#170037 (C++14) No.510 二次漸化式

• 問題: No.510 二次漸化式
• ユーザー: pekempey
• 提出日時: 2017-04-30 18:26:38
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 43 ms / 3,000 ms
• コード長: 2,839 bytes
• コンパイル時間: 840 ms
• コンパイル使用メモリ: 76,764 KB
• 実行使用メモリ: 20,440 KB
• 最終ジャッジ日時: 2024-09-13 23:54:06
• 合計ジャッジ時間: 3,198 ms
• ジャッジサーバーID （参考情報）: judge2 / judge6

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	12 ms; 5,376 KB
testcase_03	AC	11 ms; 5,376 KB
testcase_04	AC	12 ms; 5,376 KB
testcase_05	AC	12 ms; 5,376 KB
testcase_06	AC	18 ms; 5,376 KB
testcase_07	AC	18 ms; 5,504 KB
testcase_08	AC	19 ms; 5,504 KB
testcase_09	AC	18 ms; 5,376 KB
testcase_10	AC	6 ms; 5,376 KB
testcase_11	AC	6 ms; 5,376 KB
testcase_12	AC	6 ms; 5,376 KB
testcase_13	AC	6 ms; 5,376 KB
testcase_14	AC	7 ms; 5,376 KB
testcase_15	AC	6 ms; 5,376 KB
testcase_16	AC	30 ms; 20,352 KB
testcase_17	AC	27 ms; 20,352 KB
testcase_18	AC	27 ms; 20,440 KB
testcase_19	AC	27 ms; 20,352 KB
testcase_20	AC	27 ms; 20,352 KB
testcase_21	AC	27 ms; 20,212 KB
testcase_22	AC	28 ms; 20,352 KB
testcase_23	AC	39 ms; 20,352 KB
testcase_24	AC	39 ms; 20,352 KB
testcase_25	AC	37 ms; 20,352 KB
testcase_26	AC	37 ms; 20,352 KB
testcase_27	AC	37 ms; 20,216 KB
testcase_28	AC	36 ms; 20,352 KB
testcase_29	AC	38 ms; 20,388 KB
testcase_30	AC	37 ms; 20,336 KB
testcase_31	AC	43 ms; 20,380 KB
testcase_32	AC	42 ms; 20,344 KB
testcase_33	AC	42 ms; 20,260 KB
testcase_34	AC	29 ms; 20,352 KB
testcase_35	AC	25 ms; 20,392 KB

ソースコード

#include <iostream>
#include <string>
#include <algorithm>
#include <array>
#include <vector>

const int mod = 1e9 + 7;

#ifdef __linux__
#define getchar getchar_unlocked
#define putchar putchar_unlocked
#endif

char readChar() {
	int c;
	while ((c = getchar()) < 'a');
	return c;
}

int readInt() {
	int n, c;
	while ((c = getchar()) < '0');
	n = c - '0';
	while ((c = getchar()) >= '0') {
		n = n * 10 + c - '0';
	}
	return n;
}

void writeInt(int n) {
	int d[11];
	int i = 0;
	do {
		d[i++] = n % 10;
		n /= 10;
	} while (n > 0);
	while (i > 0) {
		putchar(d[--i] + '0');
	}
	putchar('\n');
}

struct modint {
	int n;
	modint(int n = 0) : n(n) {}
};

modint operator+(modint a, modint b) { return modint((a.n += b.n) >= mod ? a.n - mod : a.n); }
modint operator-(modint a, modint b) { return modint((a.n -= b.n) < 0 ? a.n + mod : a.n); }
modint operator*(modint a, modint b) { return modint(1LL * a.n * b.n % mod); }
modint &operator+=(modint &a, modint b) { return a = a + b; }
modint &operator-=(modint &a, modint b) { return a = a - b; }
modint &operator*=(modint &a, modint b) { return a = a * b; }

using V = std::array<modint, 4>;
using M = std::array<V, 4>;

M operator*(const M &a, const M &b) {
	long long c[4][4];
	for (int i = 0; i < 3; i++) {
		for (int j = 1; j < 4; j++) {
			c[i][j] = 0;
		}
	}
	for (int i = 0; i < 3; i++) {
		for (int k = 0; k < 4; k++) {
			for (int j = 1; j < 4; j++) {
				c[i][j] += 1LL * a[i][k].n * b[k][j].n;
			}
		}
	}
	M ret = {};
	for (int i = 0; i < 3; i++) {
		for (int j = 1; j < 4; j++) {
			ret[i][j] = c[i][j] % mod;
		}
	}
	ret[0][0] = 1;
	ret[3][3] = 1;
	return ret;
}

M getmat(modint x, modint y) {
	return M{
		V{1, 0, x, 0},
		V{0, y, 0, 1},
		V{0, 2 * y, y * y, 1},
		V{0, 0, 0, 1},
	};
}

int main() {
	int n = readInt();
	int q = readInt();

	std::vector<int> xs(n);
	std::vector<int> ys(n);

	int N = 1;
	while (N < n) {
		N *= 2;
	}

	std::vector<M> seg(N * 2);
	for (int i = 0; i < N * 2; i++) {
		seg[i] = getmat(0, 0);
	}
	for (int i = N - 1; i >= 1; i--) {
		seg[i] = seg[i * 2 + 1] * seg[i * 2];
	}

	auto setval = [&](int k, M v) {
		k += N;
		seg[k] = v;
		while (k > 1) {
			k /= 2;
			seg[k] = seg[k * 2 + 1] * seg[k * 2];
		}
	};

	auto getval = [&](int k) {
		if (k == N) {
			return seg[1];
		}
		k += N;
		M ret = {};
		for (int i = 0; i < 4; i++) {
			ret[i][i] = 1;
		}
		while (k > 1) {
			if (k & 1) {
				ret = ret * seg[--k];
			}
			k /= 2;
		}
		return ret;
	};

	while (q--) {
		char c = readChar();
		if (c == 'x') {
			int i = readInt();
			int v = readInt();
			xs[i] = v;
			setval(i, getmat(xs[i], ys[i]));
		} else if (c == 'y') {
			int i = readInt();
			int v = readInt();
			ys[i] = v;
			setval(i, getmat(xs[i], ys[i]));
		} else {
			int i = readInt();
			auto m = getval(i);
			writeInt((m[0][0] + m[0][1] + m[0][2] + m[0][3]).n);
		}
	}
}