Update graph_adjacency_matrix.py
理解K神这个实现主要是为了演示邻接矩阵的基本原理，但在实际使用中可能会遇到一些限制：在实际应用中，通常使用顶点的值而不是索引来操作图。所以，为了更“公平”地与邻接表方法的对比，进行了改进： 1. 引入 vertex_map：使用字典 vertex_map 来存储顶点值到索引的映射。 2. 基于值的操作：add_vertex, remove_vertex, add_edge, 和 remove_edge 方法现在都使用顶点值而不是索引。这使得图的操作更加直观和用户友好。 3. 动态索引管理：在 remove_vertex 方法中，更新了剩余顶点的索引映射。这确保了在删除顶点后，其他顶点的索引仍然保持正确。
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@ -4,113 +4,88 @@ Created Time: 2023-02-23
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Author: krahets (krahets@163.com)
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Author: krahets (krahets@163.com)
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"""
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"""
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import sys
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class ImprovedGraphAdjMat:
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from pathlib import Path
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sys.path.append(str(Path(__file__).parent.parent))
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from modules import Vertex, print_matrix
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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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def __init__(self, vertices: list[int], edges: list[list[int]]):
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def __init__(self, vertices: list[int], edges: list[list[int]]):
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"""构造方法"""
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self.vertex_map = {} # 用于存储顶点值到索引的映射
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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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self.vertices = []
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self.vertices: list[int] = []
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self.adj_mat = []
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# 邻接矩阵，行列索引对应“顶点索引”
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self.adj_mat: list[list[int]] = []
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# 添加顶点
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for val in vertices:
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for val in vertices:
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self.add_vertex(val)
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self.add_vertex(val)
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# 添加边
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# 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
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for e in edges:
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for e in edges:
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self.add_edge(e[0], e[1])
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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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return len(self.vertices)
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def add_vertex(self, val: int):
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def add_vertex(self, val: int):
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"""添加顶点"""
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if val in self.vertex_map:
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n = self.size()
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return # 如果顶点已存在，直接返回
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# 向顶点列表中添加新顶点的值
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index = len(self.vertices)
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self.vertex_map[val] = index
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self.vertices.append(val)
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self.vertices.append(val)
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# 在邻接矩阵中添加一行
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new_row = [0] * n
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# 更新邻接矩阵
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self.adj_mat.append(new_row)
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if self.adj_mat:
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# 在邻接矩阵中添加一列
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for row in self.adj_mat:
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for row in self.adj_mat:
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row.append(0)
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row.append(0)
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self.adj_mat.append([0] * (index + 1))
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def remove_vertex(self, index: int):
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def remove_vertex(self, val: int):
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"""删除顶点"""
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if val not in self.vertex_map:
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if index >= self.size():
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return # 如果顶点不存在，直接返回
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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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index = self.vertex_map[val]
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# 更新顶点列表和映射
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self.vertices.pop(index)
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self.vertices.pop(index)
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# 在邻接矩阵中删除索引 index 的行
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del self.vertex_map[val]
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for v in self.vertices[index:]:
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self.vertex_map[v] -= 1
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# 更新邻接矩阵
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self.adj_mat.pop(index)
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self.adj_mat.pop(index)
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# 在邻接矩阵中删除索引 index 的列
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for row in self.adj_mat:
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for row in self.adj_mat:
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row.pop(index)
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row.pop(index)
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def add_edge(self, i: int, j: int):
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def add_edge(self, v1: int, v2: int):
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"""添加边"""
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if v1 not in self.vertex_map or v2 not in self.vertex_map:
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# 参数 i, j 对应 vertices 元素索引
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raise ValueError("Vertex not found")
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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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i, j = self.vertex_map[v1], self.vertex_map[v2]
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raise IndexError()
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# 在无向图中，邻接矩阵关于主对角线对称，即满足 (i, j) == (j, i)
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self.adj_mat[i][j] = 1
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self.adj_mat[i][j] = 1
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self.adj_mat[j][i] = 1
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self.adj_mat[j][i] = 1
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def remove_edge(self, i: int, j: int):
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def remove_edge(self, v1: int, v2: int):
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"""删除边"""
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if v1 not in self.vertex_map or v2 not in self.vertex_map:
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# 参数 i, j 对应 vertices 元素索引
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raise ValueError("Vertex not found")
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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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i, j = self.vertex_map[v1], self.vertex_map[v2]
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raise IndexError()
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self.adj_mat[i][j] = 0
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self.adj_mat[i][j] = 0
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self.adj_mat[j][i] = 0
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self.adj_mat[j][i] = 0
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def print(self):
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def print(self):
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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("顶点列表 =", self.vertices)
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print("邻接矩阵 =")
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print("邻接矩阵 =")
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print_matrix(self.adj_mat)
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for row in self.adj_mat:
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print(row)
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# 使用示例
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graph = ImprovedGraphAdjMat([1, 3, 2, 5, 4], [[1, 3], [1, 5], [3, 2], [2, 5], [2, 4], [5, 4]])
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print("\n初始化后，图为")
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graph.print()
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"""Driver Code"""
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graph.add_edge(1, 2)
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if __name__ == "__main__":
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print("\n添加边 1-2 后，图为")
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# 初始化无向图
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graph.print()
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# 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
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vertices = [1, 3, 2, 5, 4]
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edges = [[0, 1], [0, 3], [1, 2], [2, 3], [2, 4], [3, 4]]
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graph = GraphAdjMat(vertices, edges)
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print("\n初始化后，图为")
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graph.print()
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# 添加边
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graph.remove_edge(1, 3)
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# 顶点 1, 2 的索引分别为 0, 2
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print("\n删除边 1-3 后，图为")
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graph.add_edge(0, 2)
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graph.print()
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print("\n添加边 1-2 后，图为")
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graph.print()
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# 删除边
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graph.add_vertex(6)
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# 顶点 1, 3 的索引分别为 0, 1
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print("\n添加顶点 6 后，图为")
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graph.remove_edge(0, 1)
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graph.print()
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print("\n删除边 1-3 后，图为")
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graph.print()
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# 添加顶点
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graph.remove_vertex(3)
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graph.add_vertex(6)
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print("\n删除顶点 3 后，图为")
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print("\n添加顶点 6 后，图为")
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graph.print()
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graph.print()
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# 删除顶点
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# 顶点 3 的索引为 1
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graph.remove_vertex(1)
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print("\n删除顶点 3 后，图为")
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graph.print()
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