PAT-1088 Rational Arithmetic

1088 Rational Arithmetic

part 3, 3.4

自己解法

• rational numbers：有理数；sum, difference, product and quotient：加减乘除；a pair of parentheses：一对括号
• 见到说 in the rang of long int（$2^{32}$ 和 $10^{10}$），就使用 long long
• 题目看起来复杂，实则逻辑很清晰

#include <iostream>
using namespace std;typedef long long ll;ll gcd(ll a, ll b) { return b == 0 ? abs(a) : gcd(b, a % b); }void print(ll a, ll b)
{if (b < 0){a = -a;b = -b;}ll maxg = gcd(a, b);a = a / maxg;b = b / maxg;ll x = a / b;if (x < 0)a = -a;a = a % b;if (a < 0 || x < 0)cout << '(';if (a == 0) // b = 1时a必为0cout << x;else if (a != 0 && x != 0)cout << x << ' ' << a << '/' << b;elsecout << a << '/' << b;if (a < 0 || x < 0)cout << ')';
}void sum(ll a1, ll b1, ll a2, ll b2)
{print(a1, b1);cout << " + ";print(a2, b2);cout << " = ";a1 = a1 * b2 + a2 * b1;b1 = b1 * b2;print(a1, b1);cout << endl;
}void different(ll a1, ll b1, ll a2, ll b2)
{print(a1, b1);cout << " - ";print(a2, b2);cout << " = ";a1 = a1 * b2 - a2 * b1;b1 = b1 * b2;print(a1, b1);cout << endl;
}void product(ll a1, ll b1, ll a2, ll b2)
{print(a1, b1);cout << " * ";print(a2, b2);cout << " = ";a1 = a1 * a2;b1 = b1 * b2;print(a1, b1);cout << endl;
}void quotient(ll a1, ll b1, ll a2, ll b2)
{print(a1, b1);cout << " / ";print(a2, b2);cout << " = ";a1 = a1 * b2;b1 = a2 * b1;if (b1 == 0)cout << "Inf";elseprint(a1, b1);cout << endl;
}int main()
{ll a1, b1, a2, b2;scanf("%lld/%lld %lld/%lld", &a1, &b1, &a2, &b2);sum(a1, b1, a2, b2);different(a1, b1, a2, b2);product(a1, b1, a2, b2);quotient(a1, b1, a2, b2);system("pause");return 0;
}

大神解法

• 柳神

#include <iostream>
#include <cmath>
using namespace std;
long long a, b, c, d;
long long gcd(long long t1, long long t2) {return t2 == 0 ? t1 : gcd(t2, t1 % t2);
}
void func(long long m, long long n) {if (m * n == 0) {printf("%s", n == 0 ? "Inf" : "0");return ;}bool flag = ((m < 0 && n > 0) || (m > 0 && n < 0));m = abs(m); n = abs(n);long long x = m / n;printf("%s", flag ? "(-" : "");if (x != 0) printf("%lld", x);if (m % n == 0) {if(flag) printf(")");return ;}if (x != 0) printf(" ");m = m - x * n;long long t = gcd(m, n);m = m / t; n = n / t;printf("%lld/%lld%s", m, n, flag ? ")" : "");
}
int main() {scanf("%lld/%lld %lld/%lld", &a, &b, &c, &d);func(a, b); printf(" + "); func(c, d); printf(" = "); func(a * d + b * c, b * d); printf("\n");func(a, b); printf(" - "); func(c, d); printf(" = "); func(a * d - b * c, b * d); printf("\n");func(a, b); printf(" * "); func(c, d); printf(" = "); func(a * c, b * d); printf("\n");func(a, b); printf(" / "); func(c, d); printf(" = "); func(a * d, b * c);return 0;
}