fix rational number

hitonanode · hitonanode · commit 1b07158be11a · 2024-09-22T10:22:52.000+09:00
diff --git a/rational/rational_number.hpp b/rational/rational_number.hpp
@@ -1,26 +1,29 @@
 #pragma once
+#include <cassert>
 #include <limits>
 
 // Rational number + {infinity(1 / 0), -infiity(-1 / 0), nan(0 / 0)} （有理数）
-// Do not compare any number with nan
 // Verified: Yandex Cup 2022 Final E https://contest.yandex.com/contest/42710/problems/K
-template <class Int, bool AlwaysReduce = false> struct Rational {
-    Int num, den;
+template <class Int, bool AutoReduce = false> struct Rational {
+    Int num, den; // den >= 0
+
     static constexpr Int my_gcd(Int a, Int b) {
         // return __gcd(a, b);
         if (a < 0) a = -a;
         if (b < 0) b = -b;
         while (a and b) {
-            if (a > b)
+            if (a > b) {
                 a %= b;
-            else
+            } else {
                 b %= a;
+            }
         }
         return a + b;
     }
+
     constexpr Rational(Int num = 0, Int den = 1) : num(num), den(den) { normalize(); }
     constexpr void normalize() noexcept {
-        if constexpr (AlwaysReduce) { // reduction
+        if constexpr (AutoReduce) { // reduction
             Int g = my_gcd(num, den);
             if (g) num /= g, den /= g;
         } else {
@@ -31,12 +34,16 @@ template <class Int, bool AlwaysReduce = false> struct Rational {
         }
         if (den < 0) num = -num, den = -den; // denominator >= 0
     }
+
+    constexpr bool is_finite() const noexcept { return den != 0; }
+    constexpr bool is_infinite_or_nan() const noexcept { return den == 0; }
+
     constexpr Rational operator+(const Rational &r) const noexcept {
-        if (!den and !r.den) return Rational(num + r.num, den);
+        if (is_infinite_or_nan() and r.is_infinite_or_nan()) return Rational(num + r.num, 0);
         return Rational(num * r.den + den * r.num, den * r.den);
     }
     constexpr Rational operator-(const Rational &r) const noexcept {
-        if (!den and !r.den) return Rational(num - r.num, den);
+        if (is_infinite_or_nan() and r.is_infinite_or_nan()) return Rational(num - r.num, 0);
         return Rational(num * r.den - den * r.num, den * r.den);
     }
     constexpr Rational operator*(const Rational &r) const noexcept {
@@ -51,23 +58,36 @@ template <class Int, bool AlwaysReduce = false> struct Rational {
     constexpr Rational &operator/=(const Rational &r) noexcept { return *this = *this / r; }
     constexpr Rational operator-() const noexcept { return Rational(-num, den); }
     constexpr Rational abs() const noexcept { return Rational(num > 0 ? num : -num, den); }
+
+    constexpr Int floor() const {
+        assert(is_finite());
+        if (num > 0) {
+            return num / den;
+        } else {
+            return -((-num + den - 1) / den);
+        }
+    }
+
     constexpr bool operator==(const Rational &r) const noexcept {
-        if constexpr (AlwaysReduce) {
+        if (is_infinite_or_nan() or r.is_infinite_or_nan()) {
             return num == r.num and den == r.den;
         } else {
             return num * r.den == r.num * den;
         }
     }
+
     constexpr bool operator!=(const Rational &r) const noexcept { return !(*this == r); }
+
     constexpr bool operator<(const Rational &r) const noexcept {
-        if (den == 0 and r.den == 0)
+        if (is_infinite_or_nan() and r.is_infinite_or_nan())
             return num < r.num;
-        else if (den == 0)
+        else if (is_infinite_or_nan()) {
             return num < 0;
-        else if (r.den == 0)
+        } else if (r.is_infinite_or_nan()) {
             return r.num > 0;
-        else
+        } else {
             return num * r.den < den * r.num;
+        }
     }
     constexpr bool operator<=(const Rational &r) const noexcept {
         return (*this == r) or (*this < r);
@@ -76,6 +96,7 @@ template <class Int, bool AlwaysReduce = false> struct Rational {
     constexpr bool operator>=(const Rational &r) const noexcept {
         return (r == *this) or (r < *this);
     }
+
     constexpr explicit operator double() const noexcept { return (double)num / (double)den; }
     constexpr explicit operator long double() const noexcept {
         return (long double)num / (long double)den;
