2019.3.25考试

T1

暴力写挂.jpg

正解考虑枚举有几个小塔放了奇数个，然后剩下的就变成球和盒子的问题，统一算

orz wxx，tql

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=1000005;
int fac[N],inv[N];
long long T,n,m,k,mod;
int Qpow(int x,int k)
{
    if(k<=1) return k?x:1;
    int tmp=Qpow(x,k>>1);
    return 1ll*tmp*tmp%mod*((k&1)?x:1)%mod;
}
void Pre()
{
    fac[0]=inv[0]=1;
    for(int i=1;i<mod;i++) fac[i]=1ll*fac[i-1]*i%mod;
    inv[mod-1]=Qpow(fac[mod-1],mod-2);
    for(int i=mod-2;i;i--) inv[i]=1ll*inv[i+1]*(i+1)%mod;
}
int C(int a,int b)
{
    if(a<b||a<0||b<0) return 0;
    return 1ll*fac[a]*inv[b]%mod*inv[a-b]%mod;
}
int Lucas(long long a,long long b)
{
    return b?1ll*C(a%mod,b%mod)*Lucas(a/mod,b/mod)%mod:1;
}
int main()
{
    scanf("%lld",&T);
    while(T--){
        scanf("%lld%lld%lld%lld",&n,&m,&k,&mod),Pre();
        if(!n&&!m) puts("0");
        else if(!n) printf("%d
",(k&1)?0:Lucas((k>>1)+m-1,m-1));
        else if(!m) printf("%d
",Lucas(k+n-1,n-1));
        else
        {
            int ans=0;
            for(int i=0;i<=n;i++)
                if(((k-i)&1)==0)
                    (ans+=1ll*Lucas(n,i)*Lucas(((k-i)>>1)+n+m-1,n+m-1)%mod)%=mod;
            printf("%d
",ans);
        }
    }
    return 0;
}

T2

效率垫底.jpg

用DFS序转成二维数点，然后做就完了

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=100005,M=200005,K=19;
int n,m,q,op,t1,t2,id,cnt,tot,num;
int p[N],noww[M],goal[M],upp[N][K],ans[N];
int siz[N],anc[N],dep[N],imp[N],dfn[N],top[N];
int root[N],val[N*330],lson[N*330],rson[N*330];
void Link(int f,int t)
{
    noww[++cnt]=p[f];
    goal[cnt]=t,p[f]=cnt;
    noww[++cnt]=p[t];
    goal[cnt]=f,p[t]=cnt;
}
void DFS(int nde,int fth,int dth)
{
    int tmp=0;
    siz[nde]=1,anc[nde]=fth,dep[nde]=dth;
    for(int i=p[nde],g;i;i=noww[i])
        if((g=goal[i])!=fth)
        {
            DFS(g,nde,dth+1),siz[nde]+=siz[g];
            if(siz[g]>tmp) tmp=siz[g],imp[nde]=g;
        }
}
void Decompose(int nde,int upt)
{
    dfn[nde]=++tot,top[nde]=upt;
    if(imp[nde])
    {
        Decompose(imp[nde],upt);
        for(int i=p[nde],g;i;i=noww[i])
            if((g=goal[i])!=imp[nde]&&g!=anc[nde]) Decompose(g,g);
    }
}
int LCA(int x,int y)
{
    while(top[x]!=top[y])
    {
        if(dep[top[x]]<dep[top[y]])
            swap(x,y); x=anc[top[x]];
    }
    return dep[x]<dep[y]?x:y;
}
void Pre()
{
    for(int i=1;i<=n;i++) upp[i][0]=anc[i];
    for(int i=1;i<=18;i++)
        for(int j=1;j<=n;j++)
            upp[j][i]=upp[upp[j][i-1]][i-1];
}
void Add(int &nde,int l,int r,int pos,int tsk)
{
    if(!nde) nde=++id;
    if(l==r) val[nde]+=tsk;
    else 
    {
        int mid=(l+r)>>1;
        if(pos<=mid) Add(lson[nde],l,mid,pos,tsk);
        else Add(rson[nde],mid+1,r,pos,tsk);
        val[nde]=val[lson[nde]]+val[rson[nde]];
    }
}
void Modify(int pos,int pot,int tsk)
{
    for(int i=pos;i<=n;i+=i&-i)
        Add(root[i],1,n,pot,tsk);
}
int Query(int &nde,int l,int r,int ll,int rr)
{
    if(!nde) nde=++id;
    if(ll>rr) return 0;
    if(l>=ll&&r<=rr) return val[nde];
    else
    {
        int mid=(l+r)>>1,ret=0;
        if(mid>=ll) ret+=Query(lson[nde],l,mid,ll,rr);
        if(mid<rr) ret+=Query(rson[nde],mid+1,r,ll,rr);
        return ret;
    }
}
int Count(int xa,int ya,int xb,int yb)
{
    int ret1=0,ret2=0;
    for(int i=xa-1;i;i-=i&-i)
        ret1+=Query(root[i],1,n,1,yb)-Query(root[i],1,n,1,ya-1);
    for(int i=xb;i;i-=i&-i)
        ret2+=Query(root[i],1,n,1,yb)-Query(root[i],1,n,1,ya-1);
    return ret2-ret1;
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<n;i++)
        scanf("%d%d",&t1,&t2),Link(t1,t2);
    DFS(1,0,1),Decompose(1,1),Pre();
    scanf("%d",&m);
    for(int i=1;i<=m;i++)
    {
        scanf("%d%d",&t1,&t2);
        Modify(dfn[t1],dfn[t2],1);
        Modify(dfn[t2],dfn[t1],1);
    }
    scanf("%d",&q);
    while(q--)
    {
        scanf("%d%d%d",&op,&t1,&t2);
        if(op==1) Modify(dfn[t1],dfn[t2],1),Modify(dfn[t2],dfn[t1],1);
        else if(op==2) Modify(dfn[t1],dfn[t2],-1),Modify(dfn[t2],dfn[t1],-1);
        else 
        {
            int lca=LCA(t1,t2);
            if(lca==t1)
            {
                int ly=dfn[t2],ry=dfn[t2]+siz[t2]-1,nde=t2;
                for(int i=18;~i;i--)
                    if(dep[upp[nde][i]]>dep[t1]) nde=upp[nde][i];
                int lx=dfn[nde],rx=dfn[nde]+siz[nde]-1;
                ans[++num]=Count(1,ly,lx-1,ry)+Count(rx+1,ly,n,ry);
            }
            else if(lca==t2)
            {
                swap(t1,t2);
                int ly=dfn[t2],ry=dfn[t2]+siz[t2]-1,nde=t2;
                for(int i=18;~i;i--)
                    if(dep[upp[nde][i]]>dep[t1]) nde=upp[nde][i];
                int lx=dfn[nde],rx=dfn[nde]+siz[nde]-1;
                ans[++num]=Count(1,ly,lx-1,ry)+Count(rx+1,ly,n,ry);
            }
            else
            {
                int lx=dfn[t1],rx=dfn[t1]+siz[t1]-1;
                int ly=dfn[t2],ry=dfn[t2]+siz[t2]-1;
                ans[++num]=Count(lx,ly,rx,ry);
            }
        }
    }
    for(int i=1;i<=num;i++)
    {
        printf("%d",ans[i]);
        if(i!=num) puts("");
    }
    return 0;
}

T3