Package g2001_2100.s2050_parallel_courses_iii

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    2050 - Parallel Courses III\.

    Hard

    You are given an integer n, which indicates that there are n courses labeled from 1 to n. You are also given a 2D integer array relations where <code>relationsj = prevCourse<sub>j</sub>, nextCourse<sub>j</sub></code> denotes that course <code>prevCourse<sub>j</sub></code> has to be completed before course <code>nextCourse<sub>j</sub></code> (prerequisite relationship). Furthermore, you are given a 0-indexed integer array time where time[i] denotes how many months it takes to complete the <code>(i+1)<sup>th</sup></code> course.

    You must find the minimum number of months needed to complete all the courses following these rules:

    • You may start taking a course at any time if the prerequisites are met.

    • Any number of courses can be taken at the same time.

    Return the minimum number of months needed to complete all the courses.

    Note: The test cases are generated such that it is possible to complete every course (i.e., the graph is a directed acyclic graph).

    Example 1:

    Input: n = 3, relations = \[\[1,3],2,3], time = 3,2,5

    Output: 8

    Explanation:

    The figure above represents the given graph and the time required to complete each course.

    We start course 1 and course 2 simultaneously at month 0.

    Course 1 takes 3 months and course 2 takes 2 months to complete respectively.

    Thus, the earliest time we can start course 3 is at month 3, and the total time required is 3 + 5 = 8 months.

    Example 2:

    Input: n = 5, relations = \[\[1,5],2,5,3,5,3,4,4,5], time = 1,2,3,4,5

    Output: 12

    Explanation: The figure above represents the given graph and the time required to complete each course.

    You can start courses 1, 2, and 3 at month 0.

    You can complete them after 1, 2, and 3 months respectively.

    Course 4 can be taken only after course 3 is completed, i.e., after 3 months. It is completed after 3 + 4 = 7 months.

    Course 5 can be taken only after courses 1, 2, 3, and 4 have been completed, i.e., after max(1,2,3,7) = 7 months.

    Thus, the minimum time needed to complete all the courses is 7 + 5 = 12 months.

    Constraints:

    • <code>1 <= n <= 5 * 10<sup>4</sup></code>

    • <code>0 <= relations.length <= min(n * (n - 1) / 2, 5 * 10<sup>4</sup>)</code>

    • relations[j].length == 2

    • <code>1 <= prevCourse<sub>j</sub>, nextCourse<sub>j</sub><= n</code>

    • <code>prevCourse<sub>j</sub> != nextCourse<sub>j</sub></code>

    • All the pairs <code>prevCourse<sub>j</sub>, nextCourse<sub>j</sub></code> are unique.

    • time.length == n

    • <code>1 <= timei<= 10<sup>4</sup></code>

    • The given graph is a directed acyclic graph.

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer minimumTime(Integer n, Array<IntArray> relations, IntArray time)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait