結果
問題 | No.891 隣接3項間の漸化式 |
ユーザー |
👑 ![]() |
提出日時 | 2019-09-20 21:36:45 |
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 | 5,751 bytes |
コンパイル時間 | 1,098 ms |
コンパイル使用メモリ | 120,296 KB |
最終ジャッジ日時 | 2025-01-07 18:41:19 |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 39 |
ソースコード
#include <algorithm>#include <bitset>#include <cassert>#include <cctype>#include <chrono>#define _USE_MATH_DEFINES#include <cmath>#include <cstdio>#include <cstring>#include <ctime>#include <deque>#include <functional>#include <iostream>#include <iterator>#include <map>#include <numeric>#include <queue>#include <set>#include <sstream>#include <string>#include <tuple>#include <utility>#include <vector>using namespace std;#define FOR(i,m,n) for(int i=(m);i<(n);++i)#define REP(i,n) FOR(i,0,n)#define ALL(v) (v).begin(),(v).end()const int INF = 0x3f3f3f3f;const long long LINF = 0x3f3f3f3f3f3f3f3fLL;const double EPS = 1e-8;const int MOD = 1000000007; // 998244353;const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};/*-------------------------------------------------*/int mod = MOD;struct ModInt {unsigned val;ModInt(): val(0) {}ModInt(long long x) : val(x >= 0 ? x % mod : x % mod + mod) {}ModInt pow(long long exponent) {ModInt tmp = *this, res = 1;while (exponent > 0) {if (exponent & 1) res *= tmp;tmp *= tmp;exponent >>= 1;}return res;}ModInt &operator+=(const ModInt &rhs) { if((val += rhs.val) >= mod) val -= mod; return *this; }ModInt &operator-=(const ModInt &rhs) { if((val += mod - rhs.val) >= mod) val -= mod; return *this; }ModInt &operator*=(const ModInt &rhs) { val = (unsigned long long)val * rhs.val % mod; return *this; }ModInt &operator/=(const ModInt &rhs) { return *this *= rhs.inv(); }bool operator==(const ModInt &rhs) const { return val == rhs.val; }bool operator!=(const ModInt &rhs) const { return val != rhs.val; }bool operator<(const ModInt &rhs) const { return val < rhs.val; }bool operator<=(const ModInt &rhs) const { return val <= rhs.val; }bool operator>(const ModInt &rhs) const { return val > rhs.val; }bool operator>=(const ModInt &rhs) const { return val >= rhs.val; }ModInt operator-() const { return ModInt(-val); }ModInt operator+(const ModInt &rhs) const { return ModInt(*this) += rhs; }ModInt operator-(const ModInt &rhs) const { return ModInt(*this) -= rhs; }ModInt operator*(const ModInt &rhs) const { return ModInt(*this) *= rhs; }ModInt operator/(const ModInt &rhs) const { return ModInt(*this) /= rhs; }friend ostream &operator<<(ostream &os, const ModInt &rhs) { return os << rhs.val; }friend istream &operator>>(istream &is, ModInt &rhs) { long long x; is >> x; rhs = ModInt(x); return is; }private:ModInt inv() const {// if (__gcd((int)val, mod) != 1) assert(false);unsigned a = val, b = mod; int x = 1, y = 0;while (b) {unsigned tmp = a / b;swap(a -= tmp * b, b);swap(x -= tmp * y, y);}return ModInt(x);}};ModInt abs(const ModInt &x) { return x.val; }struct Combinatorics {Combinatorics(int MAX = 5000000) {MAX <<= 1;fact.resize(MAX + 1);fact_inv.resize(MAX + 1);fact[0] = 1;FOR(i, 1, MAX + 1) fact[i] = fact[i - 1] * i;fact_inv[MAX] = ModInt(1) / fact[MAX];for (int i = MAX; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;}ModInt nCk(int n, int k) {if (n < 0 || n < k || k < 0) return ModInt(0);return fact[n] * fact_inv[k] * fact_inv[n - k];}ModInt nPk(int n, int k) {if (n < 0 || n < k || k < 0) return ModInt(0);return fact[n] * fact_inv[n - k];}ModInt nHk(int n, int k) {if (n < 0 || k < 0) return ModInt(0);return (k == 0 ? ModInt(1) : nCk(n + k - 1, k));}private:vector<ModInt> fact, fact_inv;};template <typename T>struct Matrix {Matrix(int m, int n, T val = 0) : dat(m, vector<T>(n, val)) {}int height() const { return dat.size(); }int width() const { return dat.front().size(); }Matrix pow(long long exponent) {int n = height();Matrix<T> tmp = *this, res(n, n, 0);REP(i, n) res[i][i] = 1;while (exponent > 0) {if (exponent & 1) res *= tmp;tmp *= tmp;exponent >>= 1;}return res;}inline const vector<T> &operator[](const int idx) const { return dat[idx]; }inline vector<T> &operator[](const int idx) { return dat[idx]; }Matrix &operator=(const Matrix &rhs) {int m = rhs.height(), n = rhs.width();dat.resize(m, vector<T>(n));REP(i, m) REP(j, n) dat[i][j] = rhs[i][j];return *this;}Matrix &operator+=(const Matrix &rhs) {int m = height(), n = width();REP(i, m) REP(j, n) dat[i][j] += rhs[i][j];return *this;}Matrix &operator-=(const Matrix &rhs) {int m = height(), n = width();REP(i, m) REP(j, n) dat[i][j] -= rhs[i][j];return *this;}Matrix &operator*=(const Matrix &rhs) {int m = height(), n = rhs.width(), l = width();vector<vector<T> > res(m, vector<T>(n, 0));REP(i, m) REP(j, n) {REP(k, l) res[i][j] += dat[i][k] * rhs[k][j];}swap(dat, res);return *this;}Matrix operator+(const Matrix &rhs) const { return Matrix(*this) += rhs; }Matrix operator-(const Matrix &rhs) const { return Matrix(*this) -= rhs; }Matrix operator*(const Matrix &rhs) const { return Matrix(*this) *= rhs; }private:vector<vector<T> > dat;};int main() {cin.tie(nullptr); ios::sync_with_stdio(false);// freopen("input.txt", "r", stdin);int a, b, n; cin >> a >> b >> n;if (n <= 1) {cout << n << '\n';return 0;}Matrix<ModInt> m(2, 2), r(2, 1);m[0][0] = a; m[0][1] = b; r[0][0] = 1;m[1][0] = 1; m[1][1] = 0; r[1][0] = 0;auto ans = m.pow(n - 1) * r;cout << ans[0][0] << '\n';return 0;}