#!/usr/bin/env python3.3
# -*- coding:utf-8 -*-
# Copyright 2013
'''
单源最短路径：
1）bellman_ford算法：将所有的边进行|V|-1次循环，每次循环对所有边进行松弛操作
2）dijkstra算法：将V-S中顶点按最短路径递增的次序加入到S中，并对邻接边进行松弛操作
'''
def bellman_ford(graph, graph_size, s):
low_weight = [w for w in graph[0]]
low_weight[s] = 0
for repeat in range(1, graph_size):
for u in range(graph_size):
for v in range(graph_size):
# 对每条边进行松弛操作
if low_weight[u] is not None and graph[u][v] is not None:
if low_weight[v] is None or low_weight[v] > low_weight[u] + graph[u][v]:
low_weight[v] = low_weight[u] + graph[u][v]
return low_weight
def dijkstra(graph, graph_size, s):
visit_set = {s}
low_weight = [w for w in graph[s]]
low_weight[s] = 0
for repeat in range(1, graph_size):
# 查找最小权值的顶点
k = None
for v in range(graph_size):
if v not in visit_set and low_weight[v] is not None:
if k is None or low_weight[v] < low_weight[k]:
k = v
# 对邻接边进行松弛操作
for v in range(graph_size):
if v not in visit_set and graph[k][v] is not None:
if low_weight[v] is None or low_weight[v] > low_weight[k] + graph[k][v]:
low_weight[v] = low_weight[k] + graph[k][v]
visit_set.add(k)
return low_weight
