牛客小白月赛12

牛客小白月赛12

https://ac.nowcoder.com/acm/contest/392#question

 

华华听月月唱歌

贪心

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define pb push_back
#define eb emplace_back
#define maxn 100005
#define eps 1e-8
#define pi acos(-1.0)
#define rep(k,i,j) for(int k=i;k<j;k++)
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<char,int> pci;
typedef pair<pair<int,string>,pii> ppp;
typedef unsigned long long ull;
const long long MOD=1e9+9;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */

int n,m;
vector<pii>ve;

bool cmp(pii a,pii b){
    if(a.first==b.first) return a.second>b.second;
    return a.first<b.first;
}

int main(){
    #ifndef ONLINE_JUDGE
     //   freopen("1.txt","r",stdin);
    #endif
    std::ios::sync_with_stdio(false);
    cin>>n>>m;
    int u,v;
    for(int i=1;i<=m;i++){
        cin>>u>>v;
        ve.pb(make_pair(u,v));
    }
    sort(ve.begin(),ve.end(),cmp);
    int ans=1;
    int last=ve[0].second;
    int tmp=ve[0].second;
    for(int i=1;i<ve.size();i++){
        if(ve[i].first<=last) {
            tmp=max(ve[i].second,tmp);
        }
        else{
            if(ve[i].first-last<=1){
                last=ve[i].second;
                tmp=last;
                ans++;
            }
            else if(ve[i].first-tmp<=1){
                ans+=1;
                last=tmp;
                i--;
            }
            else{
                cout<<-1<<endl;
                return 0;
            }
        }
    }
    if(last!=n&&tmp==n) ans++;
    cout<<ans<<endl;
}

华华教月月做数学

快速幂

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define pb push_back
#define eb emplace_back
#define maxn 100005
#define eps 1e-8
#define pi acos(-1.0)
#define rep(k,i,j) for(int k=i;k<j;k++)
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<char,int> pci;
typedef pair<pair<int,string>,pii> ppp;
typedef unsigned long long ull;
const long long MOD=1e9+9;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */

ll p;
ll pow_mul(ll aa,ll b){
    __int128 ans=1,a=aa%p;
    while(b){
        if(b&1){
            ans=((ans%p)*(a%p))%p;
        }
        a=((a%p)*(a%p))%p;
        b>>=1;
    }
    return ans;
}

int main(){
    #ifndef ONLINE_JUDGE
     //   freopen("1.txt","r",stdin);
    #endif
    std::ios::sync_with_stdio(false);
    int t;
    cin>>t;
    ll a,b;
    while(t--){
        cin>>a>>b>>p;
        cout<<pow_mul(a,b)<<endl;
    }
}

华华给月月出题

因为合数a可以由两个比它小的数相乘得到。所以用线性筛求出素数和合数，素数的d[i]的值只能用快速幂求出，合数可以用之前求过的两个数相乘直接得到

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define pb push_back
#define eb emplace_back
#define maxn 13000005
#define eps 1e-8
#define pi acos(-1.0)
#define rep(k,i,j) for(int k=i;k<j;k++)
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<char,int> pci;
typedef pair<pair<int,string>,pii> ppp;
typedef unsigned long long ull;
const long long MOD=1e9+7;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */

ll prime[maxn];
bool isprime[maxn];
ll d[maxn];
int tot;

ll pow_mul(ll a,ll b){
    ll ans=1;
    while(b){
        if(b&1){
            ans=ans*a%MOD;
        }
        a=a*a%MOD;
        b>>=1;
    }
    return ans;
}

void init(int n){
    memset(isprime,true,sizeof(isprime));
    for(int i=2;i<=n;i++){
        if(isprime[i]){
            prime[++tot]=i;
            d[i]=pow_mul(i,n);
        }
        for(int j=1;j<=tot&&i*prime[j]<=n;j++){
            isprime[i*prime[j]]=false;
            d[i*prime[j]]=1ll*d[i]*d[prime[j]]%MOD;
            if(i%prime[j]==0) break;
        }
    }
}


int main(){
    #ifndef ONLINE_JUDGE
     //   freopen("1.txt","r",stdin);
    #endif
    std::ios::sync_with_stdio(false);
    int n;
    cin>>n;
    init(n);
    ll ans=1;
    for(int i=1;i<=n;i++){
        ans^=d[i];
    }
    cout<<ans<<endl;
}

月月给华华出题

数学渣。。感觉这题是这套题中最难的= =，根据下图的式子，可以看出答案和欧拉函数有关，所以直接用线性筛求欧拉函数

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define pb push_back
#define eb emplace_back
#define maxn 1000006
#define eps 1e-8
#define pi acos(-1.0)
#define rep(k,i,j) for(int k=i;k<j;k++)
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<char,int> pci;
typedef pair<pair<int,string>,pii> ppp;
typedef unsigned long long ull;
const long long MOD=1e9+7;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */

int prime[maxn];
int vis[maxn];
int tot;
ll phi[maxn],ans[maxn];

void Init(int n){
    phi[1]=1;
    for(int i=2;i<=n;i++){
        if(!vis[i]){
            prime[++tot]=i;
            phi[i]=i-1;
        }
        for(int j=1;j<=tot&&i*prime[j]<=n;j++){
            vis[i*prime[j]]=true;
            if(i%prime[j]==0){
                phi[i*prime[j]]=phi[i]*prime[j];
                break;
            }
            phi[i*prime[j]]=phi[i]*(prime[j]-1);
        }
    }
}

int main(){
    #ifndef ONLINE_JUDGE
       // freopen("1.txt","r",stdin);
    #endif
    std::ios::sync_with_stdio(false);
    int n;
    scanf("%d",&n);
    Init(n);
    for(int i=2;i<=n;i++) phi[i]=phi[i]*i/2;
    for(int i=1;i<=n;i++){
        for(int j=i;j<=n;j+=i){
            ans[j]+=phi[i];
        }
    }
    for(int i=1;i<=n;i++) printf("%lld\n",ans[i]);
}

 

华华给月月准备礼物

二分

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define pb push_back
#define eb emplace_back
#define maxn 100005
#define eps 1e-8
#define pi acos(-1.0)
#define rep(k,i,j) for(int k=i;k<j;k++)
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<char,int> pci;
typedef pair<pair<int,string>,pii> ppp;
typedef unsigned long long ull;
const long long MOD=1e9+9;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */

ll n,k;
int a[200005];

bool erfen(ll mid){
    ll sum=0;
    for(int i=1;i<=n;i++){
        sum+=a[i]/mid;
    }
    if(sum>=k) return true;
    return false;
}

int main(){
    #ifndef ONLINE_JUDGE
     //   freopen("1.txt","r",stdin);
    #endif
    std::ios::sync_with_stdio(false);
    cin>>n>>k;
    ll sum=0;
    for(int i=1;i<=n;i++){
        cin>>a[i];
        sum+=a[i];
    }
    ll L=1,R=1e9,mid;
    while(L<=R){
        mid=L+R>>1;
        if(erfen(mid)){
            L=mid+1;
        }
        else{
            R=mid-1;
        }
    }
    cout<<R<<endl;
}

华华开始学信息学

分块+树状数组

当d<=sqrt(n)时，如果要更新的话，代价有点大，所以用一个数组保存当d<=sqrt(n)时的更新。当D>sqrt(n)时，暴力更新，因为复杂度不会超过sqrt(n)

然后求和的时候把d<=sqrt(n)的值更新一下就行

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define pb push_back
#define eb emplace_back
#define maxn 200005
#define eps 1e-8
#define pi acos(-1.0)
#define rep(k,i,j) for(int k=i;k<j;k++)
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<char,int> pci;
typedef pair<pair<int,string>,pii> ppp;
typedef unsigned long long ull;
const long long MOD=1e9+7;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */

ll a[100005];
ll book[1005];
int n;

int lowbit(int x){return x&(-x);}

ll getsum(int x){
    ll sum=0;
    while(x){
        sum+=a[x];
        x-=lowbit(x);
    }
    return sum;
}

void add(int x,int k){
    while(x<=n){
        a[x]+=k;
        x+=lowbit(x);
    }
}

int main(){
    #ifndef ONLINE_JUDGE
       // freopen("1.txt","r",stdin);
    #endif
    std::ios::sync_with_stdio(false);
    int m;
    cin>>n>>m;
    int pos,x,y;
    int sq=sqrt(n);
    for(int i=1;i<=m;i++){
        cin>>pos>>x>>y;
        if(pos==1){
            if(x<=sq){
                book[x]+=y;
            }
            else{
                for(int j=x;j<=n;j+=x){
                    add(j,y);
                }
            }
        }
        else{
            ll ans=getsum(y)-getsum(x-1);
            for(int j=1;j<=sq;j++){
                ans+=book[j]*(y/j-(x-1)/j);
            }
            cout<<ans<<endl;
        }
    }

}

华华对月月的忠诚

因为gcd(a,b)==gcd(b,a%b)==gcd(b,a-b)...所以是结论题

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define pb push_back
#define eb emplace_back
#define maxn 100005
#define eps 1e-8
#define pi acos(-1.0)
#define rep(k,i,j) for(int k=i;k<j;k++)
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<char,int> pci;
typedef pair<pair<int,string>,pii> ppp;
typedef unsigned long long ull;
const long long MOD=1e9+9;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */



int main(){
    #ifndef ONLINE_JUDGE
     //   freopen("1.txt","r",stdin);
    #endif
    std::ios::sync_with_stdio(false);
    ll a,b,c;
    cin>>a>>b>>c;
    cout<<__gcd(a,b)<<endl;
}

华华和月月种树

先离线，然后跑树剖就好（感觉这做法有点麻烦,用树状数组好像也可以做），注意，当新加入一个节点时，他可能已经有值了，所以在新增一个节点时，需要清空他和他子孙的值

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define pb push_back
#define eb emplace_back
#define maxn 200005
#define eps 1e-8
#define pi acos(-1.0)
#define rep(k,i,j) for(int k=i;k<j;k++)
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<char,int> pci;
typedef pair<pair<int,string>,pii> ppp;
typedef unsigned long long ull;
const long long MOD=1e9+7;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */

int tree[maxn<<3],lazy[maxn<<3],zero[maxn<<3];
int n;
int dep[maxn],fa[maxn],siz[maxn],son[maxn],id[maxn],top[maxn],cnt;
vector<int>ve[maxn];
int tot=1;

void pushup(int rt){
    tree[rt]=max(tree[rt<<1],tree[rt<<1|1]);
}

void pushdown(int rt){
    if(zero[rt]){
        zero[rt<<1]=1;
        zero[rt<<1|1]=1;
        tree[rt<<1]=0;
        tree[rt<<1|1]=0;
        lazy[rt<<1]=0;
        lazy[rt<<1|1]=0;
        zero[rt]=0;
    }
    if(lazy[rt]){
        lazy[rt<<1]+=lazy[rt];
        lazy[rt<<1|1]+=lazy[rt];
        tree[rt<<1]+=lazy[rt];
        tree[rt<<1|1]+=lazy[rt];
        lazy[rt]=0;
    }
}

void build(int l,int r,int rt){
    lazy[rt]=0;
    if(l==r){
        tree[rt]=0;
        return;
    }
    int mid=(l+r)/2;
    build(lson);
    build(rson);
    pushup(rt);
}

void init(int L,int R,int l,int r,int rt){
    if(L<=l&&R>=r){
        tree[rt]=0;
        lazy[rt]=0;
        zero[rt]=1;
        pushdown(rt);
        return;
    }
    int mid=l+r>>1;
    pushdown(rt);
    if(L<=mid) init(L,R,lson);
    if(R>mid) init(L,R,rson);
    pushup(rt);
}

void add(int L,int R,int k,int l,int r,int rt){
    if(L<=l&&R>=r){
        pushdown(rt);
        tree[rt]+=k;
        lazy[rt]+=k;
        return;
    }
    int mid=(l+r)/2;
    pushdown(rt);
    if(L<=mid) add(L,R,k,lson);
    if(R>mid) add(L,R,k,rson);
    pushup(rt);
}

int query(int L,int l,int r,int rt){
    if(l==r){
        pushdown(rt);
        return tree[rt];
    }
    int mid=(l+r)/2;
    pushdown(rt);
    int ans=0;
    if(L<=mid) return query(L,lson);
    else return query(L,rson);
    pushup(rt);
    return ans;
}

void dfs1(int now,int f,int deep){
    dep[now]=deep;
    siz[now]=1;
    fa[now]=f;
    int maxson=-1;
    for(int i=0;i<ve[now].size();i++){
        if(ve[now][i]==f) continue;
        dfs1(ve[now][i],now,deep+1);
        siz[now]+=siz[ve[now][i]];
        if(siz[ve[now][i]]>maxson){
            maxson=siz[ve[now][i]];
            son[now]=ve[now][i];
        }
    }
}

void dfs2(int now,int topp){
    id[now]=++cnt;
    top[now]=topp;
    if(!son[now]) return;
    dfs2(son[now],topp);
    for(int i=0;i<ve[now].size();i++){
        if(ve[now][i]==son[now]||ve[now][i]==fa[now]) continue;
        dfs2(ve[now][i],ve[now][i]);
    }
}


void addSon(int x,int k){
    add(id[x],id[x]+siz[x]-1,k,1,tot,1);
}

void addSon(int x){
    init(id[x],id[x]+siz[x]-1,1,tot,1);
}

struct sair{
    int pos,x,y;
}a[maxn<<1];

int main(){
    #ifndef ONLINE_JUDGE
       // freopen("1.txt","r",stdin);
    #endif
    std::ios::sync_with_stdio(false);
    cin>>n;
    int pos;
    for(int i=1;i<=n;i++){
        cin>>a[i].pos>>a[i].x;
        a[i].x++;
        if(a[i].pos==2){
            cin>>a[i].y;
        }
        if(a[i].pos==1){
            ++tot;
            ve[a[i].x].pb(tot);
            ve[tot].pb(a[i].x);
        }
    }
    cnt=0;
    dfs1(1,0,1);
    dfs2(1,1);
    build(1,tot,1);
    int co=2;
    for(int i=1;i<=n;i++){
        if(a[i].pos==1){
            addSon(co);
            co++;
        }
        else if(a[i].pos==2){
            addSon(a[i].x,a[i].y);
        }
        else if(a[i].pos==3){
            cout<<query(id[a[i].x],1,tot,1)<<endl;
        }
    }

}

华华和月月逛公园

跑tarjan就行

#include<bits/stdc++.h>
using namespace std;
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define sqr(x) ((x)*(x))
#define pb push_back
#define eb emplace_back
#define maxn 200005
#define eps 1e-8
#define pi acos(-1.0)
#define rep(k,i,j) for(int k=i;k<j;k++)
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<char,int> pci;
typedef pair<pair<int,string>,pii> ppp;
typedef unsigned long long ull;
const long long MOD=1e9+9;
/*#ifndef ONLINE_JUDGE
        freopen("1.txt","r",stdin);
#endif */

vector<int>ve[maxn];
int n,m,dfn[maxn],low[maxn],vis[maxn],tot,ans;
stack<int>st;

void dfs(int u,int pre){
    low[u]=dfn[u]=++tot;
    for(int i=0;i<ve[u].size();i++){
        int v=ve[u][i];
        if(!dfn[v]){
            dfs(v,u);
            low[u]=min(low[v],low[u]);
            if(low[v]>dfn[u]) ans++;
        }
        else if(v!=pre){
            low[u]=min(low[u],dfn[v]);
        }
    }
}


int main(){
    #ifndef ONLINE_JUDGE
     //   freopen("1.txt","r",stdin);
    #endif
    std::ios::sync_with_stdio(false);
    cin>>n>>m;
    int u,v;
    for(int i=1;i<=m;i++){
        cin>>u>>v;
        ve[u].pb(v);
        ve[v].pb(u);
    }
    dfs(1,0);
    printf("%d\n",m-ans);
}