python實(shí)現(xiàn)狄克斯特拉算法

# -*-coding:utf-8-*-
# 用散列表實(shí)現(xiàn)圖的關(guān)系
# 創(chuàng)建節(jié)點(diǎn)的開(kāi)銷(xiāo)表，開(kāi)銷(xiāo)是指從"起點(diǎn)"到該節(jié)點(diǎn)的權(quán)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(wú)窮大
infinity = float("inf")
costs = {}
costs["a"] = 6
costs["b"] = 2
costs["end"] = infinity

# 父節(jié)點(diǎn)散列表
parents = {}
parents["a"] = "start"
parents["b"] = "start"
parents["end"] = None

# 已經(jīng)處理過(guò)的節(jié)點(diǎn)，需要記錄
processed = []


# 找到開(kāi)銷(xiāo)最小的節(jié)點(diǎn)
def find_lowest_cost_node(costs):
 # 初始化數(shù)據(jù)
 lowest_cost = infinity
 lowest_cost_node = None
 # 遍歷所有節(jié)點(diǎn)
 for node in costs:
 # 該節(jié)點(diǎn)沒(méi)有被處理
 if not node in processed:
  # 如果當(dāng)前節(jié)點(diǎn)的開(kāi)銷(xiāo)比已經(jīng)存在的開(kāi)銷(xiāo)小，則更新該節(jié)點(diǎn)為開(kāi)銷(xiāo)最小的節(jié)點(diǎn)
  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(quán)的最短路徑
def dijkstra():
 # 查詢(xún)到目前開(kāi)銷(xiāo)最小的節(jié)點(diǎn)
 node = find_lowest_cost_node(costs)
 # 只要有開(kāi)銷(xiāo)最小的節(jié)點(diǎn)就循環(huán)（這個(gè)while循環(huán)在所有節(jié)點(diǎn)都被處理過(guò)后結(jié)束）
 while node is not None:
 # 獲取該節(jié)點(diǎn)當(dāng)前開(kāi)銷(xiāo)
 cost = costs[node]
 # 獲取該節(jié)點(diǎn)相鄰的節(jié)點(diǎn)
 neighbors = graph[node]
 # 遍歷當(dāng)前節(jié)點(diǎn)的所有鄰居
 for n in neighbors.keys():
  # 計(jì)算經(jīng)過(guò)當(dāng)前節(jié)點(diǎn)到達(dá)相鄰結(jié)點(diǎn)的開(kāi)銷(xiāo),即當(dāng)前節(jié)點(diǎn)的開(kāi)銷(xiāo)加上當(dāng)前節(jié)點(diǎn)到相鄰節(jié)點(diǎn)的開(kāi)銷(xiāo)
  new_cost = cost + neighbors[n]
  # 如果經(jīng)當(dāng)前節(jié)點(diǎn)前往該鄰居更近，就更新該鄰居的開(kāi)銷(xiāo)
  if new_cost < costs[n]:
  costs[n] = new_cost
  #同時(shí)將該鄰居的父節(jié)點(diǎn)設(shè)置為當(dāng)前節(jié)點(diǎn)
  parents[n] = node
 # 將當(dāng)前節(jié)點(diǎn)標(biāo)記為處理過(guò)
 processed.append(node)
 # 找出接下來(lái)要處理的節(jié)點(diǎn)，并循環(huán)
 node = find_lowest_cost_node(costs)
 # 循環(huán)完畢說(shuō)明所有節(jié)點(diǎn)都已經(jīng)處理完畢
 shortest_path = find_shortest_path()
 shortest_path.reverse()
 print(shortest_path)
# 測(cè)試
dijkstra()