python實現狄克斯特拉算法

# -*-coding:utf-8-*-
# 用散列表實現圖的關系
# 創建節點的開銷表，開銷是指從"起點"到該節點的權重
graph = {}
graph["start"] = {}
graph["start"]["a"] = 6
graph["start"]["b"] = 2

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

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

# 無窮大
infinity = float("inf")
costs = {}
costs["a"] = 6
costs["b"] = 2
costs["end"] = infinity

# 父節點散列表
parents = {}
parents["a"] = "start"
parents["b"] = "start"
parents["end"] = None

# 已經處理過的節點，需要記錄
processed = []


# 找到開銷最小的節點
def find_lowest_cost_node(costs):
 # 初始化數據
 lowest_cost = infinity
 lowest_cost_node = None
 # 遍歷所有節點
 for node in costs:
 # 該節點沒有被處理
 if not node in processed:
  # 如果當前節點的開銷比已經存在的開銷小，則更新該節點為開銷最小的節點
  if costs[node] < lowest_cost:
  lowest_cost = costs[node]
  lowest_cost_node = node
 return lowest_cost_node


# 找到最短路徑
def find_shortest_path():
 node = "end"
 shortest_path = ["end"]
 while parents[node] != "start":
 shortest_path.append(parents[node])
 node = parents[node]
 shortest_path.append("start")
 return shortest_path


# 尋找加權的最短路徑
def dijkstra():
 # 查詢到目前開銷最小的節點
 node = find_lowest_cost_node(costs)
 # 只要有開銷最小的節點就循環（這個while循環在所有節點都被處理過后結束）
 while node is not None:
 # 獲取該節點當前開銷
 cost = costs[node]
 # 獲取該節點相鄰的節點
 neighbors = graph[node]
 # 遍歷當前節點的所有鄰居
 for n in neighbors.keys():
  # 計算經過當前節點到達相鄰結點的開銷,即當前節點的開銷加上當前節點到相鄰節點的開銷
  new_cost = cost + neighbors[n]
  # 如果經當前節點前往該鄰居更近，就更新該鄰居的開銷
  if new_cost < costs[n]:
  costs[n] = new_cost
  #同時將該鄰居的父節點設置為當前節點
  parents[n] = node
 # 將當前節點標記為處理過
 processed.append(node)
 # 找出接下來要處理的節點，并循環
 node = find_lowest_cost_node(costs)
 # 循環完畢說明所有節點都已經處理完畢
 shortest_path = find_shortest_path()
 shortest_path.reverse()
 print(shortest_path)
# 測試
dijkstra()