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@@ -214,14 +214,15 @@ comments: true
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```python title="graph_adjacency_matrix.py"
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class GraphAdjMat:
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""" 基于邻接矩阵实现的无向图类 """
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"""基于邻接矩阵实现的无向图类"""
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# 顶点列表,元素代表“顶点值”,索引代表“顶点索引”
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vertices: list[int] = []
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# 邻接矩阵,行列索引对应“顶点索引”
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adj_mat: list[list[int]] = []
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def __init__(self, vertices: list[int], edges: list[list[int]]) -> None:
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""" 构造方法 """
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"""构造方法"""
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self.vertices: list[int] = []
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self.adj_mat: list[list[int]] = []
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# 添加顶点
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@@ -233,11 +234,11 @@ comments: true
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self.add_edge(e[0], e[1])
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def size(self) -> int:
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""" 获取顶点数量 """
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"""获取顶点数量"""
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return len(self.vertices)
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def add_vertex(self, val: int) -> None:
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""" 添加顶点 """
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"""添加顶点"""
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n = self.size()
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# 向顶点列表中添加新顶点的值
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self.vertices.append(val)
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@@ -249,7 +250,7 @@ comments: true
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row.append(0)
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def remove_vertex(self, index: int) -> None:
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""" 删除顶点 """
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"""删除顶点"""
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if index >= self.size():
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raise IndexError()
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# 在顶点列表中移除索引 index 的顶点
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@@ -261,7 +262,7 @@ comments: true
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row.pop(index)
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def add_edge(self, i: int, j: int) -> None:
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""" 添加边 """
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"""添加边"""
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# 参数 i, j 对应 vertices 元素索引
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# 索引越界与相等处理
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if i < 0 or j < 0 or i >= self.size() or j >= self.size() or i == j:
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@@ -271,7 +272,7 @@ comments: true
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self.adj_mat[j][i] = 1
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def remove_edge(self, i: int, j: int) -> None:
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""" 删除边 """
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"""删除边"""
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# 参数 i, j 对应 vertices 元素索引
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# 索引越界与相等处理
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if i < 0 or j < 0 or i >= self.size() or j >= self.size() or i == j:
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@@ -280,7 +281,7 @@ comments: true
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self.adj_mat[j][i] = 0
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def print(self) -> None:
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""" 打印邻接矩阵 """
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"""打印邻接矩阵"""
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print("顶点列表 =", self.vertices)
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print("邻接矩阵 =")
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print_matrix(self.adj_mat)
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@@ -966,9 +967,10 @@ comments: true
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```python title="graph_adjacency_list.py"
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class GraphAdjList:
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""" 基于邻接表实现的无向图类 """
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"""基于邻接表实现的无向图类"""
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def __init__(self, edges: list[list[Vertex]]) -> None:
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""" 构造方法 """
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"""构造方法"""
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# 邻接表,key: 顶点,value:该顶点的所有邻接顶点
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self.adj_list = dict[Vertex, Vertex]()
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# 添加所有顶点和边
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@@ -978,11 +980,11 @@ comments: true
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self.add_edge(edge[0], edge[1])
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def size(self) -> int:
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""" 获取顶点数量 """
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"""获取顶点数量"""
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return len(self.adj_list)
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def add_edge(self, vet1: Vertex, vet2: Vertex) -> None:
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""" 添加边 """
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"""添加边"""
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if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:
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raise ValueError
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# 添加边 vet1 - vet2
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@@ -990,7 +992,7 @@ comments: true
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self.adj_list[vet2].append(vet1)
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def remove_edge(self, vet1: Vertex, vet2: Vertex) -> None:
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""" 删除边 """
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"""删除边"""
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if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:
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raise ValueError
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# 删除边 vet1 - vet2
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@@ -998,14 +1000,14 @@ comments: true
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self.adj_list[vet2].remove(vet1)
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def add_vertex(self, vet: Vertex) -> None:
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""" 添加顶点 """
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"""添加顶点"""
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if vet in self.adj_list:
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return
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# 在邻接表中添加一个新链表
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self.adj_list[vet] = []
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def remove_vertex(self, vet: Vertex) -> None:
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""" 删除顶点 """
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"""删除顶点"""
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if vet not in self.adj_list:
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raise ValueError
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# 在邻接表中删除顶点 vet 对应的链表
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@@ -1016,7 +1018,7 @@ comments: true
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self.adj_list[vertex].remove(vet)
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def print(self) -> None:
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""" 打印邻接表 """
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"""打印邻接表"""
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print("邻接表 =")
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for vertex in self.adj_list:
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tmp = [v.val for v in self.adj_list[vertex]]
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@@ -94,7 +94,7 @@ BFS 通常借助「队列」来实现。队列具有“先入先出”的性质
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```python title="graph_bfs.py"
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def graph_bfs(graph: GraphAdjList, start_vet: Vertex) -> list[Vertex]:
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""" 广度优先遍历 BFS """
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"""广度优先遍历 BFS"""
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# 使用邻接表来表示图,以便获取指定顶点的所有邻接顶点
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# 顶点遍历序列
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res = []
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@@ -105,13 +105,13 @@ BFS 通常借助「队列」来实现。队列具有“先入先出”的性质
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# 以顶点 vet 为起点,循环直至访问完所有顶点
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while len(que) > 0:
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vet = que.popleft() # 队首顶点出队
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res.append(vet) # 记录访问顶点
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res.append(vet) # 记录访问顶点
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# 遍历该顶点的所有邻接顶点
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for adj_vet in graph.adj_list[vet]:
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if adj_vet in visited:
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continue # 跳过已被访问过的顶点
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continue # 跳过已被访问过的顶点
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que.append(adj_vet) # 只入队未访问的顶点
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visited.add(adj_vet) # 标记该顶点已被访问
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visited.add(adj_vet) # 标记该顶点已被访问
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# 返回顶点遍历序列
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return res
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```
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@@ -379,18 +379,18 @@ BFS 通常借助「队列」来实现。队列具有“先入先出”的性质
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```python title="graph_dfs.py"
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def dfs(graph: GraphAdjList, visited: set[Vertex], res: list[Vertex], vet: Vertex):
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""" 深度优先遍历 DFS 辅助函数 """
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res.append(vet) # 记录访问顶点
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visited.add(vet) # 标记该顶点已被访问
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"""深度优先遍历 DFS 辅助函数"""
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res.append(vet) # 记录访问顶点
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visited.add(vet) # 标记该顶点已被访问
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# 遍历该顶点的所有邻接顶点
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for adjVet in graph.adj_list[vet]:
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if adjVet in visited:
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continue # 跳过已被访问过的顶点
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continue # 跳过已被访问过的顶点
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# 递归访问邻接顶点
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dfs(graph, visited, res, adjVet)
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def graph_dfs(graph: GraphAdjList, start_vet: Vertex) -> list[Vertex]:
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""" 深度优先遍历 DFS """
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"""深度优先遍历 DFS"""
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# 顶点遍历序列
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res = []
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# 哈希表,用于记录已被访问过的顶点
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