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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```javascript
2function minTime(n, relations, time) {
3 const indegree = new Array(n + 1).fill(0);
4 const adj = Array.from({ length: n + 1 }, () => []);
5 const dp = new Array(n + 1).fill(0);
6
7 for (const [u, v] of relations) {
8 adj[u].push(v);
9 indegree[v]++;
This JavaScript implementation constructs an adjacency list and degrees array to use in topological sorting. By processing with a queue, it determines course completion order, updating a `dp` to store the minimum computation times and ultimately derives the result as the maximum time needed.
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 Python implementation effectively uses DFS with a dictionary adj to trace course dependencies, and a dp array to memorize computed outcomes. The result is determined by calculating the maximum time taken from these evaluated paths.