LCT维护生成树

把边从小到大排序，然后一条一条加边，如果成环就把环上最小的删了，我们得到的第一个生成树就是最小生成树。

然后之后每一条边都比前面的生成树的最大边大，我们用这条边的权值减去生成树里最小的，更新答案即可。

因为要维护的是最小值，用排序之后的性质，下表小的值更小来pushup

#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
#define full(a, b) memset(a, b, sizeof a)
#define FAST_IO ios::sync_with_stdio(false), cin.tie(0), cout.tie(0)
using namespace std;
typedef long long LL;
inline int lowbit(int x){ return x & (-x); }
inline int read(){int ret = 0, w = 0; char ch = 0;while(!isdigit(ch)){w |= ch == '-', ch = getchar();}while(isdigit(ch)){ret = (ret << 3) + (ret << 1) + (ch ^ 48);ch = getchar();}return w ? -ret : ret;
}
inline int lcm(int a, int b){ return a / __gcd(a, b) * b; }
template <typename A, typename B, typename C>
inline A fpow(A x, B p, C lyd){A ans = 1;for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;return ans;
}
const int N = 500005;
int n, m, cnt, tot, cur, ans, val[N], fa[N], ch[N][2], rev[N], id[N], st[N];
bool vis[N];
struct Edge {int u, v, w;bool operator < (const Edge &rhs) const {return w < rhs.w;}
} e[N];int newNode(int x){++ tot;val[tot] = x, id[tot] = tot;rev[tot] = ch[tot][0] = ch[tot][1] = fa[tot] = 0;return tot;
}bool isRoot(int x){return ch[fa[x]][0] != x && ch[fa[x]][1] != x;
}void reverse(int x){rev[x] ^= 1, swap(ch[x][0], ch[x][1]);
}void push_up(int x){id[x] = x;int l = ch[x][0], r = ch[x][1];if(id[l] > n && (id[x] <= n || id[x] > id[l])) id[x] = id[l];if(id[r] > n && (id[x] <= n || id[x] > id[r])) id[x] = id[r];
}void push_down(int x){if(rev[x]){int l = ch[x][0], r = ch[x][1];if(l) reverse(l);if(r) reverse(r);rev[x] ^= 1;}
}void rotate(int x){int y = fa[x], z = fa[y], p = (ch[y][1] == x) ^ 1;ch[y][p^1] = ch[x][p], fa[ch[x][p]] = y;if(!isRoot(y)) ch[z][ch[z][1] == y] = x;fa[x] = z, fa[y] = x, ch[x][p] = y;push_up(y), push_up(x);
}void splay(int x){int pos = 0; st[++pos] = x;for(int i = x; !isRoot(i); i = fa[i]) st[++pos] = fa[i];while(pos) push_down(st[pos--]);while(!isRoot(x)){int y = fa[x], z = fa[y];if(!isRoot(y)){(ch[y][0] == x) ^ (ch[z][0] == y) ? rotate(x) : rotate(y);}rotate(x);}push_up(x);
}void access(int x){for(int p = 0; x; p = x, x = fa[x]){splay(x), ch[x][1] = p, push_up(x);}
}void makeRoot(int x){access(x), splay(x), reverse(x);
}void link(int x, int y){makeRoot(x);fa[x] = y;
}int findRoot(int x){access(x), splay(x);while(ch[x][0]) push_down(x), x = ch[x][0];splay(x);return x;
}void split(int x, int y){makeRoot(x), access(y), splay(y);
}bool isConnect(int x, int y){makeRoot(x);return findRoot(y) == x;
}int main(){n = read(), m = read();for(int i = 1; i <= m; i ++){e[i].u = read(), e[i].v = read(), e[i].w = read();}ans = INF, cur = 1;sort(e + 1, e + m + 1);for(int i = 1; i <= n; i ++) newNode(0);for(int i = 1; i <= m; i ++) newNode(e[i].w);for(int i = 1; i <= m; i ++){int u = e[i].u, v = e[i].v, w = e[i].w;if(u == v) continue;if(!isConnect(u, v)){link(u, i + n), link(i + n, v);vis[i] = true, cnt ++;}else{split(u, v);int tmp = id[v];splay(tmp);fa[ch[tmp][0]] = fa[ch[tmp][1]] = 0;ch[tmp][0] = ch[tmp][1] = 0;vis[tmp - n] = false, vis[i] = true;link(u, i + n), link(i + n, v);while(!vis[cur]) cur ++;}if(cnt == n - 1) ans = min(ans, w - e[cur].w);}cout << ans << endl;return 0;
}