题面
Sol
好久没写\(LCT\)
然而写跪了\(TAT\)
把边从小到大加入森林
如果形成环，就替换最小的边
如果已经是树，更新答案
\(LCT\)维护
# include <bits/stdc++.h>
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(4e5 + 5);
IL int Input(){
RG int x = 0, z = 1; RG char c = getchar();
for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
return x * z;
}
int n, m, fa[_], ch[2][_], mn[_], val[_], rev[_], ans, S[_], bt[_], vis[_];
struct Edge{
int u, v, w;
IL bool operator <(RG Edge B) const{
return w < B.w;
}
} edge[_];
IL int Son(RG int x){
return ch[1][fa[x]] == x;
}
IL int Isroot(RG int x){
return ch[0][fa[x]] != x && ch[1][fa[x]] != x;
}
IL int Chk(RG int x, RG int y){
return val[x] < val[y] ? x : y;
}
IL void Update(RG int x){
mn[x] = Chk(x, Chk(mn[ch[0][x]], mn[ch[1][x]]));
}
IL void Reverse(RG int x){
if(!x) return;
rev[x] ^= 1, swap(ch[0][x], ch[1][x]);
}
IL void Pushdown(RG int x){
if(!rev[x]) return;
rev[x] = 0, Reverse(ch[0][x]), Reverse(ch[1][x]);
}
IL void Rotate(RG int x){
RG int y = fa[x], z = fa[y], c = Son(x);
if(!Isroot(y)) ch[Son(y)][z] = x; fa[x] = z;
ch[c][y] = ch[!c][x], fa[ch[c][y]] = y;
ch[!c][x] = y, fa[y] = x, Update(y);
}
IL void Splay(RG int x){
S[S[0] = 1] = x;
for(RG int y = x; !Isroot(y); y = fa[y]) S[++S[0]] = fa[y];
while(S[0]) Pushdown(S[S[0]--]);
for(RG int y = fa[x]; !Isroot(x); Rotate(x), y = fa[x])
if(!Isroot(y)) Son(x) ^ Son(y) ? Rotate(x) : Rotate(y);
Update(x);
}
IL void Access(RG int x){
for(RG int y = 0; x; y = x, x = fa[x]) Splay(x), ch[1][x] = y, Update(x);
}
IL void Makeroot(RG int x){
Access(x), Splay(x), Reverse(x);
}
IL void Link(RG int x, RG int y){
Makeroot(x), fa[x] = y;
}
IL void Split(RG int x, RG int y){
Makeroot(x), Access(y), Splay(y);
}
IL void Cut(RG int x, RG int y){
Split(x, y), ch[0][y] = fa[x] = 0, Update(y);
}
IL int Find(RG int x){
return bt[x] == x ? x : bt[x] = Find(bt[x]);
}
int main(RG int argc, RG char *argv[]){
n = Input(), m = Input(), ans = val[0] = 233233;
for(RG int i = 1; i <= n + m; ++i) bt[i] = i, val[i] = 23333;
for(RG int i = 1; i <= m; ++i){
RG int u = Input(), v = Input(), w = Input();
edge[i] = (Edge){u, v, w};
}
sort(edge + 1, edge + m + 1);
for(RG int i = 1, tot = 0, t = 1; i <= m; ++i){
RG int x = Find(edge[i].u), y = Find(edge[i].v);
val[i + n] = edge[i].w;
if(x == y){
if(edge[i].u == edge[i].v) continue;
Split(edge[i].u, edge[i].v);
RG int pos = mn[edge[i].v];
Cut(edge[pos - n].u, pos), Cut(edge[pos - n].v, pos);
Link(edge[i].u, i + n), Link(edge[i].v, i + n);
vis[i] = 1, vis[pos - n] = 0;
}
else{
vis[i] = 1, bt[x] = y, ++tot;
Link(edge[i].u, i + n), Link(edge[i].v, i + n);
}
while(!vis[t]) ++t;
if(tot == n - 1) ans = min(ans, edge[i].w - edge[t].w);
}
printf("%d\n", ans);
return 0;
}