Course Schedule II
Detailed guide and Python implementation for the 'Course Schedule II' problem.
1. 学ぶ
The 'Course Schedule II' problem is a key challenge in the Graphs section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Course Schedule II.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Course Schedule II carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
問題提起
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.
Return the ordering of courses you should take to finish all courses. If there are many valid answers, return any of them. If it is impossible to finish all courses, return an empty array.
Write a function findOrder(numCourses: int, prerequisites: List[List[int]]) -> List[int].
- •1 <= numCourses <= 2000
- •0 <= len(prerequisites) <= 5000
- •prerequisites[i].length == 2
- •0 <= ai, bi < numCourses
例
numCourses = 2, prerequisites = [[1,0]]
[0,1]
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].
numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]
[0,2,1,3]
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].
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
解決する準備はできましたか?
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インタビューの洞察とバリエーション
複雑さの分析の内訳
なぜ時間がかかるのか: Directly evaluates all possibilities.
なぜ宇宙なのか: Uses standard local memory.
なぜ時間がかかるのか: Optimized paths reduce total operations.
なぜ宇宙なのか: May trade memory for speed.
最適化されたソリューションの Python コード
最適化されたソリューションの Python コード
def find_order_opt(numCourses, prerequisites):
adj = {i: [] for i in range(numCourses)}
for crs, pre in prerequisites: adj[crs].append(pre)
output = []
visit, cycle = set(), set()
def dfs(crs):
if crs in cycle: return False
if crs in visit: return True
cycle.add(crs)
for pre in adj[crs]:
if not dfs(pre): return False
cycle.remove(crs)
visit.add(crs)
output.append(crs)
return True
for c in range(numCourses):
if not dfs(c) == False: return []
return outputブルート フォース コード (スポイラーガード付き)
ブルート フォース コード (スポイラーガード付き)
def find_order_brute(numCourses, prerequisites):
adj = {i: [] for i in range(numCourses)}
for crs, pre in prerequisites: adj[crs].append(pre)
res = []
def dfs(crs, visiting, visited):
if crs in visiting: return False
if crs in visited: return True
visiting.add(crs)
for pre in adj[crs]:
if not dfs(pre, visiting, visited): return False
visiting.remove(crs)
visited.add(crs)
res.append(crs)
return True
visit, vstd = set(), set()
for c in range(numCourses):
if not dfs(c, visit, vstd): return []
return resAlgorithm Pattern Checklist
When dealing with Graphs data patterns.
- Are constraints clear?
- Is there a linear or logarithmic optimization possible?
Key Revision Notes
Standard Graphs problem properties apply.
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