{"id":5556,"date":"2019-09-15T16:07:27","date_gmt":"2019-09-15T23:07:27","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=5556"},"modified":"2019-09-16T21:37:32","modified_gmt":"2019-09-17T04:37:32","slug":"leetcode-1192-critical-connections-in-a-network","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/graph\/leetcode-1192-critical-connections-in-a-network\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 1192. Critical Connections in a Network"},"content":{"rendered":"\n

There are n<\/code> servers numbered from 0<\/code> to n-1<\/code> connected by undirected server-to-server connections<\/code> forming a network where connections[i] = [a, b]<\/code> represents a connection between servers a<\/code> and b<\/code>. Any server can reach any other server directly or indirectly through the network.<\/p>\n\n\n\n

A critical connection<\/em> is a connection that, if removed, will make some server unable to reach some other server.<\/p>\n\n\n\n

Return all critical connections in the network in any order.<\/p>\n\n\n\n

Example 1:<\/strong><\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n
Input:<\/strong> n = 4, connections = [[0,1],[1,2],[2,0],[1,3]]\nOutput:<\/strong> [[1,3]]\nExplanation:<\/strong> [[3,1]] is also accepted.\n<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n
  • 1 <= n <= 10^5<\/code><\/li>
  • n-1 <= connections.length <= 10^5<\/code><\/li>
  • connections[i][0] != connections[i][1]<\/code><\/li>
  • There are no repeated connections.<\/li><\/ul>\n\n\n\n
    Solution: Tarjan<\/strong><\/h2>\n\n\n\n
    Time complexity: O(v+e)
    Space complexity: O(v+e)<\/p>\n\n\n\n
    \n
    C++<\/h2>\n
    \n\n
    \n\/\/ Author: Huahua\nclass Solution {\npublic:\n  vector> criticalConnections(int n, vector>& connections) {\n    vector> g(n);\n    vector ts(n, INT_MAX);\n    vector> ans;\n    int t = 0;\n    \n    function tarjan = [&](int i, int p) {\n      int min_i = ts[i] = ++t;\n      for (int j : g[i]) {\n        if (ts[j] == INT_MAX) {\n          int min_j = tarjan(j, i);\n          min_i = min(min_i, min_j);\n          if (ts[i] < min_j)\n            ans.push_back({i, j});\n        } else if (j != p) {\n          min_i = min(min_i, ts[j]);\n        }\n      }\n      return min_i;\n    };\n    \n    for (const auto& e : connections) {\n      g[e[0]].push_back(e[1]);\n      g[e[1]].push_back(e[0]);\n    }\n    \n    tarjan(0, -1);\n    return ans;\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"
    There are n servers numbered from 0 to n-1 connected by undirected server-to-server connections forming a network where connections[i] = [a, b] represents a connection between servers a and b. Any server can reach any other server directly or…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[76],"tags":[77,217,499,500],"class_list":["post-5556","post","type-post","status-publish","format-standard","hentry","category-graph","tag-graph","tag-hard","tag-ove","tag-tarjan","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5556","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/comments?post=5556"}],"version-history":[{"count":2,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5556\/revisions"}],"predecessor-version":[{"id":5564,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5556\/revisions\/5564"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=5556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=5556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=5556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}