{"id":453,"date":"2025-10-28T15:37:51","date_gmt":"2025-10-28T07:37:51","guid":{"rendered":"https:\/\/heyingnian.com\/?p=453"},"modified":"2025-10-28T15:38:21","modified_gmt":"2025-10-28T07:38:21","slug":"leetcode-437","status":"publish","type":"post","link":"https:\/\/heyingnian.com\/index.php\/2025\/10\/28\/leetcode-437\/","title":{"rendered":"\u8def\u5f84\u603b\u548c III"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\ud83d\udd17 \u8def\u5f84\u603b\u548c III<\/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\/path-sum-iii\/description\/?envType=study-plan-v2&amp;envId=top-100-liked\" target=\"_blank\" rel=\"noopener\">437. \u8def\u5f84\u603b\u548c III &#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\u6811\u7684\u6839\u8282\u70b9 <code>root<\/code> \u548c\u4e00\u4e2a\u6574\u6570 <code>targetSum<\/code>\uff0c\u6c42\u8be5\u4e8c\u53c9\u6811\u4e2d<strong>\u8282\u70b9\u503c\u4e4b\u548c\u7b49\u4e8e <code>targetSum<\/code> \u7684\u8def\u5f84\u6570\u76ee<\/strong>\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u8def\u5f84\u8981\u6c42<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e0d\u9700\u8981\u4ece\u6839\u8282\u70b9\u5f00\u59cb\uff1b<\/li>\n\n\n\n<li>\u4e0d\u9700\u8981\u5728\u53f6\u5b50\u8282\u70b9\u7ed3\u675f\uff1b<\/li>\n\n\n\n<li><strong>\u65b9\u5411\u5fc5\u987b\u662f\u5411\u4e0b\u7684<\/strong>\uff08\u53ea\u80fd\u4ece\u7236\u8282\u70b9\u5230\u5b50\u8282\u70b9\uff09\u3002<\/li>\n<\/ul>\n<\/blockquote>\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-12.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"576\" height=\"494\" data-original=\"https:\/\/heyingnian.com\/wp-content\/uploads\/2025\/10\/image-12.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-454\"  sizes=\"auto, (max-width: 576px) 100vw, 576px\" \/><\/div><\/figure>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>\u8f93\u5165\uff1aroot = [10,5,-3,3,2,null,11,3,-2,null,1], targetSum = 8<br>\u8f93\u51fa\uff1a3<\/code><\/pre>\n\n\n\n<p>\u89e3\u91ca\uff1a<br>\u548c\u4e3a 8 \u7684\u8def\u5f84\u6709 3 \u6761\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>5 \u2192 3<\/code><\/li>\n\n\n\n<li><code>5 \u2192 2 \u2192 1<\/code><\/li>\n\n\n\n<li><code>-3 \u2192 11<\/code><\/li>\n<\/ul>\n\n\n\n<p><strong>\u793a\u4f8b 2\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>\u8f93\u5165\uff1aroot = [5,4,8,11,null,13,4,7,2,null,null,5,1], targetSum = 22<br>\u8f93\u51fa\uff1a3<\/code><\/pre>\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\u4e2a\u6570\u8303\u56f4\uff1a<code>[0, 1000]<\/code><\/li>\n\n\n\n<li><code>Node.val<\/code>\u00a0\u8303\u56f4\uff1a<code>[-10\u2079, 10\u2079]<\/code><\/li>\n\n\n\n<li><code>targetSum<\/code>\u00a0\u8303\u56f4\uff1a<code>[-1000, 1000]<\/code><\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u26a0\ufe0f \u6ce8\u610f\uff1a<strong>\u8282\u70b9\u503c\u53ef\u80fd\u4e3a\u8d1f\u6570<\/strong>\uff0c\u56e0\u6b64\u4e0d\u80fd\u63d0\u524d\u526a\u679d\uff01<\/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\udca1 \u89e3\u6cd5\uff1a\u524d\u7f00\u548c + \u54c8\u5e0c\u8868 + DFS \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 targetSum;\n    Map&lt;Long, Integer> prefixSumCount = new HashMap&lt;>();\n    int result = 0;\n\n    public int pathSum(TreeNode root, int targetSum) {\n        this.targetSum = targetSum;\n        \/\/ \u521d\u59cb\u5316\uff1a\u524d\u7f00\u548c\u4e3a 0 \u7684\u8def\u5f84\u6709 1 \u6761\uff08\u7a7a\u8def\u5f84\uff09\n        prefixSumCount.put(0L, 1);\n        dfs(root, 0L);\n        return result;\n    }\n\n    private void dfs(TreeNode node, long currentSum) {\n        if (node == null) return;\n\n        \/\/ \u66f4\u65b0\u5f53\u524d\u8def\u5f84\u524d\u7f00\u548c\n        currentSum += node.val;\n\n        \/\/ \u68c0\u67e5\u662f\u5426\u5b58\u5728\u524d\u7f00\u548c = currentSum - targetSum\n        long need = currentSum - targetSum;\n        if (prefixSumCount.containsKey(need)) {\n            result += prefixSumCount.get(need);\n        }\n\n        \/\/ \u5c06\u5f53\u524d\u524d\u7f00\u548c\u52a0\u5165\u54c8\u5e0c\u8868\n        prefixSumCount.put(currentSum, prefixSumCount.getOrDefault(currentSum, 0) + 1);\n\n        \/\/ \u9012\u5f52\u5de6\u53f3\u5b50\u6811\n        dfs(node.left, currentSum);\n        dfs(node.right, currentSum);\n\n        \/\/ \u56de\u6eaf\uff1a\u79fb\u9664\u5f53\u524d\u524d\u7f00\u548c\uff08\u907f\u514d\u5f71\u54cd\u5176\u4ed6\u8def\u5f84\uff09\n        prefixSumCount.put(currentSum, prefixSumCount.get(currentSum) - 1);\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>\u4f7f\u7528\u00a0<strong>\u524d\u7f00\u548c\u601d\u60f3<\/strong>\uff1a\u82e5\u00a0<code>sum[A\u2192C] - sum[A\u2192B] = targetSum<\/code>\uff0c\u5219\u00a0<code>sum[B\u2192C] = targetSum<\/code>\uff1b<\/li>\n\n\n\n<li>\u7528\u00a0<strong>\u54c8\u5e0c\u8868\u8bb0\u5f55\u4ece\u6839\u5230\u5f53\u524d\u8282\u70b9\u8def\u5f84\u4e0a\u6240\u6709\u524d\u7f00\u548c\u7684\u51fa\u73b0\u6b21\u6570<\/strong>\uff1b<\/li>\n\n\n\n<li><strong>\u56de\u6eaf\u65f6\u5220\u9664\u5f53\u524d\u524d\u7f00\u548c<\/strong>\uff0c\u786e\u4fdd\u53ea\u7edf\u8ba1\u5f53\u524d DFS \u8def\u5f84\u4e0a\u7684\u524d\u7f00\u548c\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\u8bbf\u95ee\u4e00\u6b21\uff0c\u54c8\u5e0c\u8868\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>\u54c8\u5e0c\u8868\u6700\u591a\u5b58\u50a8\u00a0<code>h<\/code>\u00a0\u4e2a\u524d\u7f00\u548c\uff08<code>h<\/code>\u00a0\u4e3a\u6811\u9ad8\uff09\uff1b<\/li>\n\n\n\n<li>\u9012\u5f52\u6808\u6df1\u5ea6\u4e3a\u00a0<code>O(h)<\/code>\uff1b<\/li>\n\n\n\n<li>\u6700\u574f\u60c5\u51b5\uff08\u94fe\u8868\uff09\uff1a<code>h = n<\/code>\u00a0\u2192\u00a0<code>O(n)<\/code>\uff1b<\/li>\n\n\n\n<li>\u6700\u597d\u60c5\u51b5\uff08\u5e73\u8861\u6811\uff09\uff1a<code>h = log n<\/code>\u00a0\u2192\u00a0<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\u7528\u66b4\u529b DFS\uff1f<\/h3>\n\n\n\n<p>\u66b4\u529b\u505a\u6cd5\uff1a\u5bf9\u6bcf\u4e2a\u8282\u70b9\uff0c\u5411\u4e0b\u904d\u5386\u6240\u6709\u8def\u5f84\u6c42\u548c\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a<code>O(n\u00b2)<\/code>\uff08\u6bcf\u4e2a\u8282\u70b9\u4f5c\u4e3a\u8d77\u70b9\u904d\u5386\u4e00\u6b21\uff09<\/li>\n\n\n\n<li>\u5728\u00a0<code>n = 1000<\/code>\u00a0\u65f6\u52c9\u5f3a\u901a\u8fc7\uff0c\u4f46\u4e0d\u591f\u4f18\u96c5\uff0c\u4e14\u65e0\u6cd5\u5e94\u5bf9\u66f4\u5927\u89c4\u6a21\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u524d\u7f00\u548c\u7684\u6838\u5fc3\u601d\u60f3<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u7c7b\u6bd4\u6570\u7ec4\u4e2d\u7684\u201c\u548c\u4e3a K \u7684\u5b50\u6570\u7ec4\u201d\u95ee\u9898\uff08LeetCode 560\uff09<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>\u5728\u4e00\u6761\u4ece\u6839\u5230\u53f6\u7684\u8def\u5f84\u4e0a\uff0c\u8def\u5f84\u548c\u5177\u6709<strong>\u8fde\u7eed\u6027<\/strong>\u3002<br>\u8bbe\u4ece\u6839\u5230\u5f53\u524d\u8282\u70b9\u7684\u8def\u5f84\u548c\u4e3a <code>S<\/code>\uff0c\u82e5\u4e4b\u524d\u67d0\u5904\u524d\u7f00\u548c\u4e3a <code>S - targetSum<\/code>\uff0c<br>\u5219\u8fd9\u4e24\u70b9\u4e4b\u95f4\u7684\u8def\u5f84\u548c\u6b63\u597d\u4e3a <code>targetSum<\/code>\u3002<\/p>\n\n\n\n<p>\u4f8b\u5982\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8def\u5f84\uff1a<code>10 \u2192 5 \u2192 3<\/code>\uff0c\u524d\u7f00\u548c\u4f9d\u6b21\u4e3a\u00a0<code>10, 15, 18<\/code><\/li>\n\n\n\n<li><code>targetSum = 8<\/code>\uff0c\u5f53\u524d\u00a0<code>S = 18<\/code>\uff0c\u9700\u8981\u627e\u00a0<code>18 - 8 = 10<\/code><\/li>\n\n\n\n<li>\u53d1\u73b0\u524d\u7f00\u548c\u00a0<code>10<\/code>\u00a0\u51fa\u73b0\u8fc7 1 \u6b21 \u2192 \u627e\u5230\u4e00\u6761\u8def\u5f84\uff1a<code>5 \u2192 3<\/code><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e3a\u4ec0\u4e48\u9700\u8981\u56de\u6eaf\uff1f<\/h3>\n\n\n\n<p>\u56e0\u4e3a\u54c8\u5e0c\u8868\u8bb0\u5f55\u7684\u662f<strong>\u5f53\u524d DFS \u8def\u5f84\u4e0a\u7684\u524d\u7f00\u548c<\/strong>\u3002<br>\u5f53\u4ece\u5de6\u5b50\u6811\u8fd4\u56de\u65f6\uff0c\u5fc5\u987b<strong>\u79fb\u9664\u5de6\u5b50\u6811\u4ea7\u751f\u7684\u524d\u7f00\u548c<\/strong>\uff0c\u5426\u5219\u4f1a\u9519\u8bef\u5730\u5f71\u54cd\u53f3\u5b50\u6811\u7684\u7edf\u8ba1\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>\u6839\u4e3a <code>10<\/code>\uff0c\u5de6\u5b50\u6811\u8def\u5f84\u4ea7\u751f\u524d\u7f00\u548c <code>15<\/code>\uff0c\u82e5\u4e0d\u56de\u6eaf\uff0c<br>\u53f3\u5b50\u6811\u4f1a\u8bef\u4ee5\u4e3a <code>15<\/code> \u662f\u4ece\u6839\u5230\u53f3\u5b50\u6811\u67d0\u70b9\u7684\u524d\u7f00\u548c\uff0c\u5bfc\u81f4\u9519\u8bef\u8ba1\u6570\u3002<\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd17 \u8def\u5f84\u603b\u548c III \u9898\u76ee\u6765\u6e90\uff1a437. \u8def\u5f84\u603b\u548c III &#8211; \u529b\u6263\uff08LeetCode\uff09 \ud83d\udccc \u9898\u76ee [&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-453","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\/453","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=453"}],"version-history":[{"count":1,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/453\/revisions"}],"predecessor-version":[{"id":455,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/453\/revisions\/455"}],"wp:attachment":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/media?parent=453"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/categories?post=453"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/tags?post=453"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}