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This approach involves topologically sorting the courses based on their prerequisites and then calculating the minimal time to complete each course using dynamic programming.
(a,b) is a directed edge from a to b.Time Complexity: O(n + E), where n is the number of courses and E is the number of prerequisite relationships, due to traversing all nodes and edges once.
Space Complexity: O(n + E), needed to store the graph and additional arrays.
1```python
2def minTime(n, relations, time):
3 from collections import deque, defaultdict
4
5 adj = defaultdict(list)
6 indegree =
```This Python solution uses collections to define adjacency lists and maintains indegrees for each node. It efficiently processes courses using a deque for queue operations and updates the time required using a dp array, finally finding the maximum time needed to complete all courses.
This approach uses Depth-First Search (DFS) with memorization to efficiently compute the completion time for courses.
Time Complexity: O(n + E), visiting each node and edge at least once.
Space Complexity: O(n + E), due to storage for graph data and function call stack.
```This C implementation makes use of a recursive DFS function to calculate the minimum completion time for each course by traversing through its dependencies. Memorization is utilized to store the time taken to complete each course dp[u], thus optimizing the solution by preventing recalculations.