牛客网暑期ACM多校训练营（第九场）

毕姥爷场
A
FWT

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod=1e9+7;
const int inv2=500000004;
ll power(ll n,ll p){
    ll ans=1;
    ll base=n;
    while(p){
        if(p&1)ans=ans*base%mod;
        p>>=1;
        base=base*base%mod;
    }
    return ans;
}
void fwt(ll a[],int len){
    while(len!=(len&(-len)))len+=len&(-len);
    for(int i=0;1<<i<len;i++){
        for(int j=0;j<len;j+=(2<<i)){
            for(int k=0;k<1<<i;k++){
                ll l=a[j+k],r=a[j+(1<<i)+k];
                a[j+k]=(l+r)%mod;
                a[j+(1<<i)+k]=(l-r+mod)%mod;
            }
        }
    }
}
void rfwt(ll a[],int len){
    while(len!=(len&(-len)))len+=len&(-len);
    int i=31-__builtin_clz(len)-1;
    for(i;i>=0;i--){
        for(int j=0;j<len;j+=(2<<i)){
            for(int k=0;k<1<<i;k++){
                ll l=a[j+k],r=a[j+(1<<i)+k];
                a[j+k]=(l+r)*inv2%mod;
                a[j+(1<<i)+k]=(l-r+mod)*inv2%mod;
            }
        }
    }
}
int n;
ll a[1<<18];
ll b[1<<18];
ll c[1<<18];
int main(){
    scanf("%d",&n);
    for(int i=0;i<n;i++)scanf("%lld",&a[i]);
    for(int i=0;i<n;i++)scanf("%lld",&c[i]);
    fwt(a,n);
    fwt(c,n);
    for(int i=0;i<n;i++)b[i]=c[i]*power(a[i],mod-2)%mod;
    rfwt(b,n);
    for(int i=0;i<n;i++)printf("%lld\n",b[i]);
}

C
找规律dp，强行莫队

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod=1e9+7;
ll power(ll n,ll p){
    ll ans=1;
    ll base=n;
    while(p){
        if(p&1)ans=ans*base%mod;
        p>>=1;
        base=base*base%mod;
    }
    return ans;
}
ll fac[400005];
ll inv[400005];
ll C(ll x,ll y){
    ll ans=fac[x];
    ans=ans*inv[y]%mod;
    ans=ans*inv[x-y]%mod;
    return ans;
}
void debug(){
    ll x,y;
    while(cin>>x>>y){
        cout<<C(x,y)<<endl;
    }
}
ll n,m;
struct node{
    ll x,y,id;
}rec[400005];
ll tot;
bool cmp(node a,node b){
    if(a.x/400==b.x/400){
        if((a.x/400)&1)return a.y<b.y;
        return a.y>b.y;
    }
    return a.x<b.x;
}
ll res[400005];
ll rx[400005],ry[400005];
ll dir[400005];
bool flag=true;
void addquery(){
    scanf("%lld",&n);
    ll x=0,y=0;
    ll op;
    m=0;
    while(~scanf("%lld",&op)){
        m++;
    //  cout<<op<<endl;
        rx[m]=x,ry[m]=y;
        rec[++tot]=(node){2*n-x-y-1,n-y-1,2*m-1};
    //  cout<<rec[tot].x<<' '<<rec[tot].y<<endl;
        rec[++tot]=(node){2*n-x-y-1,n-x-1,2*m};
    //  cout<<rec[tot].x<<' '<<rec[tot].y<<endl;
        if(op==0){y++;dir[m]=0;}
        else {x++;dir[m]=1;}
    }
    if(x>y)flag=true;
    else flag=false;
}
void solvequery(){
    sort(rec+1,rec+1+tot,cmp);
    ll tx=1,ty=0;
    ll tmp=1;
    for(ll i=1;i<=tot;i++){
        while(tx<rec[i].x){
            tmp=(2*tmp-C(tx,ty)+mod)%mod;
            tx++;
        }
        while(ty>rec[i].y){
            tmp=(tmp-C(tx,ty)+mod)%mod;
            ty--;
        }
        while(tx>rec[i].x){
            tmp=(tmp+C(tx-1,ty))*inv[2]%mod;
            tx--;
        }
        while(ty<rec[i].y){
            tmp=(tmp+C(tx,ty+1))%mod;
            ty++;
        }
        res[rec[i].id]=tmp;
    }
}
ll path[400005];
ll totp=0;
void print(){
    for(ll i=1;i<=m;i++){
        //cout<<res[2*i-1]<<endl;
        //cout<<res[2*i]<<endl;
        ll ans=power(2,rx[i]+ry[i]);
        ll mul=(res[2*i-1]-res[2*i]+mod)%mod;
        ans=ans*mul%mod;
        path[++totp]=ans;
        //printf("%lld\n",ans);
    }
    ll ed=power(2,2*n-1);
    if(flag)path[++totp]=ed;
    else path[++totp]=(mod-ed)%mod;
    for(ll i=2;i<=totp;i++){
        if(dir[i-1]==0){
            printf("%lld\n",(path[i-1]-path[i]+mod)%mod);
        }else {
            printf("%lld\n",(path[i]-path[i-1]+mod)%mod);
        }
    }
}
int main(){
    fac[0]=inv[0]=1;
    for(ll i=1;i<=200001;i++){
        fac[i]=fac[i-1]*i%mod;
        inv[i]=power(fac[i],mod-2);
    }
    //  debug();
    addquery();
    solvequery();
    print();
}

E
dp

#include<bits/stdc++.h>
using namespace std;
#define ll long long
const ll mod=1e9+7;
const int N=1010;
ll inv100;
ll qpow(ll x, ll y){
    ll ans=1;
    while(y){
        if(y&1) ans=ans*x%mod;
        x=x*x%mod;
        y>>=1;
    }
    return ans;
}

ll inv(ll x){
    return qpow(x,mod-2);
}

int n,m;
int p[N];
ll dp[N][2];
int main(){
    inv100=inv(100);
    scanf("%d%d",&n,&m);
    for(int i=1; i<=n; i++){
        scanf("%d",&p[i]);
        dp[i][0]=(dp[i-1][0]+dp[i-1][1])*(100-p[i])%mod*inv100%mod;
        dp[i][1]=0;
        ll tmp,xs=p[i]*inv100%mod;
        for(int j=i-1; j>=0; j--){
            tmp=(dp[j][0]+qpow(i-j,m)*(100-p[j])%mod*inv100%mod)*xs%mod;
            dp[i][1]+=tmp;
            xs=xs*p[j]%mod*inv100%mod;
        }
        //cout<<i<<": "<<dp[i][0]<<" "<<dp[i][1]<<endl;
        dp[i][1]%=mod;
    }
    printf("%lld\n",(dp[n][0]+dp[n][1])%mod);
    return 0;
}

F
AC自动机反过来搞一搞
//AC自动机
//查询模式串出现次数

#include <bits/stdc++.h>
using namespace std;
queue<int>que;
int ans[100003];
vector<int>g[100003];
struct Trie{
    int ch[100003][26];
    int fail[100003];
    int end[100003];
    int sz;
    int newnode(){
        for(int i=0;i<26;i++)ch[sz][i]=-1;
        end[sz]=0;
        return sz++;
    }
    void init(){
        memset(end,0,sizeof(end));
        sz=0;
        newnode();
    }
    int idx(char c){
        return c-'a';
    }
    void insert(char s[]){
        int len=strlen(s);
        int u=0;
        for(int i=0;i<len;i++){
            int c=idx(s[i]);
            if(ch[u][c]==-1){
                ch[u][c]=newnode();
            }
            u=ch[u][c];
        }
        end[u]=1;
        //que.push(u);
        //ans[u]=1;
    }
    void build(){
        queue<int>q;
        fail[0]=0;
        for(int i=0;i<26;i++){
            if(ch[0][i]==-1)ch[0][i]=0;
            else {
                fail[ch[0][i]]=0;
                q.push(ch[0][i]);
            }
        }
        while(!q.empty()){
            int u=q.front();
            q.pop();
            for(int i=0;i<26;i++){
                if(ch[u][i]==-1){
                    ch[u][i]=ch[fail[u]][i];
                }
                else {
                    fail[ch[u][i]]=ch[fail[u]][i];
                    q.push(ch[u][i]);
                }
            }
        }
        for(int i=0;i<sz;i++){
            if(end[fail[i]])end[i]=1;
            //cout<<i<<' '<<fail[i]<<' '<<end[i]<<endl;
            if(end[i]){
                que.push(i);
                ans[i]=1;
            }
        }
    }
    void buildr(){
        for(int i=0;i<sz;i++){
            for(int j=0;j<26;j++){
                g[ch[i][j]].push_back(i);
            }
        }
    }
};

Trie T;

char s[100003];
int rec[100003];
int len=0;

int main(){
    while(!que.empty())que.pop();
    T.init();
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%s",s);
        T.insert(s);
    }
    T.build();
    T.buildr();
    while(!que.empty()){
        int u=que.front();
        que.pop();
        for(int i=0;i<g[u].size();i++){
            int v=g[u][i];
            if(ans[v])continue;
            ans[v]=ans[u]+1;
            que.push(v);
        }
    }
    scanf("%s",s);
    printf("%d\n",ans[rec[len]]-1);
    for(int i=0;s[i];i++){
        if(s[i]=='-'){
            if(len){
                len--;
            }
            printf("%d\n",ans[rec[len]]-1);
        }
        else {
            int c=s[i]-'a';
            int v=T.ch[rec[len]][c];
            rec[++len]=v;
            printf("%d\n",ans[rec[len]]-1);
        }
        //cout<<rec[len]<<endl;
    }
}

H
分块暴力

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod=1e9+7;
ll power(ll n,ll p){
    ll ans=1;
    ll base=n;
    while(p){
        if(p&1)ans=ans*base%mod;
        base=base*base%mod;
        p>>=1;
    }
    return ans;
}
ll fac[200003];
ll inv[200003];
ll C(ll n,ll m){
//  cout<<n<<' '<<m<<endl;
    ll ret=fac[n];
    ret=ret*inv[m]%mod;
    ret=ret*inv[n-m]%mod;
    return ret;
}
int n,m,k;
ll a[41][100003];
void debug(){
    ll x,y;
    while(cin>>x>>y){
        cout<<C(x,y)<<endl;
    }
}
int x[2003];
int y[2003];
int top=0;
int main(){
    fac[0]=inv[0]=1;
    for(int i=1;i<=200000;i++){
        fac[i]=fac[i-1]*i%mod;
        inv[i]=power(fac[i],mod-2);
    }
    //debug();
    scanf("%d%d%d",&n,&m,&k);
    for(int i=1;i<=m;i++){
        int op;
        scanf("%d",&op);
        if(op==1){
            int p;
            scanf("%d",&p);
            ll ans=a[k][p];
            for(int j=1;j<=top;j++){
                if(x[j]>p)continue;
                ans+=C(k-1+p-x[j],k-1)*y[j];
                ans%=mod;
            }
            printf("%d\n",ans);
        }
        else if(op==0){
            ++top;
            scanf("%d%d",&x[top],&y[top]);
        }
        if(i%2000==0){
            while(top){
                a[0][x[top]]+=y[top];
                if(a[0][x[top]]>=mod)a[0][x[top]]-=mod;
                top--;
            }
            for(int i=1;i<=k;i++){
                for(int j=1;j<=n;j++){
                    a[i][j]=a[i-1][j]+a[i][j-1];
                    if(a[i][j]>=mod)a[i][j]-=mod;
                }
            }
        }
    }
}