Update Fraction.cpp

Author: SamZhangQingChuan

数学/Fraction.cpp

@@ -1,63 +1,78 @@
 struct Fraction {
     ll numerator, denominator;
 
-    Fraction(ll n = 0, ll d = 1) {
-        ll g = gcd(n, d);
+    Fraction (ll n = 0, ll d = 1) {
+        ll g = gcd (n, d);
         n /= g;
         d /= g;
-        if(d < 0)n *= -1;
-        d = abs(d);
-        if(d == 0)n = abs(n);
+        if (d < 0)n *= -1;
+        d = abs (d);
+        if (d == 0)n = abs (n);
         numerator = n;
         denominator = d;
     }
 
-    Fraction operator+(const Fraction &o) const {
-        return Fraction(numerator * o.denominator + denominator * o.numerator, denominator * o.denominator);
+    Fraction operator+ (const Fraction &o) const {
+        return Fraction (numerator * o.denominator + denominator * o.numerator, denominator * o.denominator);
     }
 
-    Fraction operator+(const ll &o) const {
-        return *this + Fraction(o, 1);
+    Fraction operator+ (const ll &o) const {
+        return *this + Fraction (o, 1);
     }
 
-    Fraction operator-(const Fraction &o) const {
-        return Fraction(numerator * o.denominator - denominator * o.numerator, denominator * o.denominator);
+    Fraction operator- (const Fraction &o) const {
+        return Fraction (numerator * o.denominator - denominator * o.numerator, denominator * o.denominator);
     }
 
-    Fraction operator*(const Fraction &o) const {
-        return Fraction(numerator * o.numerator, denominator * o.denominator);
+    Fraction operator* (const Fraction &o) const {
+        return Fraction (numerator * o.numerator, denominator * o.denominator);
     }
 
-    Fraction operator/(const Fraction &o) const {
-        return Fraction(numerator * o.denominator, denominator * o.numerator);
+    Fraction operator/ (const Fraction &o) const {
+        return Fraction (numerator * o.denominator, denominator * o.numerator);
     }
 
-    bool operator<(const Fraction &o) const {
+    bool operator< (const Fraction &o) const {
         return numerator * o.denominator < o.numerator * denominator;
     }
 
-    bool operator==(const Fraction &o) const {
+    bool operator== (const Fraction &o) const {
         return numerator * o.denominator == o.numerator * denominator;
     }
+    
+    bool operator<= (const Fraction &o) const {
+        return *this < o or *this == o;
+    }
+    
+    bool operator> (const Fraction &o) const {
+        return !(*this <= o);
+    }
+    
+    bool operator>= (const Fraction &o) const {
+        return !(*this < o);
+    }
+    
+    friend ostream &operator<< (ostream &out, const Fraction &f) {
+        out<<f.numerator<<"/"<<f.denominator;
+        return out;
+    }
+    
+    friend Fraction smallest_fraction_in_interval (Fraction a, Fraction b);
 };
 
-ostream &operator<<(ostream &out, const Fraction &f) {
-    out << f.numerator << " " << f.denominator;
-    return out;
-}
-
-Fraction smallest_fraction_in_interval(Fraction a, Fraction b) {
-    if(b < a)swap(a, b);
-    if(a.numerator >= a.denominator) {
+//满足 a/b < p/q < c/d 的分数 p/q，分母最小的是多少
+Fraction smallest_fraction_in_interval (Fraction a, Fraction b) {
+    if (b < a)swap (a, b);
+    if (a.numerator >= a.denominator) {
         ll d = a.numerator / a.denominator;
         a.numerator -= a.denominator * d;
         b.numerator -= b.denominator * d;
-        return smallest_fraction_in_interval(a, b) + d;
+        return smallest_fraction_in_interval (a, b) + d;
     }
-    if(b.numerator > b.denominator)return Fraction(1, 1);
-    swap(a.numerator, a.denominator);
-    swap(b.numerator, b.denominator);
-    auto ans = smallest_fraction_in_interval(b, a);
-    swap(ans.numerator, ans.denominator);
+    if (b.numerator > b.denominator)return Fraction (1, 1);
+    swap (a.numerator, a.denominator);
+    swap (b.numerator, b.denominator);
+    auto ans = smallest_fraction_in_interval (b, a);
+    swap (ans.numerator, ans.denominator);
     return ans;
 }