## Problem Statement

There are ‘N’ tasks, labeled from ‘0’ to ‘N-1’. Each task can have some prerequisite tasks which need to be completed before it can be scheduled. Given the number of tasks and a list of prerequisite pairs, find out if it is possible to schedule all the tasks.

Example 1:

``````Input: Tasks=3, Prerequisites=[0, 1], [1, 2]
Output: true
to finish before '2' can be scheduled. One possible scheduling of tasks is: [0, 1, 2]
``````

Example 2:

``````Input: Tasks=3, Prerequisites=[0, 1], [1, 2], [2, 0]
Output: false
Explanation: The tasks have a cyclic dependency, therefore they cannot be scheduled.
``````

Example 3:

``````Input: Tasks=6, Prerequisites=[2, 5], [0, 5], [0, 4], [1, 4], [3, 2], [1, 3]
Output: true
Explanation: A possible scheduling of tasks is: [0 1 4 3 2 5]
``````

## Solution

This problem is asking us to find out if it is possible to find a topological ordering of the given tasks. The tasks are equivalent to the vertices and the prerequisites are the edges.

We can use a similar algorithm as described in `Topological Sort` to find the topological ordering of the tasks. If the ordering does not include all the tasks, we will conclude that some tasks have cyclic dependencies.

## Code

Here is what our algorithm will look like:

NaN
NaN

. . .
You must run your code first

## Time Complexity

In step ‘d’, each task can become a source only once, and each edge (i.e., prerequisite) will be accessed and removed once. Therefore, the time complexity of the above algorithm will be O(V+E)O(V+E), where ‘V’ is the total number of tasks and ‘E’ is the total number of prerequisites.

## Space Complexity

The space complexity will be O(V+E), since we are storing all of the prerequisites for each task in an adjacency list.

### Similar Problems

Course Schedule: There are ‘N’ courses, labeled from ‘0’ to ‘N-1’. Each course can have some prerequisite courses which need to be completed before it can be taken. Given the number of courses and a list of prerequisite pairs, find if it is possible for a student to take all the courses.

Solution: This problem is exactly similar to our parent problem. In this problem, we have courses instead of tasks.