結果

問題 No.891 隣接3項間の漸化式
ユーザー apricityapricity
提出日時 2023-03-21 21:52:43
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 5,739 bytes
コンパイル時間 1,425 ms
コンパイル使用メモリ 131,832 KB
最終ジャッジ日時 2025-02-11 15:55:34
ジャッジサーバーID
(参考情報)
judge4 / judge5
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<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<deque>
#include<unordered_map>
#include<unordered_set>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#ifdef LOCAL
# include "debug_print.hpp"
# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
# define debug(...) (static_cast<void>(0))
#endif
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
#define rrep(i,n) for(int i=(n)-1; i>=0; i--)
#define FOR(i,a,b) for(int i=(a); i<(b); i++)
#define RFOR(i,a,b) for(int i=(b-1); i>=(a); i--)
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define pb push_back
using ll = long long;
using D = double;
using LD = long double;
using P = pair<int, int>;
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
template<int mod> struct Fp {
long long val;
constexpr Fp(long long v = 0) noexcept : val(v % mod) {
if (val < 0) val += mod;
}
constexpr int getmod() { return mod; }
constexpr Fp operator - () const noexcept {
return val ? mod - val : 0;
}
constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
constexpr Fp& operator += (const Fp& r) noexcept {
val += r.val;
if (val >= mod) val -= mod;
return *this;
}
constexpr Fp& operator -= (const Fp& r) noexcept {
val -= r.val;
if (val < 0) val += mod;
return *this;
}
constexpr Fp& operator *= (const Fp& r) noexcept {
val = val * r.val % mod;
return *this;
}
constexpr Fp& operator /= (const Fp& r) noexcept {
long long a = r.val, b = mod, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b; swap(a, b);
u -= t * v; swap(u, v);
}
val = val * u % mod;
if (val < 0) val += mod;
return *this;
}
constexpr bool operator == (const Fp& r) const noexcept {
return this->val == r.val;
}
constexpr bool operator != (const Fp& r) const noexcept {
return this->val != r.val;
}
friend constexpr istream& operator >> (istream &is, const Fp<mod>& x) noexcept {
int val; is >> val;
x = Fp<mod>(val);
return is;
}
friend constexpr ostream& operator << (ostream &os, const Fp<mod>& x) noexcept {
return os << x.val;
}
friend constexpr Fp<mod> modpow(const Fp<mod> &a, long long n) noexcept {
if (n == 0) return 1;
auto t = modpow(a, n / 2);
t = t * t;
if (n & 1) t = t * a;
return t;
}
};
const int mod = 1e9+7;
// const int mod = 998244353;
using mint = Fp<mod>;
template<typename T> struct Matrix{
int r,c;
vector<vector<T>> a;
Matrix(int r, int c, T init = 0) : r(r), c(c), a(r, vector<T>(c, init)) {}
Matrix& unit(){
assert(r == c);
rep(i,r) a[i][i] = 1;
return *this;
}
const vector<T>& operator[] (int i) const {return a[i];}
vector<T>& operator[] (int i) {return a[i];}
Matrix operator* (const Matrix& b) const{
assert(c == b.r);
Matrix res(r, b.c);
rep(i,r)rep(k,c)rep(j,b.c) res[i][j] += a[i][k] * b[k][j];
return res;
}
Matrix pow(ll k) const{
assert(r == c);
Matrix now = *this;
Matrix res = Matrix(r,c).unit();
while(k){
if(k & 1) res = res * now;
now = now * now;
k >>= 1;
}
return res;
}
};
using mat = Matrix<mint>;
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int a,b,n; in(a,b,n);
if(n < 2) {out(n); return 0;}
mat m(2,2);
m[0][0] = a; m[0][1] = b; m[1][0] = 1;
mat v(2,1);
v[0][0] = 1;
v = m.pow(n-1)*v;
out(v[0][0]);
}
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