【luogu P2245 星际导航】 题解

题目链接：https://www.luogu.org/problemnew/show/P2245

= 货车运输

被逼着写过mst+lca

后来成了mst+树剖

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 100010;
int n, m, q, node[maxn], f[maxn];
struct mst{
	int u, v, w;
}ee[maxn*3];
struct edge{
	int next, to, len;
}e[maxn*3];
int head[maxn], cnt;
void add(int u, int v, int w)
{
	e[++cnt].len = w; e[cnt].next = head[u]; e[cnt].to = v; head[u] = cnt;
	e[++cnt].len = w; e[cnt].next = head[v]; e[cnt].to = u; head[v] = cnt;
}
//-----Kruskal-----
bool cmp(mst a, mst b)
{
	return a.w > b.w;
}
int find(int x)
{
	return f[x] == x ? x : f[x] = find(f[x]);
}
void Kruskal()
{
	sort(ee+1, ee+1+m, cmp);
	for(int i = 1; i <= m; i++)
	{
		if(find(ee[i].u) == find(ee[i].v)) continue;
		add(ee[i].v, ee[i].u, ee[i].w);
		f[find(ee[i].v)] = f[find(ee[i].u)];
	}
}
//----------------
int top[maxn], size[maxn], son[maxn], fa[maxn], seg[maxn], rev[maxn], deep[maxn], num = -1;
void dfs(int u, int f)
{
	fa[u] = f;
	for(int i = head[u]; i != -1; i = e[i].next)
	{
		if(e[i].to == fa[u]) continue;
		node[e[i].to] = e[i].len;
		dfs(e[i].to, u);
	}
}
void dfs1(int u)
{
	int maxson = -1;
	deep[u] = deep[fa[u]]+1;
	size[u] = 1;
	son[u] = n+1;
	for(int i = head[u]; i != -1; i = e[i].next)
	{
		int v = e[i].to;
		if(v == fa[u]) continue;
		dfs1(v);
		size[u] += size[v];
		if(maxson < size[v]) maxson = size[v], son[u] = v;
	}
}
void dfs2(int u, int t)
{
	top[u] = t;
	num++;
	seg[u] = num;
	rev[num] = u;
	if(son[u] != n+1) dfs2(son[u], t);
	for(int i = head[u]; i != -1; i = e[i].next)
	{
		if(e[i].to == fa[u] || e[i].to == son[u]) continue;
		dfs2(e[i].to, e[i].to);
	}
}
//-------------------
class Segment_Tree{
	#define lson l, mid, rt<<1
	#define rson mid+1, r, rt<<1|1
	public:
		int tree[maxn<<2];
		void build(int l, int r, int rt)
		{
			if(l == r)
			{
				tree[rt] = node[rev[l]];
				return;
			}
			int mid = (l + r) >> 1;
			build(lson);
			build(rson);
			PushUP(rt);
		}
		int query(int left, int right, int l, int r, int rt)
		{
			int res = 0x7fffffff;
			if(left <= l && r <= right) return tree[rt];
			int mid = (l + r) >> 1;
			if(left <= mid) res = min(res, query(left, right, lson));
			if(right > mid) res = min(res, query(left, right, rson));
			return res;
		}
		int Qrange(int x, int y)
		{
			int ret = 0x7fffffff;
			while(top[x] != top[y])
			{
				if(deep[top[x]] < deep[top[y]]) swap(x, y);
				ret = min(ret, query(seg[top[x]], seg[x], 1, n, 1));
				x = fa[top[x]];
			}
			if(deep[x] > deep[y]) swap(x, y);
			ret = min(ret, query(seg[x]+1, seg[y], 1, n, 1));
			return ret;
		}
	private:
		void PushUP(int rt)
		{
			tree[rt] = min(tree[rt<<1], tree[rt<<1|1]);
		}
}T;
int main()
{
	ios::sync_with_stdio(false);
	memset(head, -1, sizeof(head));
	cin>>n>>m;
	for(int i = 1; i <= m; i++) cin>>ee[i].u>>ee[i].v>>ee[i].w;
	for(int i = 1; i <= n; i++) f[i] = i;
	Kruskal();
	memset(fa, -1, sizeof(fa));
	fa[0] = 0;
	for(int i = 1; i <= n; i++) if(fa[i] == -1) dfs(i, 0);
	for(int i = 1; i <= n; i++) if(fa[i] == 0) add(i, 0, 0);
	dfs1(0);
	dfs2(0, 0);
	T.build(1, n, 1);
	cin>>q;
	for(int i = 1; i <= q; i++)
	{
		int x, y;
		cin>>x>>y;
		if(find(x) != find(y)) cout<<"-1\n";
		else cout<<T.Qrange(x, y)<<"\n";
	}
	return 0;
}