8be5\u987a\u5e8f\u6070\u597d\u662f<strong>\u4ece\u5c0f\u5230\u5927<\/strong>\u6392\u5217\u7684\u8282\u70b9\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u4ece\u6839\u8282\u70b9\u5f00\u59cb\uff0c\u9012\u5f52\u8fdb\u884c\u4e2d\u5e8f\u904d\u5386\u3002<\/li>\n\n\n\n<li>\u6bcf\u8bbf\u95ee\u4e00\u4e2a\u8282\u70b9\uff0c\u8ba1\u6570\u5668\u00a0<code>count<\/code>\u00a0\u52a0 1\u3002<\/li>\n\n\n\n<li>\u5f53\u00a0<code>count == k<\/code>\u00a0\u65f6\uff0c\u5f53\u524d\u8282\u70b9\u503c\u5373\u4e3a\u7b2c\u00a0<code>k<\/code>\u00a0\u5c0f\u7684\u5143\u7d20\u3002<\/li>\n\n\n\n<li><strong>\u5173\u952e\u4f18\u5316<\/strong>\uff1a\u4e00\u65e6\u627e\u5230\u76ee\u6807\uff0c\u7acb\u5373\u7ec8\u6b62\u540e\u7eed\u904d\u5386\uff0c\u907f\u514d\u65e0\u610f\u4e49\u64cd\u4f5c\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e3a\u4ec0\u4e48\u4e0d\u80fd\u7528\u5c42\u5e8f\u6216\u524d\u5e8f\u904d\u5386\uff1f<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u53ea\u6709<strong>\u4e2d\u5e8f\u904d\u5386<\/strong>\u80fd\u4fdd\u8bc1 BST \u8282\u70b9\u503c\u6309\u5347\u5e8f\u8bbf\u95ee\uff0c\u5176\u4ed6\u904d\u5386\u65e0\u6cd5\u76f4\u63a5\u5b9a\u4f4d\u7b2c\u00a0<code>k<\/code>\u00a0\u5c0f\u3002<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd17 \u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u7b2c k \u5c0f\u7684\u5143\u7d20 \u9898\u76ee\u6765\u6e90\uff1a230. \u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u7b2c K \u5c0f\u7684\u5143\u7d20 &#8211; \u529b\u6263\uff08Le [&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-433","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\/433","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=433"}],"version-history":[{"count":1,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/433\/revisions"}],"predecessor-version":[{"id":436,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/433\/revisions\/436"}],"wp:attachment":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/media?parent=433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/categories?post=433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/tags?post=433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}