[模板]倍增LCA

洛谷P1967

用倍增法，fa[i][j]表示节点i向上
2^j步所能到大的点
minx[i][j]表示i向上2^j步所经过的最小边

#include<iostream>
#include<cstdio>
#include<algorithm>
#define LL long long
using namespace std;
const int MAXN = 200000 + 50;
struct edge{
	int f,t,v;
}l[MAXN << 1],e[MAXN << 1];
int n,m,q;
int x,y,z;
int head[MAXN],next[MAXN << 1],tot,rank[MAXN],f[MAXN];
void init(int n){
	for(int i = 1;i <= n;i ++){
		f[i] = i;
		head[i] = -1;
	}
}
int find(int x){
	return f[x] == x ? x : f[x] = find(f[x]);
}
void build(int f,int t,int v){
	l[++tot] = (edge){f,t,v};
	next[tot] = head[f];
	head[f] = tot;
}
void merge(int a,int b){
	a = find(a);
	b = find(b);
	if(rank[a] < rank[b])swap(a,b);
	f[b] = a;
	if(rank[a] == rank[b])rank[a] ++;
}
bool cmp(edge a,edge b){
	return a.v > b.v;
}
bool same(int a,int b){
	return find(a) == find(b);
}
void smt(){
	for(int i = 1;i <= m;i ++){
		if(!same(e[i].f,e[i].t)){
			merge(e[i].f,e[i].t);
			build(e[i].f,e[i].t,e[i].v);
			build(e[i].t,e[i].f,e[i].v);
		}
	}
}
int fa[MAXN][30],minx[MAXN][30],deep[MAXN];
void dfs(int p,int u){
	for(int i = 1;i <= 29;i ++){
		fa[u][i] = fa[fa[u][i - 1]][i - 1];
		minx[u][i] = min(minx[u][i - 1],minx[fa[u][i - 1]][i - 1]);
	}
	for(int i = head[u];i != -1;i = next[i]){
		int t = l[i].t;
		if(t == p)continue;
		deep[t] = deep[u] + 1;
		minx[t][0] = l[i].v;
		fa[t][0] = u;
		dfs(u,t);
	}
}
int LCA(int a,int b){
	if(deep[a] < deep[b])swap(a,b);
	int ans = 2147483647;
	int t = deep[a] - deep[b];
	for(int i = 0;i <= 25;i ++){
		if(t & (1 << i)){
			ans = min(ans,minx[a][i]);
			a = fa[a][i];
		}
	}
	if(a == b)return ans;
	for(int i = 25;i >= 0;i --){
		if(fa[a][i] != fa[b][i]){
			ans = min(ans,min(minx[a][i],minx[b][i]));
			a = fa[a][i];
			b = fa[b][i];
		}
	}
	ans = min(ans,min(minx[a][0],minx[b][0]));
	return ans;
}

int main(){
	scanf("%d%d",&n,&m);
	init(n);
	for(int i = 1;i <= m;i ++){
		scanf("%d%d%d",&x,&y,&z);
		e[i] = (edge){x,y,z};
	}
	sort(e + 1,e + m + 1,cmp);
	smt();
	dfs(1,1);
	scanf("%d",&q);
	for(int i = 1;i <= q;i ++){
		scanf("%d%d",&x,&y);
		if(!same(x,y))printf("-1
");
		else printf("%d
",LCA(x,y));
	}
}