Pat乙级 1034 有理数四则运算

题目网址
https://pintia.cn/problem-sets/994805260223102976/problems/994805287624491008

思路

注意两个点，一是辗转相除法递归会超时，二是int范围会爆，得用long，不然测试点2、3过不去。思路就是模拟。

代码

#include<iostream>
#include<cmath>

using namespace std;

long gcd(long a, long b)
{
    if (a < b)
        swap(a, b);
//    return b == 0 ? a : gcd(b, a % b);
	while(b > 0) {
		int t = a % b;
		a = b;
		b = t;
	}
	return a;	
}

void fun(long a, long b){//化简 
	if (a == 0) {
		cout << 0;
	return ;
	}
	long t = gcd(abs(a), abs(b));//最大公因数 
	long T = abs(a * b) / t;//最小公倍数 
	a /= t;
	b /= t;
	
	if (a < 0) {
		cout << "(-";
		a = -a;
		if ((a % b) == 0)
			cout << a / b;
		else {
			if (a / b > 0)
				cout << a / b << " ";
			cout << a % b << "/" << b;
		}
		cout << ")";
	}
	else if (a == 0)
		cout << 0;
	else {
		if ((a % b) == 0)
			cout << a / b;
		else {
			if (a / b > 0)
				cout << a / b << " ";
			cout << a % b << "/" << b;
		}
	}	
}
int main() {
	long a1;
	long a2;
	long b1;
	long b2;
	long A;
	long B;
	
	scanf("%ld/%ld %ld/%ld", &a1, &a2, &b1, &b2);
	
	//加法 
	fun(a1, a2);
	cout << " + ";
	fun(b1, b2);
	cout << " = ";
	A = a1 * b2 + b1 * a2;
	B = a2 * b2;
	if (B < 0) {
		A = -A;
		B = -B;
	}
	fun(A, B);
	cout << endl;
	 
	//减法 
	fun(a1, a2);
	cout << " - ";
	fun(b1, b2);
	cout << " = ";
	A = a1 * b2 - b1 * a2;
	B = a2 * b2;
	if (B < 0) {
		A = -A;
		B = -B;
	}
	fun(A, B);
	cout << endl;
	
	//乘法
	fun(a1, a2);
	cout << " * ";
	fun(b1, b2);
	cout << " = ";
	A = a1 * b1;
	B = a2 * b2;
	if (B < 0) {
		A = -A;
		B = -B;
	}
	fun(A, B);
	cout << endl;
	
	//除法
	fun(a1, a2);
	cout << " / ";
	fun(b1, b2);
	cout << " = ";
	A = a1 * b2;
	B = a2 * b1;
	if (B < 0) {
		A = -A;
		B = -B;
	}
	if (B == 0) {
		cout << "Inf" << endl;
		return 0;
	}
	fun(A, B);
	cout << endl;
	return 0;
}