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Commit 4688815

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更新拓扑排序代码模版
1 parent 2f43b6d commit 4688815

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2 files changed

+80
-16
lines changed

2 files changed

+80
-16
lines changed
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import collections
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class Solution:
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# 拓扑排序,graph 中包含所有顶点的有向边关系(包括无边顶点)
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def topologicalSortingDFS(self, graph: dict):
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visited = set() # 记录当前顶点是否被访问过
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onStack = set() # 记录同一次深搜时,当前顶点是否被访问过
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order = [] # 用于存储拓扑序列
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hasCycle = False # 用于判断是否存在环
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def dfs(u):
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nonlocal hasCycle
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if u in onStack: # 同一次深度优先搜索时,当前顶点被访问过,说明存在环
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hasCycle = True
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if u in visited or hasCycle: # 当前节点被访问或者有环时直接返回
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return
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visited.add(u) # 标记节点被访问
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onStack.add(u) # 标记本次深搜时,当前顶点被访问
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for v in graph[u]: # 遍历顶点 u 的邻接顶点 v
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dfs(v) # 递归访问节点 v
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order.append(u) # 后序遍历顺序访问节点 u
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onStack.remove(u) # 取消本次深搜时的 顶点访问标记
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for u in graph:
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if u not in visited:
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dfs(u) # 递归遍历未访问节点 u
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if hasCycle: # 判断是否存在环
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return [] # 存在环,无法构成拓扑序列
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order.reverse() # 将后序遍历转为拓扑排序顺序
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return order # 返回拓扑序列
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def findOrder(self, n: int, edges):
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# 构建图
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graph = dict()
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for i in range(n):
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graph[i] = []
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for v, u in edges:
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graph[u].append(v)
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return self.topologicalSortingDFS(graph)
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print(Solution().findOrder(2, [[1,0]]))
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print(Solution().findOrder(4, [[1,0],[2,0],[3,1],[3,2]]))
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print(Solution().findOrder(1, []))
Lines changed: 32 additions & 16 deletions
Original file line numberDiff line numberDiff line change
@@ -1,25 +1,41 @@
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import collections
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class solution:
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def topologicalSorting(graph):
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indegrees = {u: 0 for u in graph}
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class Solution:
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# 拓扑排序,graph 中包含所有顶点的有向边关系(包括无边顶点)
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def topologicalSortingKahn(self, graph: dict):
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indegrees = {u: 0 for u in graph} # indegrees 用于记录所有节点入度
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for u in graph:
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for v in graph[u]:
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indegrees[v] += 1
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indegrees[v] += 1 # 统计所有节点入度
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# 将入度为 0 的顶点存入集合 S 中
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S = collections.deque([u for u in indegrees if indegrees[u] == 0])
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order = []
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order = []# order 用于存储拓扑序列
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while S:
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u = S.pop()
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order.append(u)
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for v in graph[u]:
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indegrees[v] -= 1
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if indegrees[v] == 0:
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S.append(v)
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u = S.pop()# 从集合中选择一个没有前驱的顶点 0
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order.append(u)# 将其输出到拓扑序列 order 中
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for v in graph[u]:# 遍历顶点 u 的邻接顶点 v
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indegrees[v] -= 1# 删除从顶点 u 出发的有向边
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if indegrees[v] == 0:# 如果删除该边后顶点 v 的入度变为 0
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S.append(v)# 将其放入集合 S 中
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size = len(indegrees)
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if size == len(S):
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return order
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return None
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if len(indegrees) != len(order): # 还有顶点未遍历(存在环),无法构成拓扑序列
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return []
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return order # 返回拓扑序列
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def findOrder(self, n: int, edges):
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# 构建图
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graph = dict()
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for i in range(n):
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graph[i] = []
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for u, v in edges:
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graph[u].append(v)
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return self.topologicalSortingKahn(graph)
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print(Solution().findOrder(2, [[1,0]]))
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print(Solution().findOrder(4, [[1,0],[2,0],[3,1],[3,2]]))
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print(Solution().findOrder(1, []))

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