# 207. Course Schedule / Medium

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 <= 10^5
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• All the pairs prerequisites[i] are unique.

# Solution 1: Backtracking / DFS

## 效能

### Complexity

• Time Complexity: O(|E|+|V|^2), where |V| is the number of courses, and |E| is the number of dependencies.
• Space Complexity: O(|E|+|V|), with the same denotation as in the above time complexity.

### LeetCode Result

• Runtime: TLE
• Memory Usage: TLE

# Solution 2: Backtracking / Postorder DFS

## 思路

1. 目前這次 DFS 的路徑是否有走過重複的點
2. 之前的 DFS 中是否有走過重複的點 ## 效能

### Complexity

• Time Complexity: O(|E|+|V|), where |V| is the number of courses, and |E| is the number of dependencies.
• Space Complexity: O(|E|+|V|), with the same denotation as in the above time complexity.

### LeetCode Result

• Runtime: 12 ms
• Memory Usage: 13.8 MB

# Solution 3: Topological Sort / BFS

## 思路 Topological Sort（拓樸排序法）便是可以將 DAG 進行排序的演算法。同時也能利用排序的結果來判斷目前的圖是否為 DAG。 Topological Sort 的過程如動畫： ## 效能

### Complexity

• Time Complexity: O(|E|+|V|), where |V| is the number of courses, and |E| is the number of dependencies.
• Space Complexity: O(|E|+|V|), with the same denotation as in the above time complexity.

### LeetCode Result

• Runtime: 18 ms
• Memory Usage: 13.3 MB