Imagine that you are managing a supercomputer that runs jobs for your clients. A client can submit a set of computing jobs, numbered from 1 to n, and the dependencies among them. The dependencies are expressed as pairs. For example, (1, 2) means job 2 depends on job 1, i. e. job 2 can only start after job 1 finishes. Write a program that determines if it is possible to finish all the jobs without actually running them. Below are some example inputs and their expected outputs.

Input: number of jobs = 2, dependencies = [(1, 2)]
Output: true
Explanation: We can run job 1 first followed by job 2.
Input: number of jobs = 2, dependencies = [(1, 2), (2, 1)]
Output: false
Explanation: We need job 1 to finish before we can run job 2, and job 2 to finish before we can run job 1. It is clearly impossible.

Implement the method canFinish in job. h. In the written part of your answer, state and justify both the time and space complexity of your algorithm. Submit both the modified job. h file and the written complexity analysis.