結果

問題 No.526 フィボナッチ数列の第N項をMで割った余りを求める
コンテスト
ユーザー morimario
提出日時 2021-01-29 14:35:49
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 7,399 bytes
コンパイル時間 2,034 ms
コンパイル使用メモリ 208,764 KB
最終ジャッジ日時 2025-01-18 08:41:01
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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 * 12
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 # 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
using ll = long long; using ull = unsigned long long;
using pii = pair<int, int>; using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using pll = pair<ll, ll>; using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;
using pdd = pair<double, double>; using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using pbb = pair<bool, bool>; using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using pss = pair<string, string>; using vs = vector<string>; using vvs = vector<vs>; using vvvs = vector<vvs>;
#define repeat(counter, start, goal, step) for (int counter = (int)(start); counter < (int)(goal); counter += step)
#define rep(counter, times) repeat(counter, 0, times, 1)
#define rep2(counter, start, goal) repeat(counter, start, goal, 1)
#define rep0(times) repeat(counter, 0, times, 1)
#define rrepeat(counter, start, goal, step) for (int counter = (int)(start); counter > (int)(goal); counter -= step)
#define rep3(counter, start, goal) rrepeat(counter, start, goal, 1)
#define rrep(counter, start, goal) rrepeat(counter, start - 1, goal - 1, 1)
#define all(container) begin(container), end(container)
template <typename T> bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; }
template <typename T> bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; }
void yn(bool flag) { cout << (flag ? "yes" : "no") << "\n"; }
void Yn(bool flag) { cout << (flag ? "Yes" : "No") << "\n"; }
void YN(bool flag) { cout << (flag ? "YES" : "NO") << "\n"; }
void set_prec(const int &digits) { cout << fixed << setprecision(digits); cerr << fixed << setprecision(digits); }
template <typename T> void pr(const T &obj) { cerr << obj; }
template <typename T, typename ...Ts> void pr(const T &first, const Ts &...rest) { pr(first); pr(", "); pr(rest...); }
template <typename S, typename T> void pr(const pair<S, T> &pair) { pr("("); pr(pair.first); pr(", "); pr(pair.second); pr(")"); }
template <typename T> void pr(const vector<T> &vec) { pr("{"); for (T obj : vec) { pr(obj); pr(", "); } pr("}"); }
template <typename T> void pr(const vector<vector<T>> &vv) { pr("\n"); rep(index, vv.size()) { pr("["); pr(index); pr("]: "); pr(vv[index]); pr("\n"); } }
template <typename T> void pr(const set<T> &vec) { pr("{"); for (T obj : vec) { pr(obj); pr(", "); } pr("}"); }
template <typename S, typename T> void pr(const map<S, T> &map) { pr("{"); for (pair<S, T> pair : map) { pr("("); pr(pair.first); pr(": "); pr(pair.second); pr("), "); } pr("}"); }
#define db(obj) cerr << #obj << ": "; pr(obj); cerr << " "
#define dl(obj) db(obj); cerr << "\n";
#define dm(...) cerr << "(" << #__VA_ARGS__ << "): ("; pr(__VA_ARGS__); cerr << ") "
#define dml(...) dm(__VA_ARGS__); cerr << "\n"
// #include <atcoder/all>
// using namespace atcoder;
// const ll MOD = 1000000007;
// const ll MOD = 998244353;

long long MOD;

template <typename T>
struct Matrix {
	int row, column;
	vector<vector<T>> val; // val[i][j]: i行j列成分
	Matrix(const int &_row, const int &_column) {
		assert(_row > 0 && _column > 0);
		row = _row;
		column = _column;
		val = vector<vector<T>>(row, vector<T>(column));
	}
	Matrix(const vector<vector<T>> &_val) {
		row = _val.size();
		column = _val[0].size();
		assert(row > 0 && column > 0);
		val = _val;
	}
	Matrix operator-() const {
		Matrix res{row, column};
		for (int i = 0; i < res.row; ++i) {
			for (int j = 0; j < res.column; ++j) {
				res.val[i][j] = -val[i][j];
			}
		}
		return res;
	}
};

template <typename T>
Matrix<T> zero(const int &m, const int &n) {
	Matrix<T> res{m, n};
	return res;
}
template <typename T>
Matrix<T> zero(const int &n) {
	Matrix<T> res{n, n};
	return res;
}

template <typename T>
Matrix<T> unit(const int &n) {
	Matrix<T> res{n, n};
	for (int k = 0; k < n; ++k) {
		res.val[k][k] = 1;
	}
	return res;
}

// スカラー倍
template <typename T>
Matrix<T> operator*(const T &k, const Matrix<T> &A) {
	Matrix<T> res{A.row, A.column};
	for (int i = 0; i < res.row; ++i) {
		for (int j = 0; j < res.column; ++j) {
			res.val[i][j] = k * A.val[i][j];
		}
	}
	return res;
}

template <typename T>
Matrix<T> operator*(const Matrix<T> &A, const T &k) {
	return k * A;
}

template <typename T>
void operator*=(Matrix<T> &A, const T &k) {
	A = A * k;
}

// 加法
template <typename T>
Matrix<T> operator+(const Matrix<T> &left, const Matrix<T> &right) {
	assert(left.row == right.row && left.column == right.column);
	Matrix<T> res{left.row, left.column};
	for (int i = 0; i < res.row; ++i) {
		for (int j = 0; j < res.column; ++j) {
			res.val[i][j] = left.val[i][j] + right.val[i][j];
		}
	}
	return res;
}

template <typename T>
Matrix<T> operator+=(Matrix<T> &left, const Matrix<T> &right) {
	left = left + right;
}

template <typename T>
Matrix<T> operator-(const Matrix<T> &left, const Matrix<T> &right) {
	return left + (-right);
}

template <typename T>
Matrix<T> operator-=(Matrix<T> &left, const Matrix<T> &right) {
	left = left - right;
}

// 行列積
template <typename T>
Matrix<T> operator*(const Matrix<T> &left, const Matrix<T> &right) {
	assert (left.column == right.row);
	Matrix<T> res{left.row, right.column};
	for (int i = 0; i < res.row; ++i) {
		for (int j = 0; j < res.column; ++j) {
			for (int k = 0; k < left.column; ++k) {
				res.val[i][j] += left.val[i][k] * right.val[k][j];
			}
		}
	}
	return res;
}

template <typename T>
Matrix<T> operator*=(Matrix<T> &left, const Matrix<T> &right) {
	left = left * right;
}

// 行列累乗
template <typename T>
Matrix<T> pow(Matrix<T> A, long long m) {
	assert(A.row == A.column);
	assert(m >= 0);
	Matrix<T> res = unit<T>(A.row), X = A;
	while (m > 0) {
		if (m & 1) {
			res = res * X;
		}
		X = X * X;
		m >>= 1;
	}
	return res;
}

// 特別な積
template <typename T>
Matrix<T> my_prod(Matrix<T> left, Matrix<T> right) {
	assert(left.column == right.row);
	Matrix<T> res{left.row, right.column};
	for (int i = 0; i < res.row; ++i) {
		for (int j = 0; j < res.column; ++j) {
			for (int k = 0; k < left.column; ++k) {
				// 演算例
				long long temp = left.val[i][k] * right.val[k][j] % MOD;
				res.val[i][j] = (res.val[i][j] + temp) % MOD;
			}
		}
	}
	return res;
}

// 特別な積についての行列累乗 ※単位行列はE?
template <typename T>
Matrix<T> my_pow(Matrix<T> A, long long m) {
	assert(A.row == A.column);
	assert(m >= 0);
	Matrix<T> res = unit<T>(A.row), X = A;
	while (m > 0) {
		if (m & 1) {
			res = my_prod(res, X);
		}
		X = my_prod(X, X);
		m >>= 1;
	}
	return res;
}

// debug
// void show(Matrix<mint> A) {
// 	for (int i = 0; i < A.row; ++i) {
// 		cout << "(";
// 		for (int j = 0; j < A.column; ++j) {
// 			cout << A.val[i][j].val() << ", ";
// 			if (j < A.val[0].size() - 1) {
// 				cout << ", ";
// 			}
// 		}
// 		cout << ")\n";
// 	}
// 	cout << "\n";
// }

template <typename T>
void show(Matrix<T> A) {
	for (int i = 0; i < A.row; ++i) {
		cout << "(";
		for (int j = 0; j < A.column; ++j) {
			cout << A.val[i][j];
			if (j < A.val[0].size() - 1) {
				cout << ", ";
			}
		}
		cout << ")\n";
	}
	cout << "\n";
}

int main() {
	int N; ll M; cin >> N >> M;
	MOD = M;
	Matrix<ll> A{{{1, 1}, {1, 0}}};

	Matrix<ll> B = my_pow(A, N - 1);
	Matrix<ll> F = {{{1}, {0}}};
	Matrix<ll> X = my_prod(B, F);
	cout << X.val[1][0] << endl;
}
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