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| #define REP(i, s, e) for (int i = s; i <= e; i++)
#include <algorithm>
#include <iostream>
#include <cstdio>
using namespace std;
const int maxn = 100000 + 10, maxm = 200000 + 10, maxN = maxn + maxm;
struct Edge
{
int x, y, z;
}E[maxN];
bool cmp(Edge A, Edge B) {return A.z > B.z;}
int n, m, S, T;
int f[maxN];
int find(int x) {return f[x] == x ? f[x] : f[x] = find(f[x]);}
void uni(int x, int y) {f[find(x)] = find(y);}
int fa[maxN], ch[maxN][2], s[maxN];
bool tag[maxN];
#define ls(p) ch[p][0]
#define rs(p) ch[p][1]
#define get(x) (rs(fa[x]) == x)
#define notroot(x) (ls(fa[x]) == x || rs(fa[x]) == x)
void pushup(int x)
{
s[x] = x;s[0] = 0;
if (E[s[x]].z < E[s[ls(x)]].z) s[x] = s[ls(x)];
if (E[s[x]].z < E[s[rs(x)]].z) s[x] = s[rs(x)];
}
void rotate(int x)
{
int y = fa[x], z = fa[y];
bool k = get(x);
if (ch[x][k ^ 1]) fa[ch[x][k ^ 1]] = y;
ch[y][k] = ch[x][k ^ 1];
if (notroot(y)) ch[z][get(y)] = x;
fa[fa[y] = x] = z;
ch[x][k ^ 1] = y;
pushup(y);pushup(x);
}
void pushdown(int x)
{
if (!tag[x]) return;
swap(ls(x), rs(x));
tag[ls(x)] ^= 1;tag[rs(x)] ^= 1;
tag[x] = 0;
}
void pushall(int x)
{
if (notroot(x)) pushall(fa[x]);
pushdown(x);
}
void splay(int x)
{
pushall(x);
while (notroot(x))
{
int y = fa[x];
if (notroot(y)) rotate(get(x) == get(y) ? y : x);
rotate(x);
}
}
void access(int x)
{
for (int t = 0; x; x = fa[t = x])
{
splay(x);
rs(x) = t;
pushup(x);
}
}
void makeroot(int x)
{
access(x);
splay(x);
tag[x] ^= 1;
}
void link(int x, int y)
{
makeroot(x);
fa[x] = y;
}
void cut(int x, int y)
{
makeroot(x);
access(y);
splay(y);
fa[x] = ls(y) = 0;
}
int query(int u, int v)
{
makeroot(u);
access(v);
splay(v);
return s[v];
}
long long ansu = 1 << 30, ansv = 1;
int main()
{
#ifndef ONLINE_JUDGE
freopen("B.in", "r", stdin);
freopen("B.out", "w", stdout);
#endif
cin >> n >> m;
REP(i, n + 1, n + m) scanf("%d%d%d", &E[i].x, &E[i].y, &E[i].z);
cin >> S >> T;
sort(E + n + 1, E + 1 + n + m, cmp);
REP(i, 1, n) f[i] = i;
REP(i, n + 1, n + m)
{
if (find(E[i].x) ^ find(E[i].y))
{
uni(E[i].x, E[i].y);
link(E[i].x, i);
link(E[i].y, i);
}
else
{
int pos = query(E[i].x, E[i].y);
if (E[pos].z <= E[i].z) continue;
cut(E[pos].x, pos);
cut(E[pos].y, pos);
link(E[i].x, i);
link(E[i].y, i);
}
if (find(S) == find(T))
{
int v = E[query(S, T)].z;
if (ansu * E[i].z >= ansv * v) ansu = v, ansv = E[i].z;
}
}
if (ansu % ansv == 0) printf("%lld\n", ansu / ansv);
else printf("%lld/%lld\n", ansu / __gcd(ansu, ansv), ansv / __gcd(ansu, ansv));
return 0;
}
|
