結果

問題 No.891 隣接3項間の漸化式
ユーザー HaarHaar
提出日時 2019-09-20 21:37:41
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 7,678 bytes
コンパイル時間 2,228 ms
コンパイル使用メモリ 197,328 KB
最終ジャッジ日時 2025-01-07 18:41:39
ジャッジサーバーID
(参考情報)
judge2 / judge6
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 * 3
other AC * 39
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#define LLI long long int
#define FOR(v, a, b) for(LLI v = (a); v < (b); ++v)
#define FORE(v, a, b) for(LLI v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(LLI v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c,x) ((c).find(x) != (c).end())
#define fst first
#define snd second
#define popcount __builtin_popcount
#define UNIQ(v) (v).erase(unique(ALL(v)), (v).end())
#define bit(i) (1LL<<(i))
#ifdef DEBUG
#include <misc/C++/Debug.cpp>
#else
#define dump(...) ((void)0)
#endif
#define gcd __gcd
using namespace std;
template <class T> constexpr T lcm(T m, T n){return m/gcd(m,n)*n;}
template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;}
template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;}
template <typename T, typename U> bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);}
template <typename T, typename U> bool chmax(T &a, const U &b){return (a<b ? a=b, true : false);}
template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);}
struct Init{
Init(){
cin.tie(0);
ios::sync_with_stdio(false);
}
}init;
template <uint32_t M> class ModInt{
public:
uint64_t val;
ModInt(): val(0){}
ModInt(int64_t n){
if(n >= M) val = n % M;
else if(n < 0) val = n % M + M;
else val = n;
}
inline constexpr ModInt operator+(const ModInt &a) const {return ModInt((val+a.val)%M);}
inline constexpr ModInt operator-(const ModInt &a) const {return ModInt((val-a.val+M)%M);}
inline constexpr ModInt operator*(const ModInt &a) const {return ModInt((val*a.val)%M);}
inline constexpr ModInt operator/(const ModInt &a) const {return ModInt((val*a.inv().val)%M);}
inline constexpr ModInt& operator=(const ModInt &a){val = a.val; return *this;}
inline constexpr ModInt& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
inline constexpr ModInt& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
inline constexpr ModInt& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
inline constexpr ModInt& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;}
inline constexpr bool operator==(const ModInt &a) const {return val==a.val;}
inline constexpr bool operator!=(const ModInt &a) const {return val!=a.val;}
inline constexpr ModInt& operator++(){*this += 1; return *this;}
inline constexpr ModInt& operator--(){*this -= 1; return *this;}
inline constexpr ModInt operator++(int){ModInt t = *this; *this += 1; return t;}
inline constexpr ModInt operator--(int){ModInt t = *this; *this -= 1; return t;}
inline constexpr static ModInt power(LLI n, LLI p){
ModInt ret = 1, e = n;
for(; p; e *= e, p >>= 1) if(p&1) ret *= e;
return ret;
}
inline constexpr ModInt power(LLI p) const {return power(val,p);}
inline constexpr ModInt inv() const {
int64_t a = val, b = M, u = 1, v = 0;
while(b){
int64_t t = a/b;
a -= t*b; swap(a,b);
u -= t*v; swap(u,v);
}
u %= M;
if(u < 0) u += M;
return u;
}
};
template <uint32_t M> ModInt<M> operator-(const ModInt<M> &a){return M-a.val;}
template <uint32_t M> ModInt<M> operator+(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)+b.val);}
template <uint32_t M> ModInt<M> operator-(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)-b.val);}
template <uint32_t M> ModInt<M> operator*(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)*b.val);}
template <uint32_t M> ModInt<M> operator/(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)/b.val);}
template <uint32_t M> istream& operator>>(istream &is, ModInt<M> &a){is >> a.val; return is;}
template <uint32_t M> ostream& operator<<(ostream &os, const ModInt<M> &a){ os << a.val; return os;}
using mint = ModInt<1000000007>;
template <typename T, int N> struct SquareMatrix{
array<array<T,N>,N> matrix;
SquareMatrix(): matrix(){}
SquareMatrix(const T &val){
REP(i,N) matrix[i].fill(val);
}
SquareMatrix(const SquareMatrix<T,N> &) = default;
SquareMatrix(SquareMatrix<T,N> &&) = default;
SquareMatrix(initializer_list<initializer_list<T>> list){
int i = 0;
ITR(it1,list){
int j = 0;
ITR(it2,*it1){
matrix[i][j] = *it2;
++j;
}
++i;
}
}
bool operator==(const SquareMatrix<T,N> &val) const {
return matrix == val.matrix;
}
bool operator!=(const SquareMatrix<T,N> &val) const {
return !(*this == val);
}
SquareMatrix& operator=(const SquareMatrix &) = default;
SquareMatrix& operator+=(const SquareMatrix &val){
REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] + val[i][j];
return *this;
}
SquareMatrix& operator-=(const SquareMatrix &val){
REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] - val[i][j];
return *this;
}
SquareMatrix& operator*=(const SquareMatrix &val){
array<array<T,N>,N> temp = {};
REP(i,N) REP(j,N) REP(k,N) temp[i][j] = temp[i][j] + matrix[i][k] * val[k][j];
swap(matrix, temp);
return *this;
}
inline const auto& operator[](size_t i) const {return matrix[i];}
inline auto& operator[](size_t i){return matrix[i];}
inline int size() const {return N;}
static SquareMatrix<T,N> make_unit(){
SquareMatrix<T,N> ret;
REP(i,N) ret[i][i] = 1;
return ret;
}
SquareMatrix<T,N> transpose() const {
SquareMatrix<T,N> ret;
REP(i,N) REP(j,N) ret[i][j] = matrix[j][i];
return ret;
}
void show(int w = 10) const {
#ifdef DEBUG
cerr << "" << string((w+1)*N, ' ') << "" << endl;
REP(i,N){
cerr << "";
REP(j,N) cerr << setw(w) << matrix[i][j] << " ";
cerr << "";
cerr << endl;
}
cerr << "" << string((w+1)*N, ' ') << "" << endl;
#endif
}
};
template <typename T, int N> SquareMatrix<T,N> operator+(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret += b; return ret;}
template <typename T, int N> SquareMatrix<T,N> operator-(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret -= b; return ret;}
template <typename T, int N> SquareMatrix<T,N> operator*(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret *= b; return ret;}
template <typename T, int N> SquareMatrix<T,N> power(SquareMatrix<T,N> a, uint64_t p){
if(p == 0) return SquareMatrix<T,N>::make_unit();
if(p == 1) return a;
SquareMatrix<T,N> temp = power(a, p/2);
auto ret = temp * temp;
if(p%2) ret *= a;
return ret;
}
template <typename T, int N> vector<T> operator*(const SquareMatrix<T,N> &a, const vector<T> &b){
vector<T> ret(N);
REP(i,N){
REP(j,N){
ret[i] += a[i][j] * b[j];
}
}
return ret;
}
template <typename T, int N> vector<T> operator*(const vector<T> &b, const SquareMatrix<T,N> &a){
vector<T> ret(N);
REP(i,N){
REP(j,N){
ret[j] += b[i] * a[i][j];
}
}
return ret;
}
using M = SquareMatrix<mint,2>;
int main(){
mint a,b;
int n;
while(cin >> a >> b >> n){
if(n == 0){
cout << 0 << endl;
}else if(n == 1){
cout << 1 << endl;
}else{
M m = {{a,b},{1,0}};
m = power(m, n-1);
mint ans = m[0][0];
cout << ans << endl;
}
}
return 0;
}
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