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73 lines
2.3 KiB
Plaintext
73 lines
2.3 KiB
Plaintext
---
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title: '210. Course Schedule II'
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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
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icon: dot
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sidebar:
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label: 'Course Schedule II'
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badge: 'Medium'
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---
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<Badge variant="accent">Depth-First Search</Badge>
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### Example 1:
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- Input: `numCourses = 2, prerequisites = [[1,0]]`
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- Output: `[0,1]`
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- 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]`.
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### Example 2:
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- Input: `numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]`
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- Output: `[0,2,1,3]`
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- 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]`.
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### Example 3:
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- Input: `numCourses = 1, prerequisites = []`
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- Output: `[0]`
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### Constraints:
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- `1 <= numCourses <= 2000`
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- `0 <= prerequisites.length <= numCourses * (numCourses - 1)`
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- `prerequisites[i].length == 2`
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- `0 <= ai, bi < numCourses`
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- `ai != bi`
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- All the pairs [ai, bi] are distinct.
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## Solution
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```py
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class Solution:
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def findOrder(self, numCourses: int, prerequisites: list[list[int]]) -> list[int]:
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prereq = {c: [] for c in range(numCourses)}
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for crs, pre in prerequisites:
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prereq[crs].append(pre)
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# course has 3 possible states:
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# visited -> crs has been added to output
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# visiting -> crs not added to output, but added to cycle
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# unvisited -> crs not added to output nor cycle
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output = []
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visit, cycle = set(), set()
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def dfs(crs):
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if crs in cycle:
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return False
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if crs in visit:
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return True
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cycle.add(crs)
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for pre in prereq[crs]:
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if dfs(pre) == False:
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return False
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cycle.remove(crs)
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visit.add(crs)
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output.append(crs)
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return True
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for c in range(numCourses):
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if dfs(c) == False:
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return []
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return output
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```
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