結果

問題 No.1086 桁和の桁和2
コンテスト
ユーザー rniya
提出日時 2020-06-19 23:13:29
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 10,350 bytes
コンパイル時間 2,118 ms
コンパイル使用メモリ 185,968 KB
実行使用メモリ 17,532 KB
最終ジャッジ日時 2024-07-03 15:34:18
合計ジャッジ時間 10,468 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 5
other AC * 9 WA * 1 TLE * 2 -- * 19
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ソースコード

diff # 

#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define FOR(i,a,b) for (int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(x) (x).begin(),(x).end()
const long long MOD=1e9+7;
// const long long MOD=998244353;
const int INF=1e9;
const long long IINF=1e18;
const int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
const char dir[4]={'D','R','U','L'};
#define LOCAL

template<typename T>
istream &operator>>(istream &is,vector<T> &v){
    for (T &x:v) is >> x;
    return is;
}
template<typename T>
ostream &operator<<(ostream &os,const vector<T> &v){
    for (int i=0;i<v.size();++i){
        os << v[i] << (i+1==v.size()?"": " ");
    }
    return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const pair<T,U> &p){
    cout << '(' << p.first << ',' << p.second << ')';
    return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const map<T,U> &m){
    os << '{';
    for (auto itr=m.begin();itr!=m.end();++itr){
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr!=m.end()) os << ',';
        --itr;
    }
    os << '}';
    return os;
}
template<typename T>
ostream &operator<<(ostream &os,const set<T> &s){
    os << '{';
    for (auto itr=s.begin();itr!=s.end();++itr){
        os << *itr;
        if (++itr!=s.end()) os << ',';
        --itr;
    }
    os << '}';
    return os;
}

void debug_out(){cerr << '\n';}
template<class Head,class... Tail>
void debug_out(Head&& head,Tail&&... tail){
    cerr << head;
    if (sizeof...(Tail)>0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) cerr << " ";\
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n';\
cerr << " ";\
debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template<typename T> T gcd(T x,T y){return y!=0?gcd(y,x%y):x;}
template<typename T> T lcm(T x,T y){return x/gcd(x,y)*y;}

template<class T1,class T2> inline bool chmin(T1 &a,T2 b){
    if (a>b){a=b; return true;} return false;
}
template<class T1,class T2> inline bool chmax(T1 &a,T2 b){
    if (a<b){a=b; return true;} return false;
}
#pragma endregion

template<uint_fast64_t Modulus> class modint{
    using u64=uint_fast64_t;
    public:
    u64 a;
    constexpr modint(const u64 x=0) noexcept:a(((x%Modulus)+Modulus)%Modulus){}
    constexpr u64 &value() noexcept{return a;}
    constexpr const u64 &value() const noexcept{return a;}
    constexpr modint &operator+=(const modint &rhs) noexcept{
        a+=rhs.a;
        if (a>=Modulus) a-=Modulus;
        return *this;
    }
    constexpr modint operator+(const modint &rhs) const noexcept{
        return modint(*this)+=rhs;
    }
    constexpr modint &operator++() noexcept{
        return ++a,*this;
    }
    constexpr modint operator++(int) noexcept{
        modint t=*this; return ++a,t;
    }
    constexpr modint &operator-=(const modint &rhs) noexcept{
        if (a<rhs.a) a+=Modulus;
        a-=rhs.a;
        return *this;
    }
    constexpr modint operator-(const modint &rhs) const noexcept{
        return modint(*this)-=rhs;
    }
    constexpr modint &operator--() noexcept{
        return --a,*this;
    }
    constexpr modint operator--(int) noexcept{
        modint t=*this; return --a,t;
    }
    constexpr modint &operator*=(const modint &rhs) noexcept{
        a=a*rhs.a%Modulus;
        return *this;
    }
    constexpr modint operator*(const modint &rhs) const noexcept{
        return modint(*this)*=rhs;
    }
    constexpr modint &operator/=(modint rhs) noexcept{
        u64 exp=Modulus-2;
        while(exp){
            if (exp&1) *this*=rhs;
            rhs*=rhs; exp>>=1;
        }
        return *this;
    }
    constexpr modint operator/(const modint &rhs) const noexcept{
        return modint(*this)/=rhs;
    }
    constexpr modint operator-() const noexcept{
        return modint(Modulus-a);
    }
    constexpr bool operator==(const modint &rhs) const noexcept{
        return a==rhs.a;
    }
    constexpr bool operator!=(const modint &rhs) const noexcept{
        return a!=rhs.a;
    }
    constexpr bool operator!() const noexcept{return !a;}
    friend constexpr modint pow(modint rhs,long long exp) noexcept{
        modint res{1};
        while(exp){
            if (exp&1) res*=rhs;
            rhs*=rhs; exp>>=1;
        }
        return res;
    }
    template<class T> friend constexpr modint operator+(T x,modint y) noexcept{
        return modint(x)+y;
    }
    template<class T> friend constexpr modint operator-(T x,modint y) noexcept{
        return modint(x)-y;
    }
    template<class T> friend constexpr modint operator*(T x,modint y) noexcept{
        return modint(x)*y;
    }
    template<class T> friend constexpr modint operator/(T x,modint y) noexcept{
        return modint(x)/y;
    }
    friend ostream &operator<<(ostream &s,const modint &rhs) noexcept{
        return s << rhs.a;
    }
    friend istream &operator>>(istream &s,modint &rhs) noexcept{
        u64 a; rhs=modint{(s >> a,a)}; return s;
    }
};

using mint=modint<MOD>;

template<class K>
struct Matrix{
    vector<vector<K>> dat;
    Matrix(size_t r,size_t c):dat(r,vector<K>(c,K())){}
    Matrix(size_t n):dat(n,vector<K>(n,K())){}
    Matrix(vector<vector<K>> dat):dat(dat){}
    size_t size() const{return dat.size();}
    vector<K> &operator[](int i){return dat[i];}
    const vector<K> &operator[](int i) const{return dat[i];}
    static Matrix I(size_t n){
        Matrix res(n);
        for (int i=0;i<n;++i) res[i][i]=K(1);
        return res;
    }
    Matrix &operator+=(const Matrix &B){
        for (int i=0;i<dat.size();++i)
            for (int j=0;j<dat[0].size();++j)
                (*this)[i][j]+=B[i][j];
        return (*this);
    }
    Matrix operator+(const Matrix &B) const{
        return Matrix(*this)+=B;
    }
    Matrix &operator-=(const Matrix &B){
        for (int i=0;i<dat.size();++i)
            for (int j=0;j<dat[0].size();++j)
                (*this)[i][j]-=B[i][j];
        return (*this);
    }
    Matrix operator-(const Matrix &B) const{
        return Matrix(*this)-=B;
    }
    Matrix &operator*=(const Matrix &B){
        vector<vector<K>> res(dat.size(),vector<K>(B[0].size(),K()));
        for (int i=0;i<dat.size();++i)
            for (int j=0;j<B[0].size();++j)
                for (int k=0;k<B.size();++k)
                    res[i][j]+=(*this)[i][k]*B[k][j];
        dat.swap(res);
        return (*this);
    }
    Matrix operator*(const Matrix &B) const{
        return Matrix(*this)*=B;
    }
    Matrix &operator^=(long long k){
        Matrix res=Matrix::I(size());
        while(k>0){
            if (k&1LL) res*=*this;
            *this*=*this; k>>=1LL;
        }
        dat.swap(res.dat);
        return (*this);
    }
    Matrix operator^(long long k) const{
        return Matrix(*this)^=k;
    }
    static Matrix Gauss_Jordan(const Matrix &A,const Matrix &B){
        int n=A.size(),l=B[0].size();
        Matrix C(n,n+l);
        for (int i=0;i<n;++i){
            for (int j=0;j<n;++j)
                C[i][j]=A[i][j];
            for (int j=0;j<l;++j)
                C[i][j+n]=B[i][j];
        }
        for (int i=0;i<n;++i){
            int p=i;
            for (int j=i;j<n;++j){
                if (abs(C[p][i])<abs(C[j][i])) p=j;
            }
            swap(C[i],C[p]);
            if (abs(C[i][i])<1e-9) return Matrix(0,0);
            for (int j=i+1;j<n+l;++j) C[i][j]/=C[i][i];
            for (int j=0;j<n;++j){
                if (i!=j) for (int k=i+1;k<n+l;++k){
                    C[j][k]-=C[j][i]*C[i][k];
                }
            }
        }
        Matrix res(n,l);
        for (int i=0;i<n;++i)
            for (int j=0;j<n;++j)
                res[i][j]=C[i][j+n];
        return res;
    }
    Matrix inv() const{
        Matrix res=I(size());
        return Gauss_Jordan(*this,res);
    }
    K determinant() const{
        Matrix A(dat);
        K res(1);
        int n=size();
        for (int i=0;i<n;++i){
            int p=i;
            for (int j=i;j<n;++j){
                if (abs(A[p][i])<abs(A[j][i])) p=j;
            }
            if (i!=p) swap(A[i],A[p]),res=-res;
            if (abs(A[i][i])<1e-9) return K(0);
            res*=A[i][i];
            for (int j=i+1;j<n;++j) A[i][j]/=A[i][i];
            for (int j=i+1;j<n;++j)
                for (int k=i+1;k<n;++k)
                    A[j][k]-=A[j][i]*A[i][k];
        }
        return res;
    }
    //sum_{k=0}^{n-1} x^k
    static K geometric_sum(K x,long long n){
        Matrix A(2);
        A[0][0]=x; A[0][1]=0;
        A[1][0]=1; A[1][1]=1;
        return (A^n)[1][0];
    }
    //sum_{k=0}^{n-1} A^k
    Matrix powsum(long long k) const{
        int n=size();
        Matrix B(n<<1),res(n);
        for (int i=0;i<n;++i){
            for (int j=0;j<n;++j)
                B[i][j]=dat[i][j];
            B[i+n][i]=B[i+n][i+n]=K(1);
        }
        B^=k;
        for (int i=0;i<n;++i)
            for (int j=0;j<n;++j)
                res[i][j]=B[i+n][j];
        return res;
    }
};

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N; cin >> N;
    vector<ll> L(N),R(N); cin >> L >> R;
    vector<int> D(N); cin >> D;
    int s=0;
    while(s<N&&!D[s]) ++s;
    if (s==N){cout << 1 << '\n'; return 0;}
    for (int i=s;i<N;++i) if (!D[i]){
        cout << 0 << '\n'; return 0;
    }
    for (int i=s;i<N;++i) D[i]%=9;
    vector<pair<ll,int>> LR;
    vector<int> x(N);
    for (int i=s;i<N;++i){
        x[i]=(i==s?D[i]:(D[i]-D[i-1]+9)%9);
        LR.emplace_back(L[i],i);
        LR.emplace_back(R[i],-(i+1));
    }
    sort(ALL(LR));
    vector<mint> l(N,0),r(N,0);
    ll pre=0;
    Matrix<mint> SM(9),M(9);
    for (int i=0;i<9;++i){
        for (int j=0;j<9;++j){
            SM[i][j]=(i==j?2:1);
            M[i][j]=(i==j?1:0);
        }
    }
    for (int i=0;i<LR.size();++i){
        if (LR[i].first==0) continue;
        ll p=LR[i].first-pre;
        Matrix<mint> MM=SM^p;
        M*=MM;
        int id=LR[i].second,num=(id>=0?id:-id-1);
        if (id>=0) l[num]=M[0][x[num]];
        else r[num]=M[0][x[num]];
        pre=LR[i].first;
    }
    mint ans=1;
    for (int i=s;i<N;++i){
        int x=(i==s?D[0]:(D[i]-D[i-1]+9)%9);
        mint sum=r[i]-l[i];
        if (!x&&L[i]>0) ++sum;
        ans*=sum;
    }
    cout << ans << '\n';
}
0