最短路问题非线性python编程代码

最短路问题是一个经典的图论问题，常见的算法有Dijkstra算法和Bellman-Ford算法。下面是一个非线性python编程代码，实现了Dijkstra算法来解决最短路问题：

import heapq

def dijkstra(graph, start, end):
    # 初始化距离字典和前驱节点字典
    dist = {node: float('inf') for node in graph}
    dist[start] = 0
    prev = {node: None for node in graph}

    # 采用堆优化的Dijkstra算法
    pq = [(0, start)]
    while pq:
        current_dist, current_node = heapq.heappop(pq)
        if current_dist > dist[current_node]:
            continue
        for neighbor, weight in graph[current_node].items():
            distance = current_dist + weight
            if distance < dist[neighbor]:
                dist[neighbor] = distance
                prev[neighbor] = current_node
                heapq.heappush(pq, (distance, neighbor))

    # 构造最短路径
    path = []
    node = end
    while node is not None:
        path.append(node)
        node = prev[node]
    path.reverse()

    return path, dist[end]

其中，graph是一个字典，表示图的邻接矩阵，start和end是起点和终点。该代码使用堆优化的Dijkstra算法，具有较好的时间复杂度。