#382128 (C++14) No.891 隣接3項間の漸化式

• 問題: No.891 隣接3項間の漸化式
• ユーザー: tko919
• 提出日時: 2019-09-21 16:51:30
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 3 ms / 2,000 ms
• コード長: 4,306 bytes
• コンパイル時間: 2,196 ms
• コンパイル使用メモリ: 180,708 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-19 02:32:09
• 合計ジャッジ時間: 3,264 ms
• ジャッジサーバーID （参考情報）: judge2 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	2 ms; 5,376 KB
testcase_21	AC	2 ms; 5,376 KB
testcase_22	AC	2 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB
testcase_24	AC	2 ms; 5,376 KB
testcase_25	AC	2 ms; 5,376 KB
testcase_26	AC	2 ms; 5,376 KB
testcase_27	AC	2 ms; 5,376 KB
testcase_28	AC	2 ms; 5,376 KB
testcase_29	AC	2 ms; 5,376 KB
testcase_30	AC	2 ms; 5,376 KB
testcase_31	AC	2 ms; 5,376 KB
testcase_32	AC	2 ms; 5,376 KB
testcase_33	AC	2 ms; 5,376 KB
testcase_34	AC	2 ms; 5,376 KB
testcase_35	AC	2 ms; 5,376 KB
testcase_36	AC	2 ms; 5,376 KB
testcase_37	AC	2 ms; 5,376 KB
testcase_38	AC	2 ms; 5,376 KB
testcase_39	AC	2 ms; 5,376 KB
testcase_40	AC	3 ms; 5,376 KB
testcase_41	AC	2 ms; 5,376 KB

ソースコード

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

//template
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(a);i>(b);i--)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll; typedef pair<ll, ll> P;
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; }
template<typename A,size_t N,typename T>void Fill(A(&array)[N],const T &val){fill((T*)array, (T*)(array+N), val);}
const int inf = INT_MAX / 2; const ll INF = LLONG_MAX / 2;
//template end

int mod = 1e9+7;
struct Mint {
    int val;
    Mint inv() const {
        int tmp, a = val, b = mod, x = 1, y = 0;
        while(b) tmp = a / b, a -= tmp * b, swap(a, b), x -= tmp * y, swap(x, y);
        return Mint(x);
    }
public:
    Mint() :val(0) {}
    Mint(ll x) :val(x >= 0 ? x % mod : x % mod + mod) {}
    int mtoi() { return this->val; }
    Mint pow(ll t) { Mint res = 1,b = *this; while(t){if(t&1)res *= b;b *= b;t >>= 1;}return res; }
    Mint& operator+=(const Mint& x) { if ((val += x.val) >= mod) val -= mod; return *this; }
    Mint& operator-=(const Mint& x) { if ((val += mod - x.val) >= mod) val -= mod; return *this; }
    Mint& operator*=(const Mint& x) { val = (ll)val * x.val % mod; return *this; }
    Mint& operator/=(const Mint& x) { return *this *= x.inv(); }
    bool operator==(const Mint& x) const { return val == x.val; }
    bool operator!=(const Mint& x) const { return val != x.val; }
    bool operator<(const Mint& x) const { return val < x.val; }
    bool operator<=(const Mint& x) const { return val <= x.val; }
    bool operator>(const Mint& x) const { return val > x.val; }
    bool operator>=(const Mint& x) const { return val >= x.val; }
    Mint operator+(const Mint& x) const { return Mint(*this) += x; }
    Mint operator-(const Mint& x) const { return Mint(*this) -= x; }
    Mint operator*(const Mint& x) const { return Mint(*this) *= x; }
    Mint operator/(const Mint& x) const { return Mint(*this) /= x; }
};
struct factorial {
    vector<Mint> Fact, Finv;
public:
    factorial(int maxx) {
        Fact.resize(maxx+1,Mint(1)),Finv.resize(maxx+1); rep(i,0,maxx)Fact[i+1]=Fact[i]*Mint(i+1);
        Finv[maxx]=Mint(1)/Fact[maxx]; rrep(i,maxx,0)Finv[i-1]=Finv[i]*Mint(i);
    }
    Mint fact(int n,bool inv) { if(inv) return Finv[n]; else return Fact[n]; }
    Mint nPr(int n,int r) { if(n<0||n<r||r<0) return Mint(0); else return Fact[n]*Finv[n-r]; }
    Mint nCr(int n,int r) { if(n<0||n<r||r<0) return Mint(0); else return Fact[n]*Finv[r]*Finv[n-r]; }
};
typedef vector<vector<Mint>> mat;
mat mul(mat a, mat b) {
    mat ans(a.size(), vector<Mint>(b[0].size(), 0));
    rep(i, 0, a.size())rep(j, 0, b[0].size())rep(k,0,b.size())ans[i][j] += a[i][k]*b[k][j];
    return ans;
}
mat matpow(mat a, ll t) {
    mat ans(a.size());
    rep(i, 0, a.size()){ans[i].resize(a.size(),0);ans[i][i]=1;}
    while(t){if(t&1)ans=mul(ans,a);a=mul(a,a);t>>=1;}
    return ans;
}
int gauss(mat &A, bool is_extended = false) {
    int m=A.size(), n=A[0].size(), rank=0;
    rep(col,0,n) {
        if (is_extended && col==n-1) break; int pivot = -1;
        rep(row,rank,m)if (A[row][col].mtoi()) {pivot = row; break;}
        if (pivot==-1) continue;
        swap(A[pivot],A[rank]); Mint inv=A[rank][col];
        rep(col2,0,n)A[rank][col2] /= inv;
        rep(row,0,m)if (row != rank && A[row][col].mtoi()) {
            Mint base=A[row][col];
            rep(col2,0,n) {A[row][col2]-=(A[rank][col2]*base);}
        } ++rank;
    } return rank;
}
int linear_equation(mat A, vector<ll> b, vector<ll> &res) {
    int m=A.size(),n=A[0].size(); mat M(m);
    rep(i,0,m){
        M[i].resize(n+1);
        rep(j,0,n) M[i][j] = A[i][j];
        M[i][n] = b[i];
    }
    int rank = gauss(M, true);
    rep(row,rank,m) if(M[row][n].mtoi()) return -1;
    res.resize(n); rep(i,0,rank)res[i] = M[i][n].mtoi();
    return rank;
}

int main(){
    int a,b; ll n; scanf("%d%d%lld",&a,&b,&n);
    mat ans(2,vector<Mint>(1)),keisu(2,vector<Mint>(2));
    ans[0][0]=1; ans[1][0]=0;
    keisu[0][0]=a; keisu[0][1]=b; keisu[1][0]=1; keisu[1][1]=0;
    keisu=matpow(keisu,n);
    ans=mul(keisu,ans);
    printf("%d\n",ans[1][0].mtoi());
    return 0;
}