結果
| 問題 | No.891 隣接3項間の漸化式 |
| ユーザー |
 jell
|
| 提出日時 | 2019-09-20 22:26:55 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 22,950 bytes |
| コンパイル時間 | 1,823 ms |
| コンパイル使用メモリ | 137,380 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-09-14 18:18:30 |
| 合計ジャッジ時間 | 2,986 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge6 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 39 |
ソースコード
#ifdef stderr_path
#define LOCAL
#define _GLIBCXX_DEBUG
#endif
#pragma GCC optimize("Ofast")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <complex>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
// #define NDEBUG
#define debug_stream std::cerr
#define iostream_untie true
#define __precision__ 10
#define rep(i, n) for(int i = 0; i < int(n); ++i)
#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
#define __odd(n) ((n)&1)
#define __even(n) (__odd(n) ^ 1)
#define __popcount(n) __builtin_popcountll(n)
#define __clz32(n) __builtin_clz(int32_t(n))
#define __clz64(n) __builtin_clzll(int64_t(n))
#define __ctz32(n) __builtin_ctz(int32_t(n))
#define __ctz64(n) __builtin_ctzll(int64_t(n))
using i64 = int_fast64_t;
using pii = std::pair<int, int>;
using pll = std::pair<int_fast64_t, int_fast64_t>;
template <class T>
using heap = std::priority_queue<T>;
template <class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T>
constexpr T inf = std::numeric_limits<T>::max() / T(2) - T(1123456);
namespace execution
{
std::chrono::system_clock::time_point start_time, end_time;
void print_elapsed_time()
{
end_time = std::chrono::system_clock::now();
std::cerr << "\n----- Exec time : ";
std::cerr << std::chrono::duration_cast<std::chrono::milliseconds>(
end_time - start_time)
.count();
std::cerr << " ms -----\n\n";
}
struct setupper
{
setupper()
{
if(iostream_untie)
{
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
}
std::cout << std::fixed << std::setprecision(__precision__);
#ifdef stderr_path
if(freopen(stderr_path, "a", stderr))
{
std::cerr << std::fixed << std::setprecision(__precision__);
}
else
fclose(stderr);
#endif
#ifdef stdout_path
if(not freopen(stdout_path, "w", stdout))
{
freopen("CON", "w", stdout);
std::cerr << "Failed to open the stdout file\n\n";
}
std::cout << "";
#endif
#ifdef stdin_path
if(not freopen(stdin_path, "r", stdin))
{
freopen("CON", "r", stdin);
std::cerr << "Failed to open the stdin file\n\n";
}
#endif
#ifdef LOCAL
atexit(print_elapsed_time);
start_time = std::chrono::system_clock::now();
#endif
}
} __setupper;
} // namespace execution
class myclock_t
{
std::chrono::system_clock::time_point built_pt, last_pt;
int built_ln, last_ln;
std::string built_func, last_func;
bool is_built;
public:
explicit myclock_t() : is_built(false)
{}
void build(int crt_ln, const std::string &crt_func)
{
is_built = true;
last_pt = built_pt = std::chrono::system_clock::now();
last_ln = built_ln = crt_ln, last_func = built_func = crt_func;
}
void set(int crt_ln, const std::string &crt_func)
{
if(is_built)
{
last_pt = std::chrono::system_clock::now();
last_ln = crt_ln, last_func = crt_func;
}
else
{
debug_stream << "[ " << crt_ln << " : " << crt_func << " ] "
<< "myclock_t::set failed (yet to be built!)\n";
}
}
void get(int crt_ln, const std::string &crt_func)
{
if(is_built)
{
std::chrono::system_clock::time_point crt_pt(
std::chrono::system_clock::now());
int64_t diff =
std::chrono::duration_cast<std::chrono::milliseconds>(crt_pt -
last_pt)
.count();
debug_stream << diff << " ms elapsed from"
<< " [ " << last_ln << " : " << last_func << " ]";
if(last_ln == built_ln) debug_stream << " (when built)";
debug_stream << " to"
<< " [ " << crt_ln << " : " << crt_func << " ]"
<< "\n";
last_pt = built_pt, last_ln = built_ln, last_func = built_func;
}
else
{
debug_stream << "[ " << crt_ln << " : " << crt_func << " ] "
<< "myclock_t::get failed (yet to be built!)\n";
}
}
};
#ifdef LOCAL
myclock_t __myclock;
#define build_clock() __myclock.build(__LINE__, __func__)
#define set_clock() __myclock.set(__LINE__, __func__)
#define get_clock() __myclock.get(__LINE__, __func__)
#else
#define build_clock() ((void)0)
#define set_clock() ((void)0)
#define get_clock() ((void)0)
#endif
namespace std
{
template <class RAitr>
void rsort(RAitr __first, RAitr __last)
{
sort(__first, __last, greater<>());
}
template <class T>
size_t hash_combine(size_t seed, T const &key)
{
return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2));
}
template <class T, class U>
struct hash<pair<T, U>>
{
size_t operator()(pair<T, U> const &pr) const
{
return hash_combine(hash_combine(0, pr.first), pr.second);
}
};
template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1>
struct tuple_hash_calc
{
static size_t apply(size_t seed, tuple_t const &t)
{
return hash_combine(
tuple_hash_calc<tuple_t, index - 1>::apply(seed, t),
get<index>(t));
}
};
template <class tuple_t>
struct tuple_hash_calc<tuple_t, 0>
{
static size_t apply(size_t seed, tuple_t const &t)
{
return hash_combine(seed, get<0>(t));
}
};
template <class... T>
struct hash<tuple<T...>>
{
size_t operator()(tuple<T...> const &t) const
{
return tuple_hash_calc<tuple<T...>>::apply(0, t);
}
};
template <class T, class U>
istream &operator>>(std::istream &s, pair<T, U> &p)
{
return s >> p.first >> p.second;
}
template <class T, class U>
ostream &operator<<(std::ostream &s, const pair<T, U> p)
{
return s << p.first << " " << p.second;
}
template <class T>
istream &operator>>(istream &s, vector<T> &v)
{
for(T &e : v)
{
s >> e;
}
return s;
}
template <class T>
ostream &operator<<(ostream &s, const vector<T> &v)
{
bool is_front = true;
for(const T &e : v)
{
if(not is_front)
{
s << ' ';
}
else
{
is_front = false;
}
s << e;
}
return s;
}
template <class tuple_t, size_t index>
struct tupleos
{
static ostream &apply(ostream &s, const tuple_t &t)
{
tupleos<tuple_t, index - 1>::apply(s, t);
return s << " " << get<index>(t);
}
};
template <class tuple_t>
struct tupleos<tuple_t, 0>
{
static ostream &apply(ostream &s, const tuple_t &t)
{
return s << get<0>(t);
}
};
template <class... T>
ostream &operator<<(ostream &s, const tuple<T...> &t)
{
return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(
s, t);
}
template <>
ostream &operator<<(ostream &s, const tuple<> &t)
{
return s;
}
string revstr(string str)
{
reverse(str.begin(), str.end());
return str;
}
} // namespace std
#ifdef LOCAL
#define dump(...) \
debug_stream << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]\n", \
dump_func(#__VA_ARGS__, __VA_ARGS__)
template <class T>
void dump_func(const char *ptr, const T &x)
{
debug_stream << '\t';
for(char c = *ptr; c != '\0'; c = *++ptr)
{
if(c != ' ') debug_stream << c;
}
debug_stream << " : " << x << '\n';
}
template <class T, class... rest_t>
void dump_func(const char *ptr, const T &x, rest_t... rest)
{
debug_stream << '\t';
for(char c = *ptr; c != ','; c = *++ptr)
{
if(c != ' ') debug_stream << c;
}
debug_stream << " : " << x << ",\n";
dump_func(++ptr, rest...);
}
#else
#define dump(...) ((void)0)
#endif
template <class P>
void read_range(P __first, P __second)
{
for(P i = __first; i != __second; ++i)
std::cin >> *i;
}
template <class P>
void write_range(P __first, P __second)
{
for(P i = __first; i != __second;
std::cout << (++i == __second ? '\n' : ' '))
{
std::cout << *i;
}
}
// substitute y for x.
template <class T>
void subst(T &x, const T &y)
{
x = y;
}
// substitue y for x iff x > y.
template <class T>
bool chmin(T &x, const T &y)
{
return x > y ? x = y, true : false;
}
// substitue y for x iff x < y.
template <class T>
bool chmax(T &x, const T &y)
{
return x < y ? x = y, true : false;
}
template <class T>
constexpr T minf(const T &x, const T &y)
{
return std::min(x, y);
}
template <class T>
constexpr T maxf(const T &x, const T &y)
{
return std::max(x, y);
}
// binary search.
template <class int_t, class F>
int_t bin(int_t ok, int_t ng, const F &f)
{
while(std::abs(ok - ng) > 1)
{
int_t mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
template <class T, class A, size_t N>
void init(A (&array)[N], const T &val)
{
std::fill((T *)array, (T *)(array + N), val);
}
void reset()
{}
template <class A, class... rest_t>
void reset(A &array, rest_t... rest)
{
memset(array, 0, sizeof(array));
reset(rest...);
}
// a integer uniformly and randomly chosen from the interval [l, r).
template <typename int_t>
int_t rand_int(int_t l, int_t r)
{
static std::random_device seed_gen;
static std::mt19937 engine(seed_gen());
std::uniform_int_distribution<int_t> unid(l, r - 1);
return unid(engine);
}
// a real number uniformly and randomly chosen from the interval [l, r).
template <typename real_t>
real_t rand_real(real_t l, real_t r)
{
static std::random_device seed_gen;
static std::mt19937 engine(seed_gen());
std::uniform_real_distribution<real_t> unid(l, r);
return unid(engine);
}
/* The main code follows. */
namespace math
{
template <int_fast32_t mod>
struct modint
{
int x;
constexpr modint() : x(0)
{}
constexpr modint(int_fast64_t y)
: x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod)
{}
constexpr modint &operator+=(const modint &p)
{
if((x += p.x) >= mod) x -= mod;
return *this;
}
constexpr modint &operator++()
{
return ++x, *this;
}
constexpr modint operator++(int)
{
modint t = *this;
return ++x, t;
}
constexpr modint &operator-=(const modint &p)
{
if((x += mod - p.x) >= mod) x -= mod;
return *this;
}
constexpr modint &operator--()
{
return --x, *this;
}
constexpr modint operator--(int)
{
modint t = *this;
return --x, t;
}
constexpr modint &operator*=(const modint &p)
{
return x = (int_fast64_t)x * p.x % mod, *this;
}
constexpr modint &operator/=(const modint &p)
{
return *this *= inverse(p);
}
// constexpr modint &operator%=(int m) { return x %= m, *this; }
constexpr modint operator-() const
{
return modint(-x);
}
constexpr modint operator+(const modint &p) const
{
return modint(*this) += p;
}
constexpr modint operator-(const modint &p) const
{
return modint(*this) -= p;
}
constexpr modint operator*(const modint &p) const
{
return modint(*this) *= p;
}
constexpr modint operator/(const modint &p) const
{
return modint(*this) /= p;
}
// constexpr modint operator%(int m) const { return modint(*this) %= m;
// }
constexpr bool operator==(const modint &p) const
{
return x == p.x;
}
constexpr bool operator!=(const modint &p) const
{
return x != p.x;
}
constexpr bool operator!() const
{
return !x;
}
// constexpr bool operator>(const modint &p) const { return x > p.x; }
// constexpr bool operator<(const modint &p) const { return x < p.x; }
// constexpr bool operator>=(const modint &p) const { return x >= p.x; }
// constexpr bool operator<=(const modint &p) const { return x <= p.x; }
constexpr friend modint inverse(const modint &p)
{
int a = p.x, b = mod, u = 1, v = 0;
while(b > 0)
{
int t = a / b;
a -= t * b;
a ^= b ^= a ^= b;
u -= t * v;
u ^= v ^= u ^= v;
}
return modint(u);
}
constexpr friend modint pow(modint p, int_fast64_t e)
{
if(e < 0) e = (e % (mod - 1) + mod - 1) % (mod - 1);
modint ret = 1;
while(e)
{
if(e & 1) ret *= p;
p *= p;
e >>= 1;
}
return ret;
}
friend std::ostream &operator<<(std::ostream &s, const modint &p)
{
return s << p.x;
}
friend std::istream &operator>>(std::istream &s, modint &p)
{
int_fast64_t x;
p = modint((s >> x, x));
return s;
}
};
} // namespace math
template <class K>
// K must be a field.
struct matrix
{
std::vector<std::vector<K>> mat;
matrix()
{}
matrix(size_t n)
{
assign(n, n);
}
matrix(size_t h, size_t w)
{
assign(h, w);
}
matrix(const matrix &x) : mat(x.mat)
{}
matrix(const std::vector<std::vector<K>> _mat) : mat(_mat)
{}
void resize(size_t h, size_t w, const K v = K(0))
{
mat.resize(h, std::vector<K>(w, v));
}
void assign(size_t h, size_t w, const K v = K())
{
mat.assign(h, std::vector<K>(w, v));
}
size_t height() const
{
return mat.size();
}
size_t width() const
{
return mat.empty() ? 0 : mat[0].size();
}
bool is_square() const
{
return height() == width();
}
std::vector<K> &operator[](const size_t i)
{
return mat[i];
}
static matrix identity(size_t n)
{
matrix ret(n, n);
for(size_t i = 0; i < n; ++i)
ret[i][i] = K(1);
return ret;
}
matrix operator-() const
{
size_t h = height(), w = width();
matrix res(*this);
for(size_t i = 0; i < h; ++i)
{
for(size_t j = 0; j < w; ++j)
{
res[i][j] = -mat[i][j];
}
}
return res;
}
matrix operator&(const matrix &x) const
{
return matrix(*this) &= x;
}
matrix operator|(const matrix &x) const
{
return matrix(*this) |= x;
}
matrix operator^(const matrix &x) const
{
return matrix(*this) ^= x;
}
matrix operator+(const matrix &x) const
{
return matrix(*this) += x;
}
matrix operator-(const matrix &x) const
{
return matrix(*this) -= x;
}
matrix operator*(const matrix &x) const
{
return matrix(*this) *= x;
}
matrix &operator&=(const matrix &x)
{
size_t h = height(), w = width();
assert(h == x.height() and w == x.width());
for(size_t i = 0; i < h; ++i)
{
for(size_t j = 0; j < w; ++j)
{
mat[i][j] &= x.mat[i][j];
}
}
return *this;
}
matrix &operator|=(const matrix &x)
{
size_t h = height(), w = width();
assert(h == x.height() and w == x.width());
for(size_t i = 0; i < h; ++i)
{
for(size_t j = 0; j < w; ++j)
{
mat[i][j] |= x.mat[i][j];
}
}
return *this;
}
matrix &operator^=(const matrix &x)
{
size_t h = height(), w = width();
assert(h == x.height() and w == x.width());
for(size_t i = 0; i < h; ++i)
{
for(size_t j = 0; j < w; ++j)
{
mat[i][j] ^= x.mat[i][j];
}
}
return *this;
}
matrix &operator+=(const matrix &x)
{
size_t h = height(), w = width();
assert(h == x.height() and w == x.width());
for(size_t i = 0; i < h; ++i)
{
for(size_t j = 0; j < w; ++j)
{
mat[i][j] += x.mat[i][j];
}
}
return *this;
}
matrix &operator-=(const matrix &x)
{
size_t h = height(), w = width();
assert(h == x.height() and w == x.width());
for(size_t i = 0; i < h; ++i)
{
for(size_t j = 0; j < w; ++j)
{
mat[i][j] -= x.mat[i][j];
}
}
return *this;
}
matrix &operator*=(const matrix &x)
{
size_t l = height(), m = width(), n = x.width();
assert(m == x.height());
matrix res(l, n);
for(size_t i = 0; i < l; ++i)
{
for(size_t j = 0; j < m; ++j)
{
for(size_t k = 0; k < n; ++k)
{
res[i][k] += mat[i][j] * x.mat[j][k];
}
}
}
return *this = res;
}
friend matrix pow(matrix x, int_fast64_t n)
{
assert(x.is_square());
matrix res = identity(x.height());
while(n)
{
if(n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
friend matrix inverse(const matrix &x)
{
assert(x.is_square());
size_t n = x.height();
matrix ext_x(x), e(identity(n)), res(n);
for(size_t i = 0; i < n; ++i)
ext_x[i].insert(end(ext_x[i]), begin(e[i]), end(e[i]));
ext_x = ext_x.row_canonical_form();
for(size_t i = 0; i < n; ++i)
{
if(std::vector<K>(begin(ext_x[i]), begin(ext_x[i]) + n) != e[i])
return matrix();
res[i] = std::vector<K>(begin(ext_x[i]) + n, end(ext_x[i]));
}
return res;
}
matrix row_canonical_form()
{
size_t h = height(), w = width(), rank = 0;
matrix res(*this);
for(size_t j = 0; j < w; ++j)
{
bool piv = false;
for(size_t i = rank; i < h; ++i)
{
if(res[i][j] != K(0))
{
if(piv)
{
K r = -res[i][j];
for(size_t k = j; k < w; ++k)
{
res[i][k] += res[rank][k] * r;
}
}
else
{
swap(res[rank], res[i]);
K r = res[rank][j];
for(size_t k = j; k < w; ++k)
{
res[rank][k] /= r;
}
for(size_t k = 0; k < rank; ++k)
{
r = -res[k][j];
for(size_t l = j; l < w; ++l)
{
res[k][l] += res[rank][l] * r;
}
}
piv = true;
}
}
}
if(piv) ++rank;
}
return res;
}
K det() const
{
matrix<K> x(*this);
assert(is_square());
size_t n = height();
K res(1);
for(size_t j = 0; j < n; ++j)
{
bool piv = false;
for(size_t i = j; i < n; ++i)
{
if(x[i][j] != K(0))
{
if(piv)
{
const K r = -x[i][j];
for(size_t k = j; k < n; ++k)
{
x[i][k] += x[j][k] * r;
}
}
else
{
swap(x[i], x[j]);
if(i != j) res = -res;
const K r = x[j][j];
res *= r;
for(size_t k = j; k < n; ++k)
{
x[j][k] /= r;
}
piv = true;
}
}
}
if(not piv)
{
return K(0);
}
}
return res;
}
friend std::istream &operator>>(std::istream &s, matrix &x)
{
size_t h = x.height(), w = x.width();
for(size_t i = 0; i < h; ++i)
{
for(size_t j = 0; j < w; ++j)
{
s >> x[i][j];
}
}
return s;
}
friend std::ostream &operator<<(std::ostream &s, const matrix &x)
{
size_t h = x.height(), w = x.width();
for(size_t i = 0; i < h; ++i)
{
if(i) s << "\n";
for(size_t j = 0; j < w; ++j)
{
s << (j ? " " : "") << x.mat[i][j];
}
}
return s;
}
};
using namespace std;
using namespace math;
signed main()
{
void __solve();
void __precalc();
unsigned int t = 1;
// cin >> t;
__precalc();
#ifdef LOCAL
t=3;
#endif
while(t--)
{
__solve();
}
}
void __precalc()
{}
void __solve()
{
int a,b,n; cin>>a>>b>>n;
matrix<modint<1000000007>> m(3,3),v(3,1);
m[0]={a,b,0},m[1]={1,0,0},m[2]={0,1,0};
m=pow(m,n);
v[0][0]=a,v[1][0]=1;
v=m*v;
std::cout << v[2][0] << "\n";
}