1. What is the runtime complexity of your solution? 2. What is the space complexity of your solution? 4. 3. What data structure you have used to solve this problem? Is your solution optimum? If not, what may be the optimum solution?

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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] = [a, b] indicates that
you must take course be first if you want to take course a..
For example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.
Return the ordering of courses you should take to finish all courses. If there are many valid answers,
return any of them. If it is impossible to finish all courses, return an empty array.
Example 1:
Input: numCourses = 2, prerequisites = [[1,0]]
Output: [0,1]
Explanation: There are a total of 2 courses to take. To take course 1 you should have
finished course 0. So the correct course order is [0,1].
Example 2:
Input: numCourses = 4, prerequisites = [[1,0], [2,0],[3,1],[3,2]]
Output: [0,2,1,3]
Explanation: There are a total of 4 courses to take. To take course 3 you should have
finished both courses 1 and 2. Both courses 1 and 2 should be taken after you
finished course 0.
So one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3].
Example 3:
Input: numCourses = 1, prerequisites =
[]
Output: [0]
Constraints:
●
●
●
●
1 <= numCourses <= 2000
0 <= prerequisites.length <= numCourses (numCourses - 1)
prerequisites [i].length == 2
0 <= a₁, b₁ < numCourses
a₁ != b₁
All the pairs [a, b] are distinct.
*
Transcribed Image Text: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] = [a, b] indicates that you must take course be first if you want to take course a.. For example, the pair [0, 1], indicates that to take course 0 you have to first take course 1. Return the ordering of courses you should take to finish all courses. If there are many valid answers, return any of them. If it is impossible to finish all courses, return an empty array. Example 1: Input: numCourses = 2, prerequisites = [[1,0]] Output: [0,1] Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is [0,1]. Example 2: Input: numCourses = 4, prerequisites = [[1,0], [2,0],[3,1],[3,2]] Output: [0,2,1,3] Explanation: There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0. So one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3]. Example 3: Input: numCourses = 1, prerequisites = [] Output: [0] Constraints: ● ● ● ● 1 <= numCourses <= 2000 0 <= prerequisites.length <= numCourses (numCourses - 1) prerequisites [i].length == 2 0 <= a₁, b₁ < numCourses a₁ != b₁ All the pairs [a, b] are distinct. *
1. What is the runtime complexity of your solution?
2. What is the space complexity of your solution?
3. What data structure you have used to solve this problem?
4. Is your solution optimum? If not, what may be the optimum
solution?
Transcribed Image Text:1. What is the runtime complexity of your solution? 2. What is the space complexity of your solution? 3. What data structure you have used to solve this problem? 4. Is your solution optimum? If not, what may be the optimum solution?
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