#!/usr/bin/env python
# coding=gb2312
# 迪杰斯特拉算法求源点到其余各点的最短路径
"""
算法步骤：
a.初始时，S只包含源点，即S＝{v}，v的距离为0。U包含除v外的其他顶点，即:U={其余顶点}，若v与U中顶点u有边，则正常有权值，若u不是v的出边邻接点，则权值为∞。
b.从U中选取一个距离v最小的顶点k，把k，加入S中（该选定的距离就是v到k的最短路径长度）。
c.以k为新考虑的中间点，修改U中各顶点的距离；若从源点v到顶点u的距离（经过顶点k）比原来距离（不经过顶点k）短，则修改顶点u的距离值，修改后的距离值的顶点k的距离加上边上的权。
d.重复步骤b和c直到所有顶点都包含在S中。
"""
import random
import sys
max_int = sys.maxint
max_vertex_num = 100
# 指定点到该点的最短路径
dist = [0 for k in range(max_vertex_num)]
# 保存前驱顶点
prev = [0 for k in range(max_vertex_num)]
# 图的邻接矩阵
matrix = [([0] * max_vertex_num) for i in range(max_vertex_num)]
# matrix = [[0, 6, 3, max_int, max_int, max_int],
# [6, 0, 2, 5, max_int, max_int],
# [3, 2, 0, 3, 4, max_int],
# [max_int, 5, 3, 0, 2, 3],
# [max_int, max_int, max_int, 2, 0, 5],
# [max_int, max_int, max_int, 3, 5, 0]]
# 生成图的邻接矩阵， matrix[i][j]表示有向边的权值，不存在有向边时权值为sys.maxint
def create_point():
for x in range(max_vertex_num):
for y in range(x):
if x == y:
value = 0
else:
value = random.randint(1, 12)
if value > 10:
value = max_int
print(str(value)),
else:
print(str(value) + ' '),
matrix[x][y] = value
matrix[y][x] = value
print '\n'
# 源点 o
def dijkstra(o):
# 标记各点是否在S中
s = [False for x in range(max_vertex_num)]
# 初始化 o 点到各顶点的距离，当之间不存在有向边时前驱顶点为-1
for index in range(max_vertex_num):
dist[index] = matrix[o][index]
if dist[index] == max_int:
prev[index] = -1
else:
prev[index] = o
dist[o] = 0
s[o] = True
# 依次将其他各点放入S中
for index in range(1, max_vertex_num, 1):
min_dist = max_int
u = o
for n in range(max_vertex_num):
if (not s[n]) and (dist[n] <= min_dist):
u = n
min_dist = dist[n]
# 将U中距离最小的电放入S中
s[u] = True
print u
# 以U为新考虑的中间点，依次更新其他各点的距离
for n in range(max_vertex_num):
if (not s[n]) and (matrix[u][n] < max_int):
if (dist[u] + matrix[u][n]) < dist[n]:
dist[n] = dist[u] + matrix[u][n]
prev[n] = u
print dist
print prev
if __name__ == '__main__':
create_point()
dijkstra(0)
