#170243 (C++11) No.280 歯車の問題(1)

• 問題: No.280 歯車の問題(1)
• ユーザー: Klay
• 提出日時: 2017-05-01 19:37:45
• 言語: C++11 (gcc 11.4.0)
• 結果: AC
• 実行時間: 2 ms / 1,000 ms
• コード長: 1,489 bytes
• コンパイル時間: 603 ms
• コンパイル使用メモリ: 54,620 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-14 01:58:27
• 合計ジャッジ時間: 3,004 ms
• ジャッジサーバーID （参考情報）: judge2 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	1 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	2 ms; 5,376 KB
testcase_21	AC	1 ms; 5,376 KB
testcase_22	AC	1 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB
testcase_24	AC	2 ms; 5,376 KB
testcase_25	AC	1 ms; 5,376 KB
testcase_26	AC	1 ms; 5,376 KB
testcase_27	AC	2 ms; 5,376 KB
testcase_28	AC	2 ms; 5,376 KB
testcase_29	AC	2 ms; 5,376 KB
testcase_30	AC	2 ms; 5,376 KB

ソースコード

#include <iostream>

/*
歯車の問題(1)

2
20 40

Z1 * theta1 = Z2 * theta2 => Z1 : Z2 = theta2 : theta1

theta2 = theta1 * (Z1 / Z2)

gr = theta1 / theta2 = Z2 / Z1

3
20 40 80
1  2  3

theta2 = theta1 * (20 / 40) = 0.5 * theta1
theta3 = theta2 * (40 / 80) = 0.5 * theta2

theta3 = 0.5 * 0.5 * theta1

theta1 / theta3 = 1 / (0.5 * 0.5)
*/

class FRACTION
{
	public:
	
	unsigned long long numerator, denominator;
	
	FRACTION operator*(FRACTION frac)
	{
		FRACTION answer;
		
		answer.numerator = numerator * frac.numerator;
		answer.denominator = denominator * frac.denominator;
		
		return answer;
	}
	
	private:
	
	unsigned long long GCD(unsigned long long a, unsigned long long b)
	{
		while(a != b)
		{
			if (a < b)
			{
				b -= a;
			}
			else
			{
				a-= b;
			}
		}
		
		return a;
	}
	
	public:
	
	void reduction(void)
	{
		unsigned long long gcd = GCD(numerator, denominator);
		
		numerator = numerator / gcd;
		denominator = denominator / gcd;
	}
};

FRACTION getGR(unsigned long long N1, unsigned long long N2)
{
	FRACTION GR;
	
	GR.numerator = N2;
	GR.denominator = N1;

	return GR;
}

int main(void)
{
	FRACTION GR;
	GR.numerator = 1;
	GR.denominator = 1;

	int N;

	std::cin >> N;
	
	unsigned long long Z[N];
	
	for(int i = 0; i < N; i ++)
	{
		std::cin >> Z[i];
	}
	
	for(int i = 0; i < N - 1; i ++)
	{
		GR = GR * getGR(Z[i], Z[i + 1]);
		
		GR.reduction();
	}
	
	std::cout << GR.numerator << "/" << GR.denominator << std::endl;
	
	return 0;
}