'''
倒着想,假设B一开始有100块钱,求倒着走,怎么才能走到A的时候钱最少
每条边的权值可以抽象为 w = 100 / (100-z)
其实求的是 w1 * w2 * w3 ..... 的最小值
如果能求log(w1*w2*w3)的最小值,也就是log(w1) + log(w2) .... 的最小值
也就等价得到了w1 * w2 * w3 ..... 的最小值
其实就转换为了单源最短路问题,边的权值做了一个对数变换
'''
from collections import deque
class SPFA:
# start_node 为起始点,edges是边的三元组(节点1, 节点2, 边权重) is_directed表示是否是有向图
def __init__(self, start_node, edges, is_directed, max_node_num):
self.edges = edges[::]
self.start_node = start_node
self.is_directed = is_directed
self.max_node_num = max_node_num
# 获取最短路径长度的列表[(节点1,长度1), (节点2, 长度2) .....]
def getMinPathLen(self):
return self.getMinInfo()
def getMinInfo(self):
link = {}
dis = [0x7fffffff] * (self.max_node_num+1)
dis[self.start_node] = 0
for a, b, w in self.edges:
if not self.is_directed:
# 无向图检查是否有负边
if w < 0:
return None
if a not in link:
link[a] = []
if b not in link:
link[b] = []
link[a].append((b, w))
link[b].append((a, w))
else:
if a not in link:
link[a] = []
link[a].append((b, w))
updated_nodes = deque()
updated_nodes.append(self.start_node)
in_que = [0] * (self.max_node_num + 1)
in_que[self.start_node] = 1
# 进行V次迭代,第V次检查是否是无解情况
iter_times = 0
while iter_times < self.max_node_num:
update_flag = False
# 利用上一轮迭代距离变小的点进行松弛操作
node_num = len(updated_nodes)
for _ in range(node_num):
a = updated_nodes.popleft()
in_que[a] = 0
if a not in link:
continue
for b, w in link[a]:
new_dis = 0x7fffffff if dis[a] == 0x7fffffff else dis[a] + w
if new_dis < dis[b]:
dis[b] = new_dis
update_flag = True
if in_que[b] == 0:
in_que[b] = 1
updated_nodes.append(b)
iter_times += 1
if iter_times == self.max_node_num:
if update_flag:
return None
if not update_flag:
break
return [[node, dis[node]] for node in range(1, self.max_node_num+1)]
import math
n, m = map(int, input().split())
edges = []
for i in range(m):
a, b, z = map(int, input().split())
w = math.log2(100 / (100-z))
edges.append((a, b, w))
A, B = map(int, input().split())
algo = SPFA(B, edges, is_directed=False, max_node_num=n)
ans = algo.getMinPathLen()
for node, w in ans:
if node == A:
print('{:.8f}'.format(100 * (2**w)))