图解算法（七）

狄克斯特拉算法

 广度优先搜索，它找出的是段数最少的路径。如果要给每一段加上时间（加权），为了找到最快的路径，可使用狄克斯特拉算法。

1.使用狄克斯特拉算法

1. 找出最便宜的节点，即可在最短时间内前往的节点
2. 对于该节点邻居，检查是否有前往它们的更短路径，如果有，就更新其开销
3. 重复这个过程，知道对图中的每个节点都这样做了
4. 计算最终路径

2.实现算法

graph = {}
graph["start"] = {}
graph["start"]["a"] = 6
graph["start"]["b"] = 2
print graph["start"].keys()
print graph["start"]["a"]
graph["a"] = {}
graph["a"]["fin"] = 1

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

infinity = float("inf")
costs = {}
costs["a"] = 6
costs["b"] = 2
costs["fin"] = infinity

parents = {}
parents["a"] = "start"
parents["b"] = "start"
parents["fin"] = None

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
processed = []

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)

3.小结

• 广度优先搜索用于非加权图中查找最短路径
• 狄克斯特拉算法用于在加权图中查找最短路径
• 仅当权重为正时狄克斯特拉算法才管用