loj#2269. 「SDOI2017」切树游戏

Posted 2021-02-17 akcqhzdy

还是loj的机子快啊。。。

普通的DP不难想到，设F[i][zt]为带上根玩出zt的方案数，G[i][zt]为子树中的方案数，后面是可以用FWT优化的

主要是复习了下动态DP

#include<cstdio>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
using namespace std;
const int _=1e2;
const int maxn=3e4+_;
const int fbin=maxn<<2;
const int maxm=128+2;
const int mod=1e4+7;
inline int ad(int x,int y){return (x>=mod-y)?(x-mod+y):x+y;}
inline int re(int x,int y){return (x<y)?(x-y+mod):x-y;}
inline int read()
{
    int x=0; char ch=getchar();
    while(!isdigit(ch))ch=getchar();
    while(isdigit(ch)){x=x*10+ch-‘0‘;ch=getchar();}
    return x;
}
inline void write(int d)
{
    if(d>=10)write(d/10);
    putchar(d%10+‘0‘);
}
int m;

struct poly
{
    int a[maxm];
    poly(){}
    void FWT(int op)
    {
        for(int i=1;i<m;i<<=1)
            for(int j=0;j<m;j+=(i<<1))
                for(int k=0;k<i;k++)
                {
                    int a1=a[j+k],a2=a[j+k+i];
                    a[j+k]=ad(a1,a2);
                    a[j+k+i]=re(a1,a2);
                    if(op==-1)
                    {
                        a[j+k]=a[j+k]*(mod/2+1)%mod;
                        a[j+k+i]=a[j+k+i]*(mod/2+1)%mod;
                    }
                }
    }
    poly(int x){memset(a,0,sizeof(a));a[x]=1;FWT(1);}
    
    friend poly operator +(poly u,poly v){for(int i=0;i<m;i++)u.a[i]=ad(u.a[i],v.a[i]); return u;}
    friend poly operator -(poly u,poly v){for(int i=0;i<m;i++)u.a[i]=re(u.a[i],v.a[i]); return u;}
    friend poly operator *(poly u,poly v){for(int i=0;i<m;i++)u.a[i]=u.a[i]*v.a[i]%mod; return u;}
}o;
struct Matrix
{
    poly a,b,c,d;
    Matrix(){}
    Matrix(poly f,poly g){a=b=c=f;d=f+g;}
    Matrix(poly A,poly B,poly C,poly D){a=A,b=B,c=C,d=D;}
    friend Matrix operator +(Matrix u,Matrix v){return Matrix(u.a*v.a,u.a*v.b+u.b,u.c*v.a+v.c,u.c*v.b+u.d+v.d);}
};
    
//----------------------------------------def------------------------------------------------------------

namespace FASEG//每个点的每个孩子的F+1 
{
    struct trnode 
    {
        int lc,rc;poly p;
    }tr[10*maxn];int trlen,rt[maxn];
    void update(int now)
    {
        int lc=tr[now].lc,rc=tr[now].rc;
        if(lc&&rc)tr[now].p=tr[lc].p*tr[rc].p;
        else if(lc)tr[now].p=tr[lc].p;
        else if(rc)tr[now].p=tr[rc].p;
    }
    void insert(int &now,int l,int r,int p,poly u)
    {
        if(now==0)now=++trlen;
        if(l==r){tr[now].p=u;return ;}
        int mid=(l+r)/2;
        if(p<=mid)insert(tr[now].lc,l,mid,p,u);
        else insert(tr[now].rc,mid+1,r,p,u);
        update(now);
    }
}
namespace LINESEG//第i个位置放的是i的重儿子转移到i的转移矩阵 
{
    #define lc (now<<1)
    #define rc (now<<1|1)
    #define mid ((ql+qr)/2)
    
    Matrix tr[fbin];
    void update(int now){tr[now]=tr[rc]+tr[lc];}
    void change(int now,int ql,int qr,int p,Matrix m)
    {
        if(ql==qr){tr[now]=m;return ;}
        if(p<=mid)change(lc,ql,mid,p,m);
        else change(rc,mid+1,qr,p,m);
        update(now);
    }
    Matrix getmatrix(int now,int ql,int qr,int l,int r)
    {
        if(ql==l&&qr==r)return tr[now];
             if(r<=mid)  return getmatrix(lc,ql,mid,l,r);
        else if(mid+1<=l)return getmatrix(rc,mid+1,qr,l,r);
        else return getmatrix(rc,mid+1,qr,mid+1,r)+getmatrix(lc,ql,mid,l,mid);
    }
    
    #undef lc
    #undef rc
    #undef mid
}

//---------------------------------------data struct----------------------------------------------------

int n;
struct node
{
    int x,y,next;
}a[2*maxn];int len,last[maxn];
void ins(int x,int y)
{
    len++;
    a[len].x=x;a[len].y=y;
    a[len].next=last[x];last[x]=len;
}
int fa[maxn],son[maxn],tot[maxn],dep[maxn];
void pre_tree_node(int x)
{
    tot[x]=1;
    for(int k=last[x];k;k=a[k].next)
    {
        int y=a[k].y;
        if(y!=fa[x])
        {
            fa[y]=x;
            dep[y]=dep[x]+1;
            pre_tree_node(y);
            if(son[x]==0||tot[son[x]]<tot[y])son[x]=y;
            tot[x]+=tot[y];
        }
    }
}
int z,ys[maxn],top[maxn],bot[maxn];
void pre_tree_edge(int x,int tp)
{
    ys[x]=++z;top[x]=tp;
    if(son[x]!=0)pre_tree_edge(son[x],tp),bot[x]=bot[son[x]];
    else bot[x]=x;
    for(int k=last[x];k;k=a[k].next)
    {
        int y=a[k].y;
        if(y!=fa[x]&&y!=son[x])
            pre_tree_edge(y,y);
    }
}

//-------------------------------------------cop----------------------------------------------------

int w[maxn],cnt[maxn],wch[maxn];//有多少轻孩子，爸爸的第几个轻孩子 
poly F[maxn],G[maxn],g[maxn];//包括x的方案数，总方案数，只有轻儿子的总方案数 
void treeDP(int x)
{
    F[x]=poly(w[x]);
    cnt[x]=1;
    for(int k=last[x];k;k=a[k].next)
    {
        int y=a[k].y;
        if(fa[x]!=y)
        {
            treeDP(y);
            F[x]=F[x]*(F[y]+o);
            G[x]=G[x]+G[y];
            if(son[x]!=y)
            {
                wch[y]=++cnt[x];
                g[x]=g[x]+G[y];
            }
        }
    }
    G[x]=G[x]+F[x];
    
    using namespace FASEG;
    insert(rt[x],1,cnt[x],1,poly(w[x]));
    for(int k=last[x];k;k=a[k].next)
    {
        int y=a[k].y;
        if(fa[x]!=y&&son[x]!=y)
            insert(rt[x],1,cnt[x],wch[y],F[y]+o);
    }
}

//-------------------------------------------pre------------------------------------------------

void query(int zt)
{
    poly u=G[1];u.FWT(-1);
    write(u.a[zt]),putchar(‘
‘);
}
Matrix ma;
void change(int x,int zt)
{
    w[x]=zt;
    using namespace FASEG;
    insert(rt[x],1,cnt[x],1,poly(w[x]));
    
    int tx=top[x];
    while(x!=0)
    {
        LINESEG::change(1,1,n,ys[x],Matrix(tr[rt[x]].p,g[x]));
        if(fa[tx]!=0)
        {
            ma=LINESEG::getmatrix(1,1,n,ys[tx],ys[bot[tx]]);
            insert(rt[fa[tx]],1,cnt[fa[tx]],wch[tx],ma.c+o);
            g[fa[tx]]=g[fa[tx]]-G[tx];
            G[tx]=ma.d;
            g[fa[tx]]=g[fa[tx]]+G[tx];
        }
        else G[tx]=LINESEG::getmatrix(1,1,n,ys[tx],ys[bot[tx]]).d;
        x=fa[tx];tx=top[x];
    }
}

char ss[10];
int main()
{
    freopen("xor.in","r",stdin);
    freopen("xor.out","w",stdout);
    int x,y;
    n=read(),m=read();
    for(int i=1;i<=n;i++)w[i]=read(); 
    for(int i=1;i<n;i++)
    {
        x=read(),y=read(); 
        ins(x,y),ins(y,x);
    }
    pre_tree_node(1);
    z=0,pre_tree_edge(1,1);
    for(int i=0;i<m;i++)o.a[i]=1;
    treeDP(1);
    for(int i=1;i<=n;i++)
        LINESEG::change(1,1,n,ys[i],Matrix(FASEG::tr[FASEG::rt[i]].p,g[i]));
    
    int Q;
    Q=read();
    while(Q--)
    {
        char ch=getchar();
        while(ch!=‘C‘&&ch!=‘Q‘)ch=getchar();
        bool bk=ch==‘C‘;
        while(ch!=‘e‘&&ch!=‘y‘)ch=getchar();
        if(!bk)
            x=read(),query(x);
        else 
        {
            x=read(),y=read(),change(x,y);
            
        /*    poly u=LINESEG::getmatrix(1,1,n,ys[1],ys[bot[1]]).d;
            u.FWT(-1);
            for(int i=0;i<=3;i++)
                printf("%d ",u.a[i]);
            puts(""); */ 
        }
    }
        
    return 0;
}