UVA 10655 Contemplation! Algebra

最新推荐文章于 2020-02-07 11:05:28 发布

Lost_in_wine

最新推荐文章于 2020-02-07 11:05:28 发布

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#include <cstdio>
#include <cstring>

typedef long long LL;

const int N = 2;

struct Matrix {
	LL ary[N][N];
	void init() {
		memset(ary, 0, sizeof(ary));
	}
	Matrix() {
		init();
	}
};

const Matrix operator*(const Matrix & A, const Matrix & B) {
	Matrix t;
	for (int i = 0; i < N; ++i)
		for (int j = 0; j < N; ++j) 
			for (int k = 0; k < N; ++k)
				t.ary[i][j] += A.ary[i][k] * B.ary[k][j];
	return t;
}

LL quick_pow(LL p, LL q, LL n) {
	if (n == 0) return 2;
	if (n == 1) return p;
	if (n == 2) return p * p - 2 * q;
	Matrix ans, tmp;
	tmp.ary[0][0] = p;
	tmp.ary[1][0] = -q;
	tmp.ary[0][1] = 1;
	tmp.ary[1][1] = 0;

	ans.ary[1][1] = p;
	ans.ary[0][1] = ans.ary[1][0] = p * p - 2 * q;
	ans.ary[0][0] = ans.ary[0][1] * p - ans.ary[1][1] * q;

	n -= 3;
	while (n) {
		if (n & 1)
			ans = ans * tmp;
		n >>= 1;
		tmp = tmp * tmp;
	}

	return ans.ary[0][0];
}

int main() {
	LL p, q, n;

	while (~scanf("%lld%lld", &p, &q)) {
		if (scanf("%lld", &n) == EOF)
			break;

		printf("%lld\n", quick_pow(p, q, n));
	}

	return 0;
}