結果

問題 No.1632 Sorting Integers (GCD of M)
ユーザー milanis48663220milanis48663220
提出日時 2021-07-30 22:43:31
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 6,050 bytes
コンパイル時間 1,625 ms
コンパイル使用メモリ 128,768 KB
最終ジャッジ日時 2025-01-23 12:23:01
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 4
other AC * 59
権限があれば一括ダウンロードができます
コンパイルメッセージ
In constructor ‘ModInt::ModInt(ll)’,
    inlined from ‘ModInt ModInt::operator*(ModInt)’ at main.cpp:65:16,
    inlined from ‘bool prod(matrix<T>, matrix<T>, matrix<T>&) [with T = ModInt]’ at main.cpp:158:46:
main.cpp:29:26: warning: ‘<unnamed>.ModInt::v’ may be used uninitialized [-Wmaybe-uninitialized]
   29 |         if(_v < 0) _v = (v%MOD)+MOD;
      |                          ^
main.cpp: In function ‘bool prod(matrix<T>, matrix<T>, matrix<T>&) [with T = ModInt]’:
main.cpp:65:34: note: ‘<anonymous>’ declared here
   65 |         return ModInt((v*n.v)%MOD);
      |                                  ^
In constructor ‘ModInt::ModInt(ll)’,
    inlined from ‘ModInt ModInt::inv()’ at main.cpp:96:32:
main.cpp:29:26: warning: ‘<unnamed>.ModInt::v’ may be used uninitialized [-Wmaybe-uninitialized]
   29 |         if(_v < 0) _v = (v%MOD)+MOD;
      |                          ^
main.cpp: In function ‘ModInt ModInt::inv()’:
main.cpp:96:44: note: ‘<anonymous>’ declared here
   96 |         else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
      |                                            ^
In constructor ‘ModInt::ModInt(ll)’,
    inlined from ‘ModInt ModInt::inv()’ at main.cpp:96:32,
    inlined from ‘ModInt ModInt::inv()’ at main.cpp:96:49:
main.cpp:29:26: warning: ‘<unnamed>.ModInt::v’ may be used uninitialized [-Wmaybe-uninitialized]
   29 |         if(_v < 0) _v = (v%MOD)+MOD;
      |                          ^
main.cpp: In function ‘ModInt ModInt::inv()’:
main.cpp:96:44: note: ‘<anonymous>’ declared here
   96 |         else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
      |                                            ^
In constructor ‘ModInt::ModInt(ll)’,
    inlined from ‘ModInt ModInt::inv()’ at main.cpp:96:32,
    inlined from ‘ModInt ModInt::inv()’ at main.cpp:96:49,
    inlined from ‘ModInt ModInt::inv()’ at main.cpp:96:49:
main.cpp:29:26: warning: ‘<unnamed>.M

ソースコード

diff # 

#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>

#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using namespace std;
typedef long long ll;

ll MOD = 1000000007;

class ModInt{
    public:
    ll v;
    ModInt(ll _v = 0){
        if(_v < 0) _v = (v%MOD)+MOD;
        if(_v >= MOD) _v %= MOD;
        v = _v;
    }
    ModInt operator+(ll n){
        return ModInt((v+n)%MOD);
    }
    ModInt operator-(ll n){
        return ModInt((v-n+MOD)%MOD);
    }
    ModInt operator*(ll n){
        if(n >= MOD) n %= MOD;
        return ModInt((v*n)%MOD);
    }
    ModInt operator/(ll n){
        return ModInt((ModInt(n).inv()*v).v%MOD);
    }

    void operator+=(ll n){
        v = (v+n)%MOD;
    }
    void operator-=(ll n){
        v = (v-n+MOD)%MOD;
    }
    void operator*=(ll n){
        v = (v*n+MOD)%MOD;
    }
    
    
    ModInt operator+(ModInt n){
        return ModInt((v+n.v)%MOD);
    }
    ModInt operator-(ModInt n){
        return ModInt((v-n.v+MOD)%MOD);
    }
    ModInt operator*(ModInt n){
        return ModInt((v*n.v)%MOD);
    }
    ModInt operator/(ModInt n){
        return ModInt((n.inv()*v).v%MOD);
    }

    void operator+=(ModInt n){
        v = (v+n.v)%MOD;
    }
    void operator-=(ModInt n){
        v = (v-n.v+MOD)%MOD;
    }
    void operator*=(ModInt n){
        v = (v*n.v)%MOD;
    }

    void operator=(ModInt n){
        v = n.v;
    }
    bool operator==(ModInt n){
        return v == n.v;
    }
    bool operator!=(ModInt n){
        return v != n.v;
    }
    void operator=(ll n){
        v = n%MOD;
    }

    ModInt inv(){
        if(v == 1) return ModInt(1);
        else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
    }
};

ostream& operator<<(ostream& os, const ModInt& m){
    os << m.v;
    return os;
}

istream & operator >> (istream &in,  ModInt &m){
    in >> m.v;
    return in;
}

ModInt pow(ModInt a, ll n) {
    assert(n >= 0);
	ModInt ans = 1;
	ModInt tmp = a;
	for (int i = 0; i <= 60; i++) {
		ll m = (ll)1 << i;
		if (m & n) {
		ans *= tmp;
		}
		tmp *= tmp;
	}
	return ans;
}

template <typename T>
struct matrix{
    int n, m;
    vector<vector<T>> dat;
    matrix(int n_, int m_){
        n = n_; m = m_;
        for(int i = 0; i < n; i++){
            dat.push_back(vector<T>(m));
        }
    }

    matrix(int n, int m, T val): n(n), m(m){
        for(int i = 0; i < n; i++){
            dat.push_back(vector<T>(m, val));
        }
    }

    matrix(int n, int m, vector<vector<T>> dat): n(n), m(m), dat(dat){
        assert((int)dat.size() == n);
        for(int i = 0; i < n; i++) assert(dat[i].size() == m);
    }
    
    vector<T>& operator[](int x) {
        return dat[x];
	}
};

template <typename T>
bool prod(matrix<T> a, matrix<T> b, matrix<T> &ans){
    assert(a.m == b.n);
    for(int i = 0; i < a.n; i++){
        for(int j = 0; j < b.m; j++){
            ans.dat[i][j] = 0;
            for(int k = 0; k < b.n; k++){
                ans.dat[i][j] += (a.dat[i][k]*b.dat[k][j]);
            }
        }
    }
    return true;
}

template <typename T>
void copy_mat(matrix<T> a, matrix<T> &b){
    assert(a.n == b.n);
    assert(a.m == b.m);
    for(int i = 0; i < a.n; i++){
        for(int j = 0; j < a.m; j++){
            b.dat[i][j] = a.dat[i][j];
        }
    }
}

template <typename T>
void pow_mat(matrix<T> a, ll n, matrix<T> &ans){
    assert(n < ((ll)1<<61));
    matrix<T> buf(a.n, a.n);
    matrix<T> tmp(a.n, a.n);
    copy_mat(a, tmp);

    for(int i = 0; i < a.n; i++) {
        for(int j = 0; j < a.n; j++){
            ans.dat[i][j] = 0;
        }
        ans.dat[i][i] = 1;
    }
    
    for(int i = 0; i <= 60; i++){
        ll m = (ll)1 << i;
        if(m&n){
            prod(tmp, ans, buf);
            copy_mat(buf, ans);
        }
        prod(tmp, tmp, buf);
        copy_mat(buf, tmp);
    }
}

template <typename T>
void print_mat(matrix<T> a){
    for(int i = 0; i < a.n; i++){
        for(int j = 0; j < a.m; j++){
            cout << a.dat[i][j] << ' ';
        }
        cout << endl;
    }
}

template <typename T>
ostream& operator<<(ostream& os, const matrix<T>& m){
    print_mat<T>(m);
    return os;
}

// x^0 + x^1 + ... + x^n-1
ModInt sum_pow(ModInt x, ll n){
    matrix<ModInt> m(2, 2);
    m.dat[0][0] = x; m.dat[0][1] = 0;
    m.dat[1][0] = 1; m.dat[1][1] = 1;
    matrix<ModInt> v(2,1);
    v.dat[0][0] = 1;
    v.dat[1][0] = 0;
    matrix<ModInt> p(2, 2);
    pow_mat<ModInt>(m, n, p);
    matrix<ModInt> p_sum(2, 1);
    prod(p, v, p_sum);
    return p_sum.dat[1][0];
}

using mint = ModInt;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    int n; cin >> n;
    vector<int> c(10);
    for(int i = 1; i <= 9; i++) cin >> c[i];
    int cnt = 0;
    for(int i = 1; i <= 9; i++) {
        if(c[i] > 0) cnt++;
    }
    if(cnt == 1){
        int x = 0;
        for(int i = 1; i <= 9; i++) {
            if(c[i] > 0) x = i;
        }
        mint ans = (pow(mint(10), n)-1)*x/9;
        cout << ans << endl;
        return 0;
    }
    int g = 0;
    for(int i = 1; i <= 9; i++){
        for(int j = i+1; j <= 9; j++){
            if(c[i] > 0 && c[j] > 0){
                int a = i*10+j;
                int b = j*10+i;
                g = gcd(g, abs(b-a));
            }
        }
    }
    // cout << sum_pow(mint(10), 5)*4*pow(mint(10), 3) << endl;
    MOD = g;
    int sum = 0;
    mint rem = 0;
    for(int i = 1; i <= 9; i++){
        rem += sum_pow(mint(10), c[i])*i*pow(mint(10), sum);
        sum += c[i];
    }
    cout << gcd(g, rem.v) << endl;
}
0