【題解】LuoGu2245：星際導航

原題傳送門
最小瓶頸路
與NOIp題貨車運輸類似
$kruskal$建最小生成樹，$st$表維護最大值
Code：

#include <bits/stdc++.h>
#define maxn 300010
using namespace std;
struct Edge{
	int to, next, len;
}edge[maxn << 1];
struct Line{
	int x, y, z;
}line[maxn];
int num, head[maxn], f[maxn], d[maxn], len[maxn][25], fa[maxn][25], n, m, q;

inline int read(){
	int s = 0, w = 1;
	char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') w = -1;
	for (; isdigit(c); c = getchar()) s = (s << 1) + (s << 3) + (c ^ 48);
	return s * w;
}

bool cmp(Line x, Line y){ return x.z < y.z; }
void addedge(int x, int y, int z){ edge[++num] = (Edge){y, head[x], z}, head[x] = num; }
int getfa(int k){ return k == f[k] ? k : f[k] = getfa(f[k]); }

void dfs(int u, int pre){
	d[u] = d[pre] + 1, fa[u][0] = pre;
	for (int i = 0; fa[u][i]; ++i) fa[u][i + 1] = fa[fa[u][i]][i], len[u][i + 1] = max(len[u][i], len[fa[u][i]][i]);
	for (int i = head[u]; i; i = edge[i].next){
		int v = edge[i].to;
		if (v != pre) len[v][0] = edge[i].len, dfs(v, u);
	}
}

int lca(int u, int v){
	int sum = 0;
	if (d[u] >= d[v]) swap(u, v);
	for (int i = 20; i >= 0; --i) if (d[u] <= d[v] - (1 << i)) sum = max(sum, len[v][i]), v = fa[v][i];
	if (u == v) return sum;
	for (int i = 20; i >= 0; --i)
		if (fa[u][i] != fa[v][i]) sum = max(sum, max(len[u][i], len[v][i])), u = fa[u][i], v = fa[v][i];
	return max(sum, max(len[u][0], len[v][0]));
}

int main(){
	n = read(), m = read();
	for (int i = 1; i <= m; ++i) line[i] = (Line){read(), read(), read()};
	sort(line + 1, line + 1 + m, cmp);
	for (int i = 1; i <= n; ++i) f[i] = i;
	for (int i = 1; i <= m; ++i){
		int s1 = getfa(line[i].x), s2 = getfa(line[i].y);
		if (s1 != s2){
			f[s1] = s2;
			addedge(line[i].x, line[i].y, line[i].z), addedge(line[i].y, line[i].x, line[i].z);
		}
	}
	for (int i = 1; i <= n; ++i)
		if (!d[i]) dfs(i, 0);
	q = read();
	while (q--){
		int x = read(), y = read(), s1 = getfa(x), s2 = getfa(y);
		if (s1 != s2) puts("impossible"); else printf("%d\n", lca(x, y));
	}
	return 0;
}