結果

問題 No.1649 Manhattan Square
コンテスト
ユーザー mugen_1337
提出日時 2021-08-14 20:49:02
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 600 ms / 3,000 ms
コード長 7,063 bytes
コンパイル時間 2,622 ms
コンパイル使用メモリ 220,264 KB
最終ジャッジ日時 2025-01-23 22:13:30
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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ファイルパターン 結果
sample AC * 2
other AC * 43
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ソースコード

diff # 

#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 1000000007
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;

template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}

template<ll Mod>
struct ModInt{
    long long x;
    ModInt():x(0){}
    ModInt(long long y):x(y>=0?y%Mod:(Mod-(-y)%Mod)%Mod){}
    ModInt &operator+=(const ModInt &p){
        if((x+=p.x)>=Mod) x-=Mod;
        return *this;
    }
    ModInt &operator-=(const ModInt &p){
        if((x+=Mod-p.x)>=Mod)x-=Mod;
        return *this;
    }
    ModInt &operator*=(const ModInt &p){
        x=(int)(1ll*x*p.x%Mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p){
        (*this)*=p.inverse();
        return *this;
    }
    ModInt operator-()const{return ModInt(-x);}
    ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;}
    ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;}
    ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;}
    ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;}
    bool operator==(const ModInt &p)const{return x==p.x;}
    bool operator!=(const ModInt &p)const{return x!=p.x;}
    ModInt inverse()const{
        int a=x,b=Mod,u=1,v=0,t;
        while(b>0){
            t=a/b;
            swap(a-=t*b,b);swap(u-=t*v,v);
        }
        return ModInt(u);
    }
    ModInt pow(long long n)const{
        ModInt ret(1),mul(x);
        while(n>0){
            if(n&1) ret*=mul;
            mul*=mul;n>>=1;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os,const ModInt &p){return os<<p.x;}
    friend istream &operator>>(istream &is,ModInt &a){long long t;is>>t;a=ModInt<Mod>(t);return (is);}
    static int get_mod(){return Mod;}
};

using mint=ModInt<998244353>;

template<typename Monoid>
struct SegmentTree{
    using F=function<Monoid(Monoid,Monoid)>;

    private:
    int sz;
    vector<Monoid> seg;

    Monoid query(int a,int b,int k,int l,int r){
        if(a<=l and r<=b)   return seg[k];
        if(b<=l or r<=a)    return M0;
        Monoid L=query(a,b,2*k,l,(l+r)/2);
        Monoid R=query(a,b,2*k+1,(l+r)/2,r);
        return f(L,R);
    }
    template<typename C>
    int find_first(int a,const C &check,Monoid &acc,int k,int l,int r){
        if(k>=sz){
            acc=f(acc,seg[k]);
            if(check(acc))  return -1;
            else            return k-sz;
        }
        int m=(l+r)/2;
        if(m<=a) return find_first(a,check,acc,2*k+1,m,r);
        if(a<=l and check(f(acc,seg[k]))){
            acc=f(acc,seg[k]);
            return -1;
        }
        int x=find_first(a,check,acc,2*k+0,l,m);
        if(x>=0) return x;
        return find_first(a,check,acc,2*k+1,m,r);
    }
    template<typename C>
    int find_last(int b,const C &check,Monoid &acc,int k,int l,int r){
        if(k>=sz){
            acc=f(acc,seg[k]);
            if(check(acc))  return -1;
            else            return k-sz+1;//ここはfalse, +1した位置はtrue
        }
        int m=(l+r)/2;
        if(b<=m) return find_last(b,check,acc,2*k,l,m);
        if(r<=b and check(f(acc,seg[k]))){
            acc=f(acc,seg[k]);
            return -1;
        }
        int x=find_last(b,check,acc,2*k+1,m,r);
        if(x>=0) return x;
        return find_last(b,check,acc,2*k,l,m);
    }

    public:

    F f;
    Monoid M0;// モノイドの元
    SegmentTree(int n,F f,Monoid M0):f(f),M0(M0){
        sz=1;
        while(sz<n)sz<<=1;
        seg.assign(2*sz,M0);
    }
    void set(int k,Monoid x){
        seg[k+sz]=x;
    }
    void build(){
        for(int k=sz-1;k>0;k--) seg[k]=f(seg[2*k],seg[2*k+1]);
    }
    void update(int k,Monoid x){
        k+=sz;
        seg[k]=x;
        k>>=1;
        for(;k;k>>=1) seg[k]=f(seg[2*k],seg[2*k+1]);
    }
    Monoid query(int a,int b){
        return query(a,b,1,0,sz);
    }
    Monoid operator[](const int &k)const{
        return seg[k+sz];
    }

    // http://codeforces.com/contest/914/submission/107505449
    // max x, check(query(a, x)) = true 
    template<typename C>
    int find_first(int a,const C &check){
        Monoid val=M0;
        return find_first(a,check,val,1,0,sz);
    }
    // http://codeforces.com/contest/914/submission/107505582
    // min x, check(query(x, b)) = true
    template<typename C>
    int find_last(int b,C &check){
        Monoid val=M0;
        return find_last(b,check,val,1,0,sz);
    }
};




mint ManhattanSquareSum(vector<ll> x,vector<ll> y){
    int N=(int)x.size();
    mint ret=0;
    {
        mint sx=0,sy=0,sxx=0,syy=0;
        for(int i=0;i<N;i++){
            ret+=(mint)x[i]*x[i]*i+sxx-sx*x[i]*2;
            ret+=(mint)y[i]*y[i]*i+syy-sy*y[i]*2;
            sx+=x[i],sy+=y[i];
            sxx+=(mint)x[i]*x[i];
            syy+=(mint)y[i]*y[i];
        }
    }

    {
        vector<int> idx(N);
        iota(begin(idx),end(idx),0);
        sort(begin(idx),end(idx),[&](int i,int j){return x[i]>x[j];});
        auto nx=x,ny=y;
        for(int i=0;i<N;i++) nx[i]=x[idx[i]],ny[i]=y[idx[i]];
        swap(x,nx);
        swap(y,ny);
    }

    {
        vector<int> yid(N),yp(N);
        iota(begin(yid),end(yid),0);
        sort(begin(yid),end(yid),[&](int i,int j){return y[i]<y[j];});
        for(int i=0;i<N;i++) yp[yid[i]]=i;

        using P=pair<mint,mint>;
        auto segf=[&](P a,P b){
            a.first+=b.first;
            a.second+=b.second;
            return a;
        };
        SegmentTree<P> sega(N,segf,P(0,0)),segb(N,segf,P(0,0));
        for(int i=0;i<N;i++){
            sega.set(yp[i],P(y[i],1));
            segb.set(i,P(0,0));
        }
        sega.build();
        segb.build();

        for(int i=0;i<N;i++){
            int j=yp[i];
            auto l=sega.query(0,j);
            auto r=sega.query(j+1,N);
            mint add=mint(y[i])*l.second-l.first+r.first-mint(y[i])*r.second;

            l=segb.query(0,j);
            r=segb.query(j+1,N);
            mint sub=mint(y[i])*l.second-l.first+r.first-mint(y[i])*r.second;
            ret+=(add-sub)*x[i]*2;
            sega.update(j,P(0,0));
            segb.update(j,P(y[i],1));
        }
    }
    return ret;
}


signed main(){
    int N;cin>>N;
    vector<ll> x(N),y(N);
    rep(i,N) cin>>x[i]>>y[i];
    cout<<ManhattanSquareSum(x,y)<<endl;
    return 0;
}
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