带有矩阵的有向图Dijkstra算法python代码

以下是带有矩阵的有向图Dijkstra算法的Python代码实现：

import numpy as np

def dijkstra(graph, start):
    n = graph.shape[0]
    visited = [False] * n
    distances = [float('inf')] * n
    distances[start] = 0
    
    for _ in range(n):
        u = np.argmin([distances[i] for i in range(n) if not visited[i]])
        visited[u] = True
        
        for v in range(n):
            if graph[u][v] != 0 and not visited[v]:
                new_distance = distances[u] + graph[u][v]
                if new_distance < distances[v]:
                    distances[v] = new_distance
                    
    return distances

其中，`graph`是一个Numpy矩阵，表示有向图的邻接矩阵；`start`是起点的编号。该算法返回一个列表，表示起点到每个点的最短距离。

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python实现矩阵Dijkstra有向图算法代码

下面是Python实现矩阵Dijkstra有向图算法的代码：

import sys

def dijkstra(graph, src):
    """
    矩阵Dijkstra有向图算法
    :param graph: 有向图
    :param src: 源节点
    :return: 距离列表
    """
    n = len(graph)
    dist = [sys.maxsize] * n  # 起点到各个节点的距离列表
    visited = [False] * n  # 节点是否已访问的标记

    dist[src] = 0  # 起点到起点的距离为0

    for _ in range(n):
        u = min_distance(dist, visited)  # 未访问节点中距离最短的节点
        visited[u] = True  # 标记为已访问

        # 更新未访问节点的距离
        for v in range(n):
            if graph[u][v] > 0 and not visited[v] and dist[v] > dist[u] + graph[u][v]:
                dist[v] = dist[u] + graph[u][v]

    return dist


def min_distance(dist, visited):
    """
    从未访问节点中选择距离最短的节点
    :param dist: 距离列表
    :param visited: 是否已访问的标记
    :return: 距离最短的节点
    """
    min_dist = sys.maxsize
    min_index = -1

    for v in range(len(dist)):
        if not visited[v] and dist[v] < min_dist:
            min_dist = dist[v]
            min_index = v

    return min_index

其中，`graph`参数是一个二维矩阵，表示有向图的邻接矩阵，`src`参数是源节点的下标。函数返回的是距离列表，列表中的第`i`个元素表示从源节点到第`i`个节点的最短距离。

迪杰斯特拉算法 python代码实现有向图

迪杰斯特拉(Dijkstra's Algorithm)是一种用于寻找图中两点之间最短路径的算法，通常应用于带权重的有向图或无向图。以下是Python中使用邻接矩阵表示的有向图实现Dijkstra算法的一个简单示例：

import heapq

def dijkstra(graph, start):
    distances = {node: float('inf') for node in graph}
    distances[start] = 0
    queue = [(0, start)]
    
    while queue:
        current_distance, current_node = heapq.heappop(queue)
        
        if current_distance > distances[current_node]:
            continue
        
        for neighbor, weight in graph[current_node].items():
            distance = current_distance + weight
            if distance < distances[neighbor]:
                distances[neighbor] = distance
                heapq.heappush(queue, (distance, neighbor))
                
    return distances

# 示例：有向图的邻接矩阵表示，其中weights是从start到end的距离
graph = {
    'A': {'B': 1, 'C': 4},
    'B': {'A': 1, 'C': 2, 'D': 5},
    'C': {'A': 4, 'B': 2, 'D': 1},
    'D': {'B': 5, 'C': 1}
}

start = 'A'
shortest_distances = dijkstra(graph, start)
print("从{}到各个节点的最短距离: {}".format(start, shortest_distances))