Comet OJ - Contest #11 D isaster 重构树+倍增+dfs序+线段树

发现对于任意一条边，起决定性作用的是节点编号更大的点.

于是，对于每一条边，按照节点编号较大值作为边权，按照最小生成树的方式插入即可.

最后用线段树维护 dfs 序做一个区间查询即可.

Code:

#include <bits/stdc++.h>
#define N 400005
#define ll long long
#define mod 998244353
#define setIO(s) freopen(s".in","r",stdin)
using namespace std;
ll val[N],mul[N<<2],V[N];
int n,m,Q,tot,edges,tt;
int p[N],cc[N],hd[N],to[N],nex[N],dfn[N],st[N],ed[N],size[N],Fa[21][N],F[21][N];
struct Edge
{
    int u,v,c;
    Edge(int u=0,int v=0,int c=0):u(u),v(v),c(c){}
}e[N];
void pushup(int l,int r,int now)
{
    ll re=1;
    int mid=(l+r)>>1;
    if(l<=mid)re=re*mul[now<<1]%mod;
    if(r>mid) re=re*mul[now<<1|1]%mod;
    mul[now]=re;
}
void build(int l,int r,int now)
{
    if(l==r)
    {
        mul[now]=V[l]%mod;
        return;
    }
    int mid=(l+r)>>1;
    if(l<=mid) build(l,mid,now<<1);
    if(r>mid)  build(mid+1,r,now<<1|1);
    pushup(l,r,now);
}
void update(int l,int r,int now,int p,int v)
{
    if(l==r)
    {
        V[l]=mul[now]=1ll*v%mod;
        return;
    }
    int mid=(l+r)>>1;
    if(p<=mid) update(l,mid,now<<1,p,v);
    else update(mid+1,r,now<<1|1,p,v);
    pushup(l,r,now);
}
ll query(int l,int r,int now,int L,int R)
{
    if(l>=L&&r<=R) return mul[now];
    ll re=1;
    int mid=(l+r)>>1;
    if(L<=mid) re=re*query(l,mid,now<<1,L,R)%mod;
    if(R>mid)  re=re*query(mid+1,r,now<<1|1,L,R)%mod;
    return re;
}
int find(int x)
{
    return p[x]==x?x:p[x]=find(p[x]);
}
bool cmp(Edge a,Edge b)
{
    return a.c<b.c;
}
void addedge(int u,int v)
{
    nex[++edges]=hd[u],hd[u]=edges,to[edges]=v;
}
void dfs(int u,int ff)
{
    st[u]=dfn[u]=++tt, size[u]=1, V[dfn[u]]=val[u];
    Fa[0][u]=ff, F[0][u]=max(cc[ff], cc[u]);
    for(int i=1;i<=20;++i)
    {
        Fa[i][u]=Fa[i-1][Fa[i-1][u]];
        F[i][u]=max(F[i-1][u], F[i-1][Fa[i-1][u]]);
    }
    for(int i=hd[u];i;i=nex[i])
    {
        int v=to[i];
        dfs(v, u);
        size[u]+=size[v];
    }
    ed[u]=tt;
}
int get(int x,int k)
{
    for(int i=20;i>=0;--i)
        if(Fa[i][x] && F[i][x] <= k) x=Fa[i][x];
    return x;
}
int main()
{
    int i,j,k;
    // setIO("input");
    scanf("%d%d%d",&n,&m,&Q);
    tot=n;
    for(i=1;i<N;++i) p[i]=i;
    for(i=1;i<=n;++i) scanf("%lld",&val[i]),cc[i]=i;
    for(i=1;i<=m;++i)
    {
        scanf("%d%d",&e[i].u,&e[i].v);
        e[i].c=max(e[i].u, e[i].v);
    }
    sort(e+1,e+1+m,cmp);
    for(i=1;i<=m;++i)
    {
        int u=e[i].u, v=e[i].v;
        int x=find(u),y=find(v);
        if(x!=y)
        {
            ++tot;
            val[tot]=1ll;
            cc[tot]=e[i].c;
            p[x]=tot,p[y]=tot;
            addedge(tot,x), addedge(tot,y);
        }
    }
    cc[0]=1000000000;
    dfs(tot,0);
    build(1,tot,1);
    for(i=1;i<=Q;++i)
    {
        int op;
        scanf("%d",&op);
        if(op==1)
        {
            int x,y;
            scanf("%d%d",&x,&y);
            if(x>y) printf("0\n");
            else
            {
                int k=get(x,y);
                int L=st[k], R=ed[k];
                printf("%lld\n",query(1,tot,1,L,R));
            }
        }
        if(op==2)
        {
            int x,y;
            scanf("%d%d",&x,&y);
            update(1,tot,1,dfn[x],y);
        }
    }
    return 0;
}