# 000207-courses-schedule

### Problem

<https://leetcode.com/problems/course-schedule/description/>

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] = \[ai, bi] indicates that you must take course bi first if you want to take course ai.

For example, the pair \[0, 1], indicates that to take course 0 you have to first take course 1. Return true if you can finish all courses. Otherwise, return false.

Example 1:

Input: numCourses = 2, prerequisites = \[\[1,0]] Output: true Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So it is possible.

Example 2:

Input: numCourses = 2, prerequisites = \[\[1,0],\[0,1]] Output: false Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.

Constraints:

1 <= numCourses <= 2000 0 <= prerequisites.length <= 5000 prerequisites\[i].length == 2 0 <= ai, bi < numCourses All the pairs prerequisites\[i] are unique.

### Solution

BFS

```python
class Solution:
    def canFinish(self, numCourses: int, prerequisites: List[List[int]]) -> bool:
        courses, indegree = collections.defaultdict(list), [0]*numCourses
        for a, b in prerequisites:
            courses[b].append(a)
            indegree[a] += 1
        queue = collections.deque()
        # no dependencies, add into queue
        for c in range(numCourses):
            if indegree[c] == 0:
                queue.append(c)
        completedCourses = len(queue)
        # print("complectd courses: ", completedCourses)
        while queue:
            start = queue.popleft()
            for c in courses[start]:
                indegree[c] -= 1
                if indegree[c] == 0:
                    queue.append(c)
                    completedCourses += 1
        
        return completedCourses == numCourses
```


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