結果
| 問題 |
No.906 Y字グラフ
|
| コンテスト | |
| ユーザー |
 ゆにぽけ
|
| 提出日時 | 2024-01-04 21:12:46 |
| 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 | 5,861 bytes |
| コンパイル時間 | 1,788 ms |
| コンパイル使用メモリ | 133,632 KB |
| 最終ジャッジ日時 | 2025-02-18 16:11:28 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 28 |
ソースコード
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <array>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <cassert>
#include <cmath>
#include <ctime>
#include <iomanip>
#include <numeric>
#include <stack>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <bitset>
#include <random>
#include <utility>
#include <functional>
using namespace std;
template<int m> struct modint
{
private:
unsigned int value;
static constexpr int mod() {return m;}
public:
constexpr modint(const long long x = 0) noexcept
{
long long y = x;
if(y < 0 || y >= mod())
{
y %= mod();
if(y < 0) y += mod();
}
value = (unsigned int)y;
}
constexpr unsigned int val() noexcept {return value;}
constexpr modint &operator+=(const modint &other) noexcept
{
value += other.value;
if(value >= mod()) value -= mod();
return *this;
}
constexpr modint &operator-=(const modint &other) noexcept
{
unsigned int x = value;
if(x < other.value) x += mod();
x -= other.value;
value = x;
return *this;
}
constexpr modint &operator*=(const modint &other) noexcept
{
unsigned long long x = value;
x *= other.value;
value = (unsigned int) (x % mod());
return *this;
}
constexpr modint &operator/=(const modint &other) noexcept
{
return *this *= other.inverse();
}
constexpr modint inverse() const noexcept
{
assert(value);
long long a = value,b = mod(),x = 1,y = 0;
while(b)
{
long long q = a/b;
a -= q*b; swap(a,b);
x -= q*y; swap(x,y);
}
return modint(x);
}
constexpr modint power(long long N) const noexcept
{
assert(N >= 0);
modint p = *this,ret = 1;
while(N)
{
if(N & 1) ret *= p;
p *= p;
N >>= 1;
}
return ret;
}
constexpr modint operator+() {return *this;}
constexpr modint operator-() {return modint() - *this;}
constexpr modint &operator++(int) noexcept {return *this += 1;}
constexpr modint &operator--(int) noexcept {return *this -= 1;}
friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;}
friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;}
friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;}
friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;}
friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;}
};
/* using mint = modint<998244353>; */
using mint = modint<1000000007>;
template<class T> struct mat
{
private:
vector<vector<T>> m;
int h,w;
public:
constexpr mat(int _h,int _w,T x = 0) noexcept {m.assign(_h,vector<T>(_w,x));h = _h,w = _w;}
constexpr vector<T> operator[](const int i) const {assert(0 <= i && i < h); return m[i];}
constexpr vector<T> &operator[](const int i) noexcept {assert(0 <= i && i < h); return m[i];}
constexpr mat operator+(mat &other) noexcept
{
mat tmp = *this;
return tmp += other;
}
constexpr mat operator-(mat &other) noexcept
{
mat tmp = *this;
return tmp -= other;
}
constexpr mat operator*(mat &other) noexcept
{
mat tmp = *this;
return tmp *= other;
}
constexpr mat &operator+=(mat &other) noexcept
{
assert(h == other.h && w == other.w);
for(int i = 0;i < h;i++)for(int j = 0;j < w;j++) m[i][j] += other[i][j];
return *this;
}
constexpr mat &operator-=(mat &other) noexcept
{
assert(h == other.h && w == other.w);
for(int i = 0;i < h;i++)for(int j = 0;j < w;j++) m[i][j] -= other[i][j];
return *this;
}
constexpr mat &operator*=(mat &other) noexcept
{
assert(w == other.h);
mat tmp(h,other.w);
for(int i = 0;i < h;i++)for(int j = 0;j < other.w;j++)for(int k = 0;k < w;k++) tmp[i][j] += m[i][k]*other[k][j];
for(int i = 0;i < h;i++)
{
m[i].resize(other.w);
for(int j = 0;j < other.w;j++) m[i][j] = tmp[i][j];
}
return *this;
}
constexpr mat power(long n) noexcept
{
assert(h == w);
assert(n >= 0);
mat res(h,w);
for(int i = 0;i < h;i++) res[i][i] = 1;
mat p = *this;
long ex = n;
while(ex)
{
if(ex & 1) res *= p;
p *= p;
ex >>= 1;
}
return res;
}
constexpr bool operator==(mat &other) noexcept
{
assert(h == other.h && w == other.w);
bool res = true;
for(int i = 0;i < h;i++)for(int j = 0;j < w;j++) if(m[i][j] != other[i][j]) res = false;
return res;
}
constexpr bool operator!=(mat &other) noexcept
{
assert(h == other.h && w == other.w);
bool res = false;
for(int i = 0;i < h;i++)for(int j = 0;j < w;j++) if(m[i][j] != other[i][j]) res = true;
return res;
}
template<class S> friend ostream &operator<<(ostream &os,const mat<S> &x);
};
template<class S> ostream &operator<<(ostream &os,const mat<S> &x)
{
for(int i = 0;i < x.h;i++)for(int j = 0;j < x.w;j++)
{
os << x[i][j] << (j+1 == x.w && i+1 < x.h ? "\n":" ");
return os;
}
}
void solve()
{
long long N;
cin >> N;
mint ans = 0;
N -= 4;
//x + y + z = N 0 <= x <= y <= z
mat<mint> dp(6,6);
dp[0][1] = 1,dp[0][2] = 1,dp[0][4] = -1,dp[0][5] = 1;
for(int i = 1;i < 5;i++) dp[i][i-1] = 1;
dp[5][5] = 1;
mat<mint> S(6,1);
S[0][0] = 4;
S[1][0] = 3;
S[2][0] = 2;
S[3][0] = 1;
S[4][0] = 1;
S[5][0] = 1;
if(N >= 4)
{
S = dp.power(N-4) * S;
cout << S[0][0] << "\n";
}
else
{
cout << S[4 - N][0] << "\n";
}
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(nullptr);
int tt = 1;
/* cin >> tt; */
while(tt--) solve();
}