PAT (Advanced) 1081. Rational Sum (20)

原创于 2014-08-26 12:21:54 发布 · 662 阅读

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本文介绍了一种计算两个整数的最大公约数和最小公倍数的高效算法，通过循环和取余操作实现。该算法不仅适用于初学者理解，也适用于在实际编程中提高效率。

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#include <iostream>

using namespace std;

long long gcd(long long a, long long b)
{
	long long r;
	while (b > 0)
	{
		r = a % b;
		a = b;
		b = r;
	}
	return a;
}

long long lcm(long long a, long long b)
{
	return a / gcd(a, b) * b;
}

int main()
{
	int n;
	cin >> n;
	long long a1 = 0, b1 = 1, a2, b2;
	long long multiple, factor;

	for (int i = 0; i < n; i++)
	{
		cin >> a2;
		getchar();
		cin >> b2;

		multiple = lcm(b1, b2);
		a1 *= multiple / b1;
		a2 *= multiple / b2;
		a1 += a2;
		b1 = multiple;

		factor = gcd(a1, b1);
		a1 /= factor;
		b1 /= factor;
		if (a1 == 0)
			b1 = 1;
	}
	if (a1 == 0)
		cout << 0;
	else
	{
		if (a1 / b1 != 0)
		{
			cout << a1 / b1;
			a1 %= b1;
			if (a1 != 0)
				cout << " ";
		}
		if (a1 != 0)
			cout << a1 << "/" << b1;
	}
	cout << endl;
}