P1967 货车运输

大致题意

给一张\(n\)个点,\(m\)条边的带边权无向图,现在有\(q\)次询问,每次询问都给一个\(x\)和\(y\),求\(x\)到\(y\)的路径上长度最小的边的大小

分析

大水题

先跑一遍最小生成树

然后把点权转成边权,上树剖即可

\(code\)

#include<bits/stdc++.h>
using namespace std;
#define lson (node<<1)
#define rson (node<<1|1)
#define inf 1145141919
const int MAXN = 20010;
struct e{
	int u,v,w,next;
}edge[MAXN<<1];
struct koishi{
	int u,v,w;
	bool operator < (const koishi &k)const{
		return w>k.w;
	}
}a[MAXN<<2];
int head[MAXN<<2];
int w[MAXN<<2],n,m;
int dep[MAXN],son[MAXN],fa[MAXN],size[MAXN],faa[MAXN];
int id[MAXN],val[MAXN],tot = 0,cnt = 1,top[MAXN];
int find(int x){
	if(faa[x]==x) return x;
	else return faa[x] = find(faa[x]);
}
void add(int u,int v,int w){
	edge[cnt].u = u;
	edge[cnt].v = v;
	edge[cnt].w = w;
	edge[cnt].next = head[u];
	head[u] = cnt++;
}
void dfs1(int u,int f,int deep){
	dep[u] = deep;
	fa[u] = f;
	size[u] = 1;
	int maxson = -1;
	for(int i=head[u];i;i=edge[i].next){
		int v = edge[i].v;
		if(v==f) continue;
		w[v] = edge[i].w;
		dfs1(v,u,deep+1);
		size[u]+=size[v];
		if(size[v]>maxson){
			son[u] = v;
			maxson = size[v];
		}
	}
}
void dfs2(int u,int topf){
	id[u] = ++tot;
	val[tot] = u;
	top[u] = topf;
	if(!son[u]) return;
	dfs2(son[u],topf);
	for(int i=head[u];i;i=edge[i].next){
		int v = edge[i].v;
		if(v==son[u]||v==fa[u]) continue;
		dfs2(v,v);
	} 
}

struct st{
	int minn,l,r,tag;
}tree[MAXN<<2];

void update(int node){
	tree[node].minn = min(tree[lson].minn,tree[rson].minn);
	return;
}

void build(int node,int l,int r){
	tree[node].l = l,tree[node].r = r;
	if(l==r){
		tree[node].minn = w[val[l]];
		return;
	}
	int mid = (l+r)>>1;
	build(lson,l,mid);
	build(rson,mid+1,r);
	update(node);
}

int query(int node,int x,int y){
	
	if(x<=tree[node].l&&tree[node].r<=y){
		return tree[node].minn;
	}
	
	int mid = (tree[node].l+tree[node].r)>>1;
	int now = inf;
	if(x<=mid) now = min(now,query(lson,x,y));
	if(y>mid) now = min(now,query(rson,x,y));
	return now;
} 

int qb(int u,int v){
	int ans = inf;
	while(top[u]!=top[v]){
		if(dep[top[u]]<dep[top[v]]) swap(u,v);
		ans=min(ans,query(1,id[top[u]],id[u]));
		u = fa[top[u]];
	}
	if(dep[u]>dep[v]) swap(u,v);
	ans=min(ans,query(1,id[u]+1,id[v]));
	return ans;
}

void kruskal(){
	for(int i=1;i<=m;i++){
		faa[i] = i;
	}
	int tot = 0;
	for(int i=1;i<=m;i++){
		int x = find(a[i].u),y = find(a[i].v);
		if(x!=y){
			faa[x] = y;
			add(a[i].u,a[i].v,a[i].w),add(a[i].v,a[i].u,a[i].w);
			tot++;
		}
		if(tot==n-1) return;
	}
} 
int main(){
	memset(w,-1,sizeof(w));
	cin>>n>>m;
	for(int i=1;i<=m;i++){
		cin>>a[i].u>>a[i].v>>a[i].w;
	}
	sort(a+1,a+1+m);
	kruskal();
	dfs1(1,0,1);
	dfs2(1,1);
	build(1,1,n);
	int q;
	cin>>q;
	for(int i=1;i<=q;i++){
		int x,y;
		cin>>x>>y;
		int xx = find(x),yy = find(y);
		if(xx!=yy) cout<<-1<<endl;
		else cout<<qb(x,y)<<endl;
	}
}

水博客好爽啊