最大公约数和最小公倍数(编程之美2.7)

1.辗转相除法求最大公约数(递归式)

unsigned int gcdRecursion(unsigned int x, unsigned int y) {
	if (0 == x || 0 == y) {
		return 0;
	}

	if (x < y) {
		std::swap(x, y);
	}

	while (y != 0) {
		int temp = y;
		y = (x % y);
		x = temp;
	}

	return x;
}

2.辗转相除法求最大公约数(非递归)

unsigned int gcdLoop(unsigned int x, unsigned int y) {
	if (0 == x || 0 == y) {
		return 0;
	}

	if (x < y) {
		std::swap(x, y);
	}

	return !(x % y) ? y : gcdLoop(y, x % y);
}

3.最小公倍数

unsigned int lcm(unsigned int x, unsigned int y) {
	if (0 == x || 0 == y) {
		return 0;
	}

	return (x * y) / gcdRecursion(x, y);
}

4.测试代码

#include
using namespace std;

int main() {
	unsigned int m = 1, n = 1;
	cout << "请输入两个数：" << endl;
	while (cin >> m >> n) {
		cout << "其最大公约数(递归)是：" << gcdRecursion(m, n) << endl;

		cout << "其最大公约数(非递归)是：" << gcdLoop(m, n) << endl;

		cout << "其最小公倍数是:" << lcm(m, n) << endl;

		cout << "请输入两个数：" << endl;
	}

	return 0;
}