{"id":476,"date":"2025-11-28T15:04:54","date_gmt":"2025-11-28T07:04:54","guid":{"rendered":"https:\/\/heyingnian.com\/?p=476"},"modified":"2025-11-28T15:09:08","modified_gmt":"2025-11-28T07:09:08","slug":"leetcode-207","status":"publish","type":"post","link":"https:\/\/heyingnian.com\/index.php\/2025\/11\/28\/leetcode-207\/","title":{"rendered":"\u8bfe\u7a0b\u8868"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\ud83d\udd17 \u8bfe\u7a0b\u8868<\/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\/course-schedule\/description\/?envType=study-plan-v2&amp;envId=top-100-liked\" target=\"_blank\" rel=\"noopener\">207. \u8bfe\u7a0b\u8868 &#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>\u4f60\u8fd9\u4e2a\u5b66\u671f\u5fc5\u987b\u9009\u4fee <code>numCourses<\/code> \u95e8\u8bfe\u7a0b\uff0c\u8bfe\u7a0b\u7f16\u53f7\u4e3a <code>0<\/code> \u5230 <code>numCourses - 1<\/code>\u3002<\/p>\n\n\n\n<p>\u67d0\u4e9b\u8bfe\u7a0b\u6709<strong>\u5148\u4fee\u8981\u6c42<\/strong>\uff0c\u4ee5\u6570\u7ec4 <code>prerequisites<\/code> \u7ed9\u51fa\uff0c\u5176\u4e2d <code>prerequisites[i] = [a\u1d62, b\u1d62]<\/code> \u8868\u793a\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u60f3\u8981\u5b66\u4e60\u8bfe\u7a0b <code>a\u1d62<\/code>\uff0c\u5fc5\u987b\u5148\u5b8c\u6210\u8bfe\u7a0b <code>b\u1d62<\/code>\u3002<\/p>\n<\/blockquote>\n\n\n\n<p>\u8bf7\u4f60\u5224\u65ad\u662f\u5426<strong>\u53ef\u80fd\u5b8c\u6210\u6240\u6709\u8bfe\u7a0b\u7684\u5b66\u4e60<\/strong>\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5982\u679c\u53ef\u4ee5\uff0c\u8fd4\u56de\u00a0<code>true<\/code>\uff1b<\/li>\n\n\n\n<li>\u5426\u5219\uff0c\u8fd4\u56de\u00a0<code>false<\/code>\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\">\u2705 \u793a\u4f8b\u89e3\u6790<\/h2>\n\n\n\n<p><strong>\u793a\u4f8b 1\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>\u8f93\u5165\uff1anumCourses = 2, prerequisites = [[1,0]]<br>\u8f93\u51fa\uff1atrue<br>\u89e3\u91ca\uff1a\u5148\u5b66\u8bfe\u7a0b 0\uff0c\u518d\u5b66\u8bfe\u7a0b 1\uff0c\u53ef\u884c\u3002<\/code><\/pre>\n\n\n\n<p><strong>\u793a\u4f8b 2\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>\u8f93\u5165\uff1anumCourses = 2, prerequisites = [[1,0],[0,1]]<br>\u8f93\u51fa\uff1afalse<br>\u89e3\u91ca\uff1a\u8bfe\u7a0b 0 \u4f9d\u8d56\u8bfe\u7a0b 1\uff0c\u8bfe\u7a0b 1 \u53c8\u4f9d\u8d56\u8bfe\u7a0b 0 \u2192 \u5f62\u6210\u5faa\u73af\u4f9d\u8d56\uff0c\u65e0\u6cd5\u5b8c\u6210\u3002<\/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><code>1 &lt;= numCourses &lt;= 2000<\/code><\/li>\n\n\n\n<li><code>0 &lt;= prerequisites.length &lt;= 5000<\/code><\/li>\n\n\n\n<li>\u6240\u6709\u8bfe\u7a0b\u5bf9\u4e92\u4e0d\u76f8\u540c<\/li>\n\n\n\n<li>\u8bfe\u7a0b\u7f16\u53f7\u5728\u00a0<code>[0, numCourses)<\/code>\u00a0\u8303\u56f4\u5185<\/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\u62d3\u6251\u6392\u5e8f\uff08Kahn \u7b97\u6cd5\uff09\u2014\u2014 O(V + E) \u65f6\u95f4\uff0cO(V + E) \u7a7a\u95f4<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>Solution {\n    public boolean canFinish(int numCourses, int&#91;]&#91;] prerequisites) {\n        \/\/ \u5165\u5ea6\u6570\u7ec4\uff1ard&#91;i] \u8868\u793a\u8bfe\u7a0b i \u7684\u5148\u4fee\u8bfe\u7a0b\u6570\u91cf\n        int&#91;] inDegree = new int&#91;numCourses];\n        \/\/ \u90bb\u63a5\u8868\uff1alist&#91;i] \u5b58\u50a8\u5b66\u5b8c\u8bfe\u7a0b i \u540e\u53ef\u89e3\u9501\u7684\u8bfe\u7a0b\n        List&lt;List&lt;Integer>> graph = new ArrayList&lt;>();\n        \n        for (int i = 0; i &lt; numCourses; i++) {\n            graph.add(new ArrayList&lt;>());\n        }\n\n        \/\/ \u6784\u5efa\u56fe\u4e0e\u5165\u5ea6\n        for (int&#91;] pre : prerequisites) {\n            int course = pre&#91;0];      \/\/ \u8981\u5b66\u7684\u8bfe\n            int prerequisite = pre&#91;1]; \/\/ \u5148\u4fee\u8bfe\n            graph.get(prerequisite).add(course);\n            inDegree&#91;course]++;\n        }\n\n        \/\/ \u521d\u59cb\u5316\u961f\u5217\uff1a\u6240\u6709\u5165\u5ea6\u4e3a 0 \u7684\u8bfe\u7a0b\uff08\u65e0\u5148\u4fee\u8981\u6c42\uff09\n        Queue&lt;Integer> queue = new LinkedList&lt;>();\n        for (int i = 0; i &lt; numCourses; i++) {\n            if (inDegree&#91;i] == 0) {\n                queue.offer(i);\n            }\n        }\n\n        \/\/ \u62d3\u6251\u6392\u5e8f\n        while (!queue.isEmpty()) {\n            int current = queue.poll();\n            numCourses--; \/\/ \u5b8c\u6210\u4e00\u95e8\u8bfe\u7a0b\n\n            \/\/ \u89e3\u9501\u540e\u7eed\u8bfe\u7a0b\n            for (int next : graph.get(current)) {\n                inDegree&#91;next]--;\n                if (inDegree&#91;next] == 0) {\n                    queue.offer(next);\n                }\n            }\n        }\n\n        \/\/ \u82e5\u6240\u6709\u8bfe\u7a0b\u90fd\u80fd\u5b8c\u6210\uff0c\u5219\u65e0\u73af\uff1b\u5426\u5219\u5b58\u5728\u5faa\u73af\u4f9d\u8d56\n        return numCourses == 0;\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>\u5c06\u8bfe\u7a0b\u4f9d\u8d56\u5173\u7cfb\u5efa\u6a21\u4e3a<strong>\u6709\u5411\u56fe<\/strong>\uff1b<\/li>\n\n\n\n<li>\u4f7f\u7528\u00a0<strong>Kahn \u7b97\u6cd5<\/strong>\u8fdb\u884c\u62d3\u6251\u6392\u5e8f\uff1b<\/li>\n\n\n\n<li>\u82e5\u6700\u7ec8\u80fd\u5904\u7406\u5b8c\u6240\u6709\u8bfe\u7a0b \u2192\u00a0<strong>\u65e0\u73af<\/strong>\u00a0\u2192 \u53ef\u5b8c\u6210\uff1b<\/li>\n\n\n\n<li>\u82e5\u5269\u4f59\u8bfe\u7a0b > 0 \u2192\u00a0<strong>\u5b58\u5728\u73af<\/strong>\u00a0\u2192 \u4e0d\u53ef\u5b8c\u6210\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(V + E)<\/code>\n<ul class=\"wp-block-list\">\n<li><code>V = numCourses<\/code>\uff08\u9876\u70b9\u6570\uff09<\/li>\n\n\n\n<li><code>E = prerequisites.length<\/code>\uff08\u8fb9\u6570\uff09<\/li>\n\n\n\n<li>\u6bcf\u4e2a\u8282\u70b9\u548c\u6bcf\u6761\u8fb9\u4ec5\u88ab\u8bbf\u95ee\u4e00\u6b21\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7a7a\u95f4\u590d\u6742\u5ea6<\/strong>\uff1a<code>O(V + E)<\/code>\n<ul class=\"wp-block-list\">\n<li>\u90bb\u63a5\u8868\u5b58\u50a8\u56fe\u7ed3\u6784\uff1b<\/li>\n\n\n\n<li>\u5165\u5ea6\u6570\u7ec4\u548c\u961f\u5217\u6700\u591a\u5b58\u50a8\u00a0<code>V<\/code>\u00a0\u4e2a\u5143\u7d20\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\">\u6838\u5fc3\u601d\u60f3\uff1a\u68c0\u6d4b\u6709\u5411\u56fe\u4e2d\u662f\u5426\u5b58\u5728\u73af<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u8bfe\u7a0b\u5b89\u6392\u95ee\u9898 \u21e8 \u6709\u5411\u56fe\u62d3\u6251\u6392\u5e8f\u95ee\u9898 \u21e8 \u5224\u73af\u95ee\u9898<\/strong><\/p>\n<\/blockquote>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6bcf\u95e8\u8bfe\u7a0b\u662f\u4e00\u4e2a<strong>\u8282\u70b9<\/strong>\uff1b<\/li>\n\n\n\n<li>\u6bcf\u4e2a\u5148\u4fee\u5173\u7cfb\u00a0<code>[a, b]<\/code>\u00a0\u662f\u4e00\u6761<strong>\u6709\u5411\u8fb9\u00a0<code>b \u2192 a<\/code><\/strong>\uff1b<\/li>\n\n\n\n<li>\u5982\u679c\u56fe\u4e2d\u5b58\u5728<strong>\u73af<\/strong>\uff0c\u5219\u65e0\u6cd5\u6ee1\u8db3\u6240\u6709\u4f9d\u8d56 \u2192 \u65e0\u6cd5\u5b8c\u6210\u8bfe\u7a0b\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e3a\u4ec0\u4e48\u7528\u62d3\u6251\u6392\u5e8f\uff1f<\/h3>\n\n\n\n<p>\u62d3\u6251\u6392\u5e8f\u7684\u5b9a\u4e49\u662f\uff1a<strong>\u5bf9\u6709\u5411\u65e0\u73af\u56fe\uff08DAG\uff09\u7684\u7ebf\u6027\u6392\u5e8f<\/strong>\uff0c\u4f7f\u5f97\u5bf9\u4e8e\u6bcf\u6761\u8fb9 <code>u \u2192 v<\/code>\uff0c<code>u<\/code> \u5728\u6392\u5e8f\u4e2d\u51fa\u73b0\u5728 <code>v<\/code> \u4e4b\u524d\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u2705 \u80fd\u5b8c\u6210\u62d3\u6251\u6392\u5e8f \u21e8 \u56fe\u65e0\u73af \u21e8 \u8bfe\u7a0b\u53ef\u5b8c\u6210<br>\u274c \u65e0\u6cd5\u5b8c\u6210\u62d3\u6251\u6392\u5e8f \u21e8 \u56fe\u6709\u73af \u21e8 \u8bfe\u7a0b\u4e0d\u53ef\u5b8c\u6210<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">Kahn \u7b97\u6cd5\u6d41\u7a0b<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8ba1\u7b97\u6bcf\u4e2a\u8282\u70b9\u7684\u5165\u5ea6<\/strong>\uff1b<\/li>\n\n\n\n<li><strong>\u5c06\u5165\u5ea6\u4e3a 0 \u7684\u8282\u70b9\u5165\u961f<\/strong>\uff08\u65e0\u4f9d\u8d56\uff0c\u53ef\u7acb\u5373\u5b66\u4e60\uff09\uff1b<\/li>\n\n\n\n<li><strong>\u4f9d\u6b21\u51fa\u961f\uff0c\u79fb\u9664\u5176\u51fa\u8fb9\uff0c\u66f4\u65b0\u90bb\u5c45\u5165\u5ea6<\/strong>\uff1b<\/li>\n\n\n\n<li><strong>\u82e5\u90bb\u5c45\u5165\u5ea6\u53d8\u4e3a 0\uff0c\u5165\u961f<\/strong>\uff1b<\/li>\n\n\n\n<li><strong>\u91cd\u590d\u76f4\u5230\u961f\u5217\u4e3a\u7a7a<\/strong>\uff1b<\/li>\n\n\n\n<li><strong>\u82e5\u5904\u7406\u7684\u8282\u70b9\u6570 = \u603b\u8282\u70b9\u6570 \u2192 \u65e0\u73af<\/strong>\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd17 \u8bfe\u7a0b\u8868 \u9898\u76ee\u6765\u6e90\uff1a207. \u8bfe\u7a0b\u8868 &#8211; \u529b\u6263\uff08LeetCode\uff09 \ud83d\udccc \u9898\u76ee\u63cf\u8ff0 \u4f60\u8fd9\u4e2a\u5b66\u671f\u5fc5\u987b [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12,40],"tags":[60,61,58,14],"class_list":["post-476","post","type-post","status-publish","format-standard","hentry","category-algorithm","category-graph","tag-graphs","tag-topological-sort","tag-dfs","tag-algorithm"],"_links":{"self":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/476","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=476"}],"version-history":[{"count":1,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/476\/revisions"}],"predecessor-version":[{"id":477,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/posts\/476\/revisions\/477"}],"wp:attachment":[{"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/media?parent=476"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/categories?post=476"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heyingnian.com\/index.php\/wp-json\/wp\/v2\/tags?post=476"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}