luogu P2245 星际导航 题解

Posted 2021-01-13 misakaazusa

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
";
        else cout<<T.Qrange(x, y)<<"
";
    }
    return 0;
}