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hello-algo/codes/python/chapter_graph/graph_adjacency_matrix.py

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3.6 KiB

"""
File: graph_adjacency_matrix.py
Created Time: 2023-02-23
Author: Krahets (krahets@163.com)
"""
import sys, os.path as osp
sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
from modules import *
class GraphAdjMat:
"""基于邻接矩阵实现的无向图类"""
# 顶点列表,元素代表“顶点值”,索引代表“顶点索引”
vertices: list[int] = []
# 邻接矩阵,行列索引对应“顶点索引”
adj_mat: list[list[int]] = []
def __init__(self, vertices: list[int], edges: list[list[int]]) -> None:
"""构造方法"""
self.vertices: list[int] = []
self.adj_mat: list[list[int]] = []
# 添加顶点
for val in vertices:
self.add_vertex(val)
# 添加边
# 请注意edges 元素代表顶点索引,即对应 vertices 元素索引
for e in edges:
self.add_edge(e[0], e[1])
def size(self) -> int:
"""获取顶点数量"""
return len(self.vertices)
def add_vertex(self, val: int) -> None:
"""添加顶点"""
n = self.size()
# 向顶点列表中添加新顶点的值
self.vertices.append(val)
# 在邻接矩阵中添加一行
new_row = [0] * n
self.adj_mat.append(new_row)
# 在邻接矩阵中添加一列
for row in self.adj_mat:
row.append(0)
def remove_vertex(self, index: int) -> None:
"""删除顶点"""
if index >= self.size():
raise IndexError()
# 在顶点列表中移除索引 index 的顶点
self.vertices.pop(index)
# 在邻接矩阵中删除索引 index 的行
self.adj_mat.pop(index)
# 在邻接矩阵中删除索引 index 的列
for row in self.adj_mat:
row.pop(index)
def add_edge(self, i: int, j: int) -> None:
"""添加边"""
# 参数 i, j 对应 vertices 元素索引
# 索引越界与相等处理
if i < 0 or j < 0 or i >= self.size() or j >= self.size() or i == j:
raise IndexError()
# 在无向图中,邻接矩阵沿主对角线对称,即满足 (i, j) == (j, i)
self.adj_mat[i][j] = 1
self.adj_mat[j][i] = 1
def remove_edge(self, i: int, j: int) -> None:
"""删除边"""
# 参数 i, j 对应 vertices 元素索引
# 索引越界与相等处理
if i < 0 or j < 0 or i >= self.size() or j >= self.size() or i == j:
raise IndexError()
self.adj_mat[i][j] = 0
self.adj_mat[j][i] = 0
def print(self) -> None:
"""打印邻接矩阵"""
print("顶点列表 =", self.vertices)
print("邻接矩阵 =")
print_matrix(self.adj_mat)
"""Driver Code"""
if __name__ == "__main__":
# 初始化无向图
# 请注意edges 元素代表顶点索引,即对应 vertices 元素索引
vertices: list[int] = [1, 3, 2, 5, 4]
edges: list[list[int]] = [[0, 1], [0, 3], [1, 2], [2, 3], [2, 4], [3, 4]]
graph = GraphAdjMat(vertices, edges)
print("\n初始化后,图为")
graph.print()
# 添加边
# 顶点 1, 2 的索引分别为 0, 2
graph.add_edge(0, 2)
print("\n添加边 1-2 后,图为")
graph.print()
# 删除边
# 顶点 1, 3 的索引分别为 0, 1
graph.remove_edge(0, 1)
print("\n删除边 1-3 后,图为")
graph.print()
# 添加顶点
graph.add_vertex(6)
print("\n添加顶点 6 后,图为")
graph.print()
# 删除顶点
# 顶点 3 的索引为 1
graph.remove_vertex(1)
print("\n删除顶点 3 后,图为")
graph.print()