{"id":6841,"date":"2020-05-30T18:07:46","date_gmt":"2020-05-31T01:07:46","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=6841"},"modified":"2020-05-30T18:09:59","modified_gmt":"2020-05-31T01:09:59","slug":"leetcode-1462-course-schedule-iv","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/graph\/leetcode-1462-course-schedule-iv\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 1462. Course Schedule IV"},"content":{"rendered":"\n

There are a total of n<\/code> courses you have to take, labeled from 0<\/code> to n-1<\/code>.<\/p>\n\n\n\n

Some courses may have direct prerequisites, for example, to take course 0 you have first to take course 1, which is expressed as a pair: [1,0]<\/code><\/p>\n\n\n\n

Given the total number of courses n<\/code>, a list of direct prerequisite<\/code> pairs<\/strong> and a list of queries<\/code> pairs<\/strong>.<\/p>\n\n\n\n

You should answer for each queries[i]<\/code> whether the course queries[i][0]<\/code> is a prerequisite of the course queries[i][1]<\/code> or not.<\/p>\n\n\n\n

Return a list of boolean<\/em>, the answers to the given queries<\/code>.<\/p>\n\n\n\n

Please note that if course a<\/strong> is a prerequisite of course b<\/strong> and course b<\/strong> is a prerequisite of course c<\/strong>, then, course a<\/strong> is a prerequisite of course c<\/strong>.<\/p>\n\n\n\n

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

\"\"\/<\/figure>\n\n\n\n
Input:<\/strong> n = 2, prerequisites = [[1,0]], queries = [[0,1],[1,0]]\nOutput:<\/strong> [false,true]\nExplanation:<\/strong> course 0 is not a prerequisite of course 1 but the opposite is true.\n<\/pre>\n\n\n\n
Example 2:<\/strong><\/p>\n\n\n\n
Input:<\/strong> n = 2, prerequisites = [], queries = [[1,0],[0,1]]\nOutput:<\/strong> [false,false]\nExplanation:<\/strong> There are no prerequisites and each course is independent.\n<\/pre>\n\n\n\n
Example 3:<\/strong><\/p>\n\n\n\n
\"\"\/<\/figure>\n\n\n\n
Input:<\/strong> n = 3, prerequisites = [[1,2],[1,0],[2,0]], queries = [[1,0],[1,2]]\nOutput:<\/strong> [true,true]\n<\/pre>\n\n\n\n
Example 4:<\/strong><\/p>\n\n\n\n
Input:<\/strong> n = 3, prerequisites = [[1,0],[2,0]], queries = [[0,1],[2,0]]\nOutput:<\/strong> [false,true]\n<\/pre>\n\n\n\n
Example 5:<\/strong><\/p>\n\n\n\n
Input:<\/strong> n = 5, prerequisites = [[0,1],[1,2],[2,3],[3,4]], queries = [[0,4],[4,0],[1,3],[3,0]]\nOutput:<\/strong> [true,false,true,false]\n<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n
  • 2 <= n <= 100<\/code><\/li>
  • 0 <= prerequisite.length <= (n * (n - 1) \/ 2)<\/code><\/li>
  • 0 <= prerequisite[i][0], prerequisite[i][1] < n<\/code><\/li>
  • prerequisite[i][0] != prerequisite[i][1]<\/code><\/li>
  • The prerequisites graph has no cycles.<\/li>
  • The prerequisites graph has no repeated edges.<\/li>
  • 1 <= queries.length <= 10^4<\/code><\/li>
  • queries[i][0] != queries[i][1]<\/code><\/li><\/ul>\n\n\n\n
    Solution: Floyd-Warshall Algorithm (All pairs shortest paths<\/strong>)<\/h2>\n\n\n\n
    Time complexity: O(n^3 + q)
    Space complexity: O(n^2)<\/p>\n\n\n\n
    \n
    C++<\/h2>\n
    \n\n
    \n\/\/ Author: Huahua\nclass Solution {\npublic:\n  vector checkIfPrerequisite(int n, \n      vector>& prerequisites, vector>& queries) {\n    vector> g(n, vector(n));\n    for (const auto& p : prerequisites)\n      g[p[0]][p[1]] = 1;\n    for (int k = 0; k < n; ++k)\n      for (int i = 0; i < n; ++i)\n        for (int j = 0; j < n; ++j)          \n          g[i][j] |= g[i][k] & g[k][j];\n    vector ans;\n    for (const auto& q : queries)\n      ans.push_back(g[q[0]][q[1]]);\n    return ans;\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"
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