Dijkstra Algorithm 迪克特斯拉算法--Python

迪克斯拉特算法：

1、找出代价最小的节点，即可在最短时间内到达的节点；

2、更新节点的邻居的开销；

3、重复这个过程，直到图中的每个节点都这样做了；

4、计算最终路径。

 

'''
迪克斯特拉算法：
1、以字典的方式更新图，包括权重
2、创建开销字典，关键在于起点临近的点开销为实际数值，其他点为暂时未到达，开销为无穷，随后更新
3、创建父节点列表保存每个点的父节点，以便记录走过的路径
'''
from queue import LifoQueue

graph = {}
graph['start'] = {}
graph['start']['a'] = 6
graph['start']['b'] = 2
graph['a'] = {}
graph['a']['end'] = 4
graph['b'] = {}
graph['b']['a'] = 3
graph['b']['c'] = 2
graph['c'] = {}
graph['c']['end'] = 3
graph['end'] = {}
print(graph)

infinity = float('inf')
costs = {}
costs['a'] = 6
costs['b'] = 2
costs['c'] = infinity
costs['end'] = infinity

parents = {}
parents['a'] = 'start'
parents['b'] = 'start'
parents['c'] = 'b'
parents['end'] = None

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

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)

#输出最短路径
p = 'end'
path = LifoQueue()
while(True):
    path.put(p)
    if(p == 'start'):
        break
    p = parents[p]

while not path.empty():
    print(path.get())