{"id":135,"date":"2025-08-22T16:39:05","date_gmt":"2025-08-22T08:39:05","guid":{"rendered":"https:\/\/heyingnian.com\/?p=135"},"modified":"2025-08-26T15:41:49","modified_gmt":"2025-08-26T07:41:49","slug":"leetcode-42","status":"publish","type":"post","link":"https:\/\/heyingnian.com\/index.php\/2025\/08\/22\/leetcode-42\/","title":{"rendered":"\u63a5\u96e8\u6c34"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\ud83d\udd17 \u63a5\u96e8\u6c34<\/h1>\n\n\n\n<p>\u9898\u76ee\u6765\u6e90\uff1a<a target=\"_blank\" rel=\"noreferrer noopener\"><\/a><a href=\"https:\/\/leetcode.cn\/problems\/trapping-rain-water\/description\/?envType=study-plan-v2&amp;envId=top-100-liked\" target=\"_blank\" rel=\"noopener\">42. \u63a5\u96e8\u6c34 &#8211; \u529b\u6263\uff08LeetCode\uff09<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83d\udccc \u9898\u76ee\u63cf\u8ff0<\/p>\n\n\n\n<p>\u7ed9\u5b9a <code>n<\/code> \u4e2a\u975e\u8d1f\u6574\u6570\u8868\u793a\u6bcf\u4e2a\u5bbd\u5ea6\u4e3a <code>1<\/code> \u7684\u67f1\u5b50\u7684\u9ad8\u5ea6\u56fe\uff0c\u8ba1\u7b97\u6309\u6b64\u6392\u5217\u7684\u67f1\u5b50\uff0c\u4e0b\u96e8\u4e4b\u540e\u80fd\u63a5\u591a\u5c11\u96e8\u6c34\u3002<\/p>\n\n\n\n<p>\u6bcf\u4e2a\u67f1\u5b50\u7684\u5bbd\u5ea6\u4e3a <code>1<\/code>\uff0c\u9ad8\u5ea6\u7531\u6570\u7ec4 <code>height<\/code> \u7ed9\u51fa\u3002<\/p>\n\n\n\n<p>\u8fd4\u56de\u53ef\u4ee5\u63a5\u4f4f\u7684\u96e8\u6c34\u7684<strong>\u603b\u91cf<\/strong>\uff08\u5355\u4f4d\uff1a\u9762\u79ef\uff09\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u2705 \u793a\u4f8b\u89e3\u6790<\/p>\n\n\n\n<p>\u793a\u4f8b 1\uff1a<\/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\/08\/image-1.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"412\" height=\"161\" data-original=\"https:\/\/heyingnian.com\/wp-content\/uploads\/2025\/08\/image-1.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-136\"  sizes=\"auto, (max-width: 412px) 100vw, 412px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8f93\u5165\uff1a<code>height = [0,1,0,2,1,0,1,3,2,1,2,1]<\/code><\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a<code>6<\/code><\/li>\n\n\n\n<li>\u89e3\u91ca\uff1a\u4e0a\u9762\u662f\u7531\u6570\u7ec4 [0,1,0,2,1,0,1,3,2,1,2,1] \u8868\u793a\u7684\u9ad8\u5ea6\u56fe\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u63a5 6 \u4e2a\u5355\u4f4d\u7684\u96e8\u6c34\uff08\u84dd\u8272\u90e8\u5206\u8868\u793a\u96e8\u6c34\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u793a\u4f8b 2\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8f93\u5165\uff1a<code>height = [4,2,0,3,2,5]<\/code><\/li>\n\n\n\n<li>\u8f93\u51fa\uff1a<code>9<\/code><\/li>\n\n\n\n<li>\u89e3\u91ca\uff1a\u4ece\u7d22\u5f15&nbsp;<code>2<\/code>&nbsp;\u5230&nbsp;<code>4<\/code>&nbsp;\u7684\u4f4e\u6d3c\u533a\u57df\u88ab\u4e24\u4fa7\u9ad8\u67f1\u5305\u56f4\uff0c\u53ef\u79ef\u6c34&nbsp;<code>9<\/code>&nbsp;\u5355\u4f4d\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u26a0\ufe0f \u63d0\u793a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>n == height.length<\/code><\/li>\n\n\n\n<li><code>1 &lt;= n &lt;= 2 \u00d7 10\u2074<\/code><\/li>\n\n\n\n<li><code>0 &lt;= height[i] &lt;= 10\u2075<\/code><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83d\udca1 \u89e3\u6cd5\uff1a\u5355\u8c03\u6808\uff08Monotonic Stack\uff09\u2014\u2014 O(n) \u65f6\u95f4\uff0cO(n) \u7a7a\u95f4<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><strong>class<\/strong> <strong>Solution<\/strong> {\n    <strong>public<\/strong> <strong>int<\/strong> <strong>trap<\/strong>(<strong>int<\/strong>&#91;] height) {\n        Stack&lt;Integer&gt; stack = <strong>new<\/strong> Stack&lt;&gt;();\n        <strong>int<\/strong> ans = 0;\n\n        <strong>for<\/strong> (<strong>int<\/strong> i = 0; i &lt; height.length; i++) {\n          \n            <strong>while<\/strong> (!stack.isEmpty() &amp;&amp; height&#91;i] &gt; height&#91;stack.peek()]) {\n                <strong>int<\/strong> bottom = stack.pop(); \n\n                <strong>if<\/strong> (stack.isEmpty()) {\n                    <strong>break<\/strong>; \n                }\n\n                <strong>int<\/strong> left = stack.peek(); \n                <strong>int<\/strong> waterHeight = Math.min(height&#91;left], height&#91;i]) - height&#91;bottom];\n                <strong>int<\/strong> width = i - left - 1; \n\n                ans += waterHeight * width; \n            }\n            stack.push(i); \n        }\n\n        <strong>return<\/strong> ans;\n    }\n}<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83d\udcca \u590d\u6742\u5ea6\u5206\u6790<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(n)<\/strong><br>\u6bcf\u4e2a\u7d22\u5f15\u6700\u591a\u5165\u6808\u548c\u51fa\u6808\u4e00\u6b21\uff0c\u6574\u4f53\u904d\u5386\u4e3a\u7ebf\u6027\u65f6\u95f4\u3002<\/li>\n\n\n\n<li><strong>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(n)<\/strong><br>\u6808\u7684\u7a7a\u95f4\u6700\u591a\u5b58\u50a8 <code>n<\/code> \u4e2a\u7d22\u5f15\uff0c\u5728\u6700\u574f\u60c5\u51b5\u4e0b\uff08\u9012\u51cf\u5e8f\u5217\uff09\u8fbe\u5230 O(n)\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83e\udde9 \u89e3\u9898\u601d\u8def<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6838\u5fc3\u601d\u60f3\uff1a\u51f9\u69fd\u79ef\u6c34<\/strong><br>\u96e8\u6c34\u53ea\u80fd\u5728\u201c\u51f9\u201d\u5f62\u533a\u57df\u4e2d\u79ef\u805a\uff0c\u5373\u5b58\u5728\u5de6\u53f3\u4e24\u4e2a\u201c\u9ad8\u70b9\u201d\uff0c\u4e2d\u95f4\u8f83\u4f4e\u3002<br>\u6bcf\u5f53\u51fa\u73b0\u4e00\u4e2a<strong>\u53f3\u4fa7\u66f4\u9ad8\u67f1\u5b50<\/strong>\u65f6\uff0c\u5c31\u53ef\u80fd\u4e0e\u524d\u9762\u7684\u51f9\u69fd\u5f62\u6210\u201c\u5bb9\u5668\u201d\u6765\u63a5\u6c34\u3002<\/li>\n\n\n\n<li><strong>\u5355\u8c03\u6808\u7684\u4f5c\u7528<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u7ef4\u62a4\u4e00\u4e2a<strong>\u5355\u8c03\u9012\u51cf<\/strong>\u7684\u67f1\u5b50\u9ad8\u5ea6\u7d22\u5f15\u6808\u3002<\/li>\n\n\n\n<li>\u5f53\u9047\u5230\u4e00\u4e2a\u66f4\u9ad8\u7684\u67f1\u5b50\uff08<code>height[i] &gt; height[stack.peek()]<\/code>\uff09\u65f6\uff0c\u8bf4\u660e\u53ef\u80fd\u5f62\u6210\u4e86\u4e00\u4e2a\u53f3\u8fb9\u754c\uff0c\u53ef\u4ee5\u5f00\u59cb\u8ba1\u7b97\u79ef\u6c34\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97\u79ef\u6c34\u9762\u79ef<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li><code>bottom<\/code>\uff1a\u5f39\u51fa\u7684\u6808\u9876\uff0c\u662f\u51f9\u69fd\u5e95\u90e8\uff08\u6700\u4f4e\u70b9\uff09<\/li>\n\n\n\n<li><code>left<\/code>\uff1a\u65b0\u7684\u6808\u9876\uff0c\u662f\u5de6\u8fb9\u754c<\/li>\n\n\n\n<li><code>i<\/code>\uff1a\u5f53\u524d\u7d22\u5f15\uff0c\u662f\u53f3\u8fb9\u754c<\/li>\n\n\n\n<li>\u6c34\u9762\u9ad8\u5ea6\uff1a<code>min(height[left], height[i])<\/code><\/li>\n\n\n\n<li>\u5b9e\u9645\u79ef\u6c34\u9ad8\u5ea6\uff1a<code>\u6c34\u9762\u9ad8\u5ea6 - bottom\u9ad8\u5ea6<\/code><\/li>\n\n\n\n<li>\u5bbd\u5ea6\uff1a<code>i - left - 1<\/code><\/li>\n\n\n\n<li>\u9762\u79ef\uff1a<code>\u9ad8\u5ea6 \u00d7 \u5bbd\u5ea6<\/code><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u4e3a\u4ec0\u4e48\u662f\u5355\u8c03\u9012\u51cf\uff1f<\/strong><br>\u53ea\u6709\u5f53\u67f1\u5b50\u9ad8\u5ea6\u4e0b\u964d\u65f6\uff0c\u624d\u53ef\u80fd\u5f62\u6210\u51f9\u69fd\u3002\u4e00\u65e6\u4e0a\u5347\uff0c\u5c31\u5c1d\u8bd5\u201c\u586b\u8865\u201d\u524d\u9762\u7684\u51f9\u9677\u533a\u57df\u3002<\/li>\n\n\n\n<li><strong>\u4e3e\u4f8b\u8bf4\u660e<\/strong>\uff1a<br>\u5bf9\u4e8e <code>[0,1,0,2,...]<\/code>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5f53&nbsp;<code>i=3<\/code>\uff08\u9ad8\u5ea6&nbsp;<code>2<\/code>\uff09\u5230\u6765\u65f6\uff0c\u53d1\u73b0\u5b83\u6bd4&nbsp;<code>stack.peek()<\/code>\uff08\u7d22\u5f15&nbsp;<code>2<\/code>\uff0c\u9ad8\u5ea6&nbsp;<code>0<\/code>\uff09\u9ad8\uff0c\u5f00\u59cb\u51fa\u6808\u3002<\/li>\n\n\n\n<li>\u5f39\u51fa&nbsp;<code>2<\/code>\uff08\u9ad8\u5ea6&nbsp;<code>0<\/code>\uff09\uff0c\u5de6\u8fb9\u754c\u662f&nbsp;<code>1<\/code>\uff08\u9ad8\u5ea6&nbsp;<code>1<\/code>\uff09\uff0c\u6c34\u9762\u9ad8\u5ea6\u4e3a&nbsp;<code>min(1,2)=1<\/code>\uff0c\u79ef\u6c34\u9ad8\u5ea6&nbsp;<code>1-0=1<\/code>\uff0c\u5bbd\u5ea6&nbsp;<code>3-1-1=1<\/code>\uff0c\u9762\u79ef&nbsp;<code>1<\/code>\u3002<\/li>\n\n\n\n<li>\u7ee7\u7eed\u5224\u65ad\u662f\u5426\u6bd4\u65b0\u7684\u6808\u9876\u9ad8\uff0c\u76f4\u5230\u6808\u6062\u590d\u5355\u8c03\u6027\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd17 \u63a5\u96e8\u6c34 \u9898\u76ee\u6765\u6e90\uff1a42. \u63a5\u96e8\u6c34 &#8211; \u529b\u6263\uff08LeetCode\uff09 \ud83d\udccc \u9898\u76ee\u63cf\u8ff0 \u7ed9\u5b9a n \u4e2a\u975e\u8d1f [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20,12],"tags":[19,14],"class_list":["post-135","post","type-post","status-publish","format-standard","hentry","category-double_pointers","category-algorithm","tag-monotonous_stack","tag-algorithm"],"_links":{"self":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/135","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=135"}],"version-history":[{"count":2,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/135\/revisions"}],"predecessor-version":[{"id":138,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/135\/revisions\/138"}],"wp:attachment":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/media?parent=135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/categories?post=135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/tags?post=135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}