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119 lines
3.6 KiB
Python
119 lines
3.6 KiB
Python
"""
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File: graph_adjacency_matrix.py
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Created Time: 2023-02-23
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Author: Krahets (krahets@163.com)
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"""
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import sys, os.path as osp
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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from modules import *
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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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# 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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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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for val in vertices:
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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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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) -> None:
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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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# 在邻接矩阵中添加一行
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new_row = [0] * n
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self.adj_mat.append(new_row)
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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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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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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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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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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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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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# 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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raise IndexError()
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# 在无向图中，邻接矩阵沿主对角线对称，即满足 (i, j) == (j, i)
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self.adj_mat[i][j] = 1
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self.adj_mat[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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# 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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raise IndexError()
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self.adj_mat[i][j] = 0
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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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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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"""Driver Code"""
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if __name__ == "__main__":
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# 初始化无向图
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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: list[int] = [1, 3, 2, 5, 4]
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edges: list[list[int]] = [[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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# 顶点 1, 2 的索引分别为 0, 2
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graph.add_edge(0, 2)
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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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# 顶点 1, 3 的索引分别为 0, 1
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graph.remove_edge(0, 1)
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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.add_vertex(6)
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print("\n添加顶点 6 后，图为")
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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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