用python写一个 Prim算法代码（必须有每行注释）

# Prim's Algorithm in Python for finding minimum spanning tree (MST)
import sys

def prim(graph, start):
    # 初始化：标记所有边为未访问，创建空集合用于存放已选择的最小权重边，以及一个字典保存每个顶点的最短路径起点
    visited = [False] * len(graph)
    edges = []
    parent = [-1] * len(graph)

    # 将起始顶点的距离设置为0，并加入已访问集合
    distance[start] = 0
    visited[start] = True

    while edges != len(graph) - 1:  # 边的数量还没达到n-1，因为MST需要n-1条边
        min_distance = float('inf')  # 初始化最小距离为无穷大
        u = -1  # 存储当前最小边的起点

        # 遍历所有未访问的顶点，找到到它们的最小边
        for v in range(len(graph)):
            if visited[v] == False and graph[start][v] != 0 and graph[start][v] < min_distance:
                min_distance = graph[start][v]
                u = v

        # 更新节点信息，将找到的最小边加入edges，并将其终点添加为已访问
        visited[u] = True
        edges.append((start, u))  # 添加起点u到之前的起点(start)
        parent[u] = start  # 设置parent[u]为起点
        start = u  # 将搜索焦点转移到下一个未访问的起点u

    return edges, parent

# 示例图的邻接矩阵表示，其中0表示不存在边，正数表示权重
graph = [
    [0, 2, 0, 6],
    [2, 0, 3, 8],
    [0, 3, 0, 5],
    [6, 8, 5, 0]
]

# 使用Prim算法从第一个节点开始找MST
result_edges, _ = prim(graph, 0)

print("Minimum Spanning Tree Edges (from node 0):")
for edge in result_edges:
    print(f"Edge from {edge[0]} to {edge[1]} with weight {graph[edge[0]][edge[1]]}")