狄克斯特拉算法

狄克斯特拉算法用于在加权图中查找最短路径。

仅当权重为时算法才管用，如果图中包含负权边，请使用贝尔曼-福得算法。

#  有向无环图
graph = {}

graph["start"] = {}
graph["start"]["a"] = 6
graph["start"]["b"] = 2

graph["a"] = {}
graph["a"]["fin"] = 1

graph["b"] = {}
graph["b"]["a"] = 3
graph["b"]["fin"] = 5

graph["fin"] = {}

# 开销表，节点的开销指的是从起点出发前往该节点需要多长时间
infinity = float("inf")  # 表示无穷大
costs = {}
costs["a"] = 6
costs["b"] = 2
costs["fin"] = infinity

# 存储父节点的散列表
parents = {}
parents["a"] = "start"
parents["b"] = "start"
parents["fin"] = None

# 记录处理过的节点
processed = []

def find_lowest_cost_node(costs):

    lowest_cost = float("inf")
    lowest_cost_node = None
    for node in costs:  # 遍历所有的节点
        cost = costs[node]
        if cost and lowest_cost and node not in processed:  # 如果当前节点的开销更低且未处理过
            lowest_cost = cost
            lowest_cost_node = node

    return lowest_cost_node

node = find_lowest_cost_node(costs)  # 在未处理的节点中找出开销最小的节点
while node is not None:  # 所有节点处理过后结束
    cost = costs[node]
    neighbors = graph[node]
    for n in neighbors.keys():  # 遍历当前节点的所有邻居
        new_cost = cost + neighbors[n]
        if costs[n] > new_cost:  # 如果 从【当前节点】前往邻居节点比 从【起点】前往邻居节点更近
            costs[n] = new_cost  # 就更新改邻居节点的开销
            parents[n] = node  # 同时将改邻居的父节点设置为当前节点

    processed.append(node)  # 将当前节点标记为处理过
    node = find_lowest_cost_node(costs)  # 找出接下来要处理的节点，并循环

原文地址：https://www.cnblogs.com/lt1548748657/p/12620030.html