{"id":9032,"date":"2021-12-05T09:36:35","date_gmt":"2021-12-05T17:36:35","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=9032"},"modified":"2021-12-05T18:17:27","modified_gmt":"2021-12-06T02:17:27","slug":"leetcode-2097-valid-arrangement-of-pairs","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/graph\/leetcode-2097-valid-arrangement-of-pairs\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 2097. Valid Arrangement of Pairs"},"content":{"rendered":"\n

You are given a 0-indexed<\/strong> 2D integer array pairs<\/code> where pairs[i] = [starti<\/sub>, endi<\/sub>]<\/code>. An arrangement of pairs<\/code> is valid<\/strong> if for every index i<\/code> where 1 <= i < pairs.length<\/code>, we have endi-1<\/sub> == starti<\/sub><\/code>.<\/p>\n\n\n\n

Return any<\/strong> valid arrangement of <\/em>pairs<\/code>.<\/p>\n\n\n\n

Note:<\/strong> The inputs will be generated such that there exists a valid arrangement of pairs<\/code>.<\/p>\n\n\n\n

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

Input:<\/strong> pairs = [[5,1],[4,5],[11,9],[9,4]]\nOutput:<\/strong> [[11,9],[9,4],[4,5],[5,1]]\nExplanation:\n<\/strong>This is a valid arrangement since endi-1<\/sub> always equals starti<\/sub>.\nend0<\/sub> = 9 == 9 = start1<\/sub> \nend1<\/sub> = 4 == 4 = start2<\/sub>\nend2<\/sub> = 5 == 5 = start3<\/sub>\n<\/pre>\n\n\n\n
Example 2:<\/strong><\/p>\n\n\n\n
Input:<\/strong> pairs = [[1,3],[3,2],[2,1]]\nOutput:<\/strong> [[1,3],[3,2],[2,1]]\nExplanation:<\/strong>\nThis is a valid arrangement since endi-1<\/sub> always equals starti<\/sub>.\nend0<\/sub> = 3 == 3 = start1<\/sub>\nend1<\/sub> = 2 == 2 = start2<\/sub>\nThe arrangements [[2,1],[1,3],[3,2]] and [[3,2],[2,1],[1,3]] are also valid.\n<\/pre>\n\n\n\n
Example 3:<\/strong><\/p>\n\n\n\n
Input:<\/strong> pairs = [[1,2],[1,3],[2,1]]\nOutput:<\/strong> [[1,2],[2,1],[1,3]]\nExplanation:<\/strong>\nThis is a valid arrangement since endi-1<\/sub> always equals starti<\/sub>.\nend0<\/sub> = 2 == 2 = start1<\/sub>\nend1<\/sub> = 1 == 1 = start2<\/sub>\n<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n
  • 1 <= pairs.length <= 105<\/sup><\/code><\/li>
  • pairs[i].length == 2<\/code><\/li>
  • 0 <= starti<\/sub>, endi<\/sub> <= 109<\/sup><\/code><\/li>
  • starti<\/sub> != endi<\/sub><\/code><\/li>
  • No two pairs are exactly the same.<\/li>
  • There exists<\/strong> a valid arrangement of pairs<\/code>.<\/li><\/ul>\n\n\n\n
    Solution: Eulerian trail<\/strong><\/h2>\n\n\n\n
    The goal of the problem is to find a Eulerian trail in the graph.<\/p>\n\n\n\n
    If there is a vertex whose out degree – in degree == 1 which means it’s the starting vertex. Otherwise wise, the graph must have a Eulerian circuit thus we can start from any vertex.<\/p>\n\n\n\n
    We can use Hierholzer’s algorithm to find it.<\/p>\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> validArrangement(vector>& pairs) {    \n    unordered_map> g;\n    unordered_map degree; \/\/ out - in  \n    for (const auto& p : pairs) {\n      g[p[0]].push(p[1]);\n      ++degree[p[0]];\n      --degree[p[1]];\n    }\n    \n    int s = pairs[0][0];\n    for (const auto& [u, d] : degree)\n      if (d == 1) s = u;\n    \n    vector> ans;\n    function dfs = [&](int u) {\n      while (!g[u].empty()) {\n        int v = g[u].front(); g[u].pop();\n        dfs(v);\n        ans.push_back({u, v});\n      }\n    };\n    dfs(s);\n    return {rbegin(ans), rend(ans)};\n  }\n};\n<\/pre>\n\n<\/div>
    Python3<\/h2>\n
    \n\n
    \n# Author: Huahua\nclass Solution:\n  def validArrangement(self, pairs: List[List[int]]) -> List[List[int]]:\n    g = defaultdict(list)\n    d = defaultdict(int)\n    for u, v in pairs:\n      g[u].append(v)\n      d[u] += 1\n      d[v] -= 1\n    \n    s = pairs[0][0]\n    for u in d:\n      if d[u] == 1: s = u\n    \n    ans = []\n    def dfs(u: int) -> None:\n      while g[u]:\n        v = g[u].pop()\n        dfs(v)\n        ans.append([u, v])\n\n    dfs(s)\n    return ans[::-1]\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"
    You are given a 0-indexed 2D integer array pairs where pairs[i] = [starti, endi]. An arrangement of pairs is valid if for every index i where 1 <= i < pairs.length, we have endi-1 == starti. Return any valid arrangement of pairs.…<\/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":[741,77],"class_list":["post-9032","post","type-post","status-publish","format-standard","hentry","category-graph","tag-eulerian","tag-graph","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/9032","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=9032"}],"version-history":[{"count":4,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/9032\/revisions"}],"predecessor-version":[{"id":9037,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/9032\/revisions\/9037"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=9032"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=9032"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=9032"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}