bzoj2759

Posted 2020-10-17 宣毅鸣

题解：

lct+解线性方程组

首先先把每一个环搞出来，然后再建立一个额外的点

然后解方程。。

代码：

#include <bits/stdc++.h>
using namespace std;
const int N=300005,M=10007;
int n,Q,tim,fa[N],dir[N],x,k,p,b,vis[N],ch[N][2],ni[N];
char s[4];
int which(int x){return ch[fa[x]][1]==x;}
struct node
{
    int k,b;
    node(){}
    node(int k,int b):k(k),b(b){}
    friend node operator + (const node &r1,const node &r2)
     {return node(r1.k*r2.k%M,(r2.k*r1.b%M+r2.b)%M);}
}a[N],sum[N];
void dfs(int x)
{
    if (vis[x])return;
    vis[x]=tim;
    if (vis[fa[x]]==tim)
     {
        dir[x]=fa[x];
        fa[x]=0;
     }
    else dfs(fa[x]);
}
int isroot(int x){return !fa[x]||ch[fa[x]][which(x)]!=x;}
void pushup(int x)
{
    sum[x]=a[x];
    if (ch[x][0])sum[x]=sum[ch[x][0]]+a[x];
    if (ch[x][1])sum[x]=sum[x]+sum[ch[x][1]];
}
void rotate(int x)
{
    int y=fa[x],k=which(x);
    ch[y][k]=ch[x][k^1];
    ch[x][k^1]=y;
    if (!isroot(y))ch[fa[y]][which(y)]=x;
    fa[x]=fa[y];fa[y]=x;
    fa[ch[y][k]]=y;
    pushup(y);pushup(x);
}
void splay(int x)
{
    for (int y=fa[x];!isroot(x);rotate(x),y=fa[x])
     if (!isroot(y))rotate((ch[y][0]==x)==(ch[fa[y]][0]==y)?y:x);
}
void access(int x)
{
    int t=0;
    while(x)
     {
        splay(x);
        ch[x][1]=t;
        pushup(x);
        t=x;x=fa[x];
     }
}
int findroot(int x)
{
    access(x);splay(x);
    while(ch[x][0])x=ch[x][0];
    splay(x);
    return x;
}
int inc(int x,int y)
{
    access(dir[y]);splay(dir[y]);
    splay(x);
    return x==dir[y]||!isroot(dir[y]);
}
void cut(int x){access(x);splay(x);ch[x][0]=fa[ch[x][0]]=0;pushup(x);}
int main()
{
    ni[1]=1;
    for (int i=2;i<M;i++)ni[i]=(M-M/i)*ni[M%i]%M;
    scanf("%d",&n);
    for (int i=1;i<=n;i++)scanf("%d%d%d",&a[i].k,&fa[i],&a[i].b);
    for (int i=1;i<=n;i++)
     if (!vis[i])tim++,dfs(i);
    scanf("%d",&Q);
    while (Q--)
     {
        scanf("%s",s+1);
        if (s[1]==‘A‘)
         {
            scanf("%d",&x);
            access(x);splay(x);
            node t1=sum[x];
            int t=findroot(x);
            access(dir[t]);splay(dir[t]);
            node t2=sum[dir[t]];
            if (t2.k==1)
             {
                if (t2.b)puts("-1");
                else puts("-2");
                continue;
             }
            int v1=ni[(1-t2.k+M)%M]*t2.b%M;
            printf("%d\n",(t1.k*v1%M+t1.b)%M);
         }
        else 
         {
            scanf("%d%d%d%d",&x,&k,&p,&b);
            access(x);splay(x);
            a[x]=node(k,b);pushup(x);
            int t=findroot(x);
            if (t==x)
             {
                if (findroot(p)==t)dir[t]=p;
                else dir[t]=0,fa[t]=p;
             }
            else
             {
                if (inc(x,t))
                 {
                    cut(x);
                    access(t);splay(t);
                    fa[t]=dir[t];dir[t]=0;
                    if (findroot(p)==x)dir[x]=p;
                    else fa[x]=p;
                 }
                else 
                 {
                    cut(x);
                    if (findroot(p)==x)dir[x]=p;
                    else fa[x]=p;
                 }
             }
         }
     }
    return 0;
}