1462. Course Schedule IV

Description

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course ai first if you want to take course bi.

• For example, the pair [0, 1] indicates that you have to take course 0 before you can take course 1.

Prerequisites can also be indirect. If course a is a prerequisite of course b, and course b is a prerequisite of course c, then course a is a prerequisite of course c.

You are also given an array queries where queries[j] = [uj, vj]. For the jth query, you should answer whether course uj is a prerequisite of course vj or not.

Return a boolean array answer, where answer[j] is the answer to the jth query.

 

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]], queries = [[0,1],[1,0]]
Output: [false,true]
Explanation: The pair [1, 0] indicates that you have to take course 1 before you can take course 0.
Course 0 is not a prerequisite of course 1, but the opposite is true.

Example 2:

Input: numCourses = 2, prerequisites = [], queries = [[1,0],[0,1]]
Output: [false,false]
Explanation: There are no prerequisites, and each course is independent.

Example 3:

Input: numCourses = 3, prerequisites = [[1,2],[1,0],[2,0]], queries = [[1,0],[1,2]]
Output: [true,true]

 

Constraints:

• 2 <= numCourses <= 100
• 0 <= prerequisites.length <= (numCourses * (numCourses - 1) / 2)
• prerequisites[i].length == 2
• 0 <= ai, bi <= n - 1
• ai != bi
• All the pairs [ai, bi] are unique.
• The prerequisites graph has no cycles.
• 1 <= queries.length <= 104
• 0 <= ui, vi <= n - 1
• ui != vi

 

Solutions

Solution: Depth-First Search

• Time complexity: O(n²)
• Space complexity: O(n²)

 

JavaScript

/**
 * @param {number} numCourses
 * @param {number[][]} prerequisites
 * @param {number[][]} queries
 * @return {boolean[]}
 */
const checkIfPrerequisite = function (numCourses, prerequisites, queries) {
  const courses = Array.from({ length: numCourses }, () => []);
  const memo = Array.from({ length: numCourses }, () => {
    return new Array(numCourses).fill(null);
  });

  for (const [a, b] of prerequisites) {
    courses[b].push(a);
  }

  const isPrerequisite = (preCourse, course) => {
    if (preCourse === course) return true;
    if (memo[course][preCourse] !== null) {
      return memo[course][preCourse];
    }

    for (const pre of courses[course]) {
      if (isPrerequisite(preCourse, pre)) {
        memo[course][preCourse] = true;
        return true;
      }
    }
    memo[course][preCourse] = false;
    return false;
  };

  return queries.map(([a, b]) => isPrerequisite(a, b));
};