第七章 狄克斯特拉算法

狄克斯特拉算法找出的是总权重最小的路径

术语介绍：

狄克斯特拉算法用于每条边都有关联数字的图，这些数字称为权重。

带权重的图称为加权图，不带权重的图称为非加权图。

计算非加权图的最短路径，可使用广度优先搜索。要计算加权图中的最短路径，可使用狄克斯特拉算法。

不能将狄克斯特拉算法用于包含负权边的图。

#实现
graph = {}
graph["you"] = ["alice","bob","claire"]
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"] = 2
graph["fin"] = {}

#创建开销表的代码如下：
infinity = float("inf")
costs = {}
costs["a"] = 6
costs["b"] = 2
costs["fin"] = infinity

#创建父节点表的代码如下：
parents = {}
parents["a"] = "start"
parents["b"] = "start"
parents["fin"] = None
#创建一个数组，用于记录处理过的节点
processed = []
def find_lowest_cost_node(costs):
    lowest_cost = float("inf")
    lowest_cost_node = None
    for node in costs:
        cost = costs[node]
        if cost < lowest_cost and node not in processed:
            lowest_cost = cost
            lowest_cost_node = node
    return lowest_cost_node
#开始狄克斯特拉算法的实现
node = find_lowest_cost_node(costs)
while node is not None:
    cost = costs[node]
    neighbors = graph[node]
    for n in neighbors.keys():
        new_cost = cost + neighbors[n]
        if costs[n] > new_cost:
            costs[n] = new_cost
            parents[n] = node
    processed.append(node)
    node = find_lowest_cost_node(costs)