USTC-ACM-Prob1014

/**
* Solve it using the standard equation, that a smaller difference should
be reached
* each time.
* Be careful about the output format and extreme cases.
* Either one is zero, second is the factor of the first one, equal.
* Take of the case of ceil and floor function when the argument is
integer
* itself.
*/

Author: chunyang-wen

USTC-ACM-Prob1014.cpp

@@ -0,0 +1,104 @@
+
+/**
+ * Solve it using the standard equation, that a smaller difference should be reached
+ * each time.
+ * Be careful about the output format and extreme cases.
+ * Either one is zero, second is the factor of the first one, equal.
+ * Take of the case of ceil and floor function when the argument is integer
+ * itself.
+ */
+
+#include <iostream>
+#include <cmath>
+
+using namespace std;
+
+int gcd(int lhs, int rhs)
+{
+	if (lhs == rhs)
+		return lhs;
+	while(rhs)
+	{
+		lhs ^= rhs;
+		rhs ^= lhs; /* rhs = lhs */
+		lhs ^= rhs; /* lhs = rhs */
+		rhs %= lhs;
+	}
+	return lhs;
+}
+
+int main()
+{
+	int a,b; /* input two numbers */
+	int divisor;
+	int nom, den;
+
+	int nom_next, den_next; // 
+
+	int nom_1, nom_2;
+
+	double prev;
+	double next;
+
+	// int up_limit;
+	// int down_limit;
+	bool is_last = false;
+
+	while (cin>>a>>b)
+	{
+		if (is_last)
+			cout<<endl;
+		is_last = true;
+
+		if (a== 0 || b == 0)
+		{
+			cout<<a<<"/"<<b<<endl;
+			continue;
+		}
+		else if (a == b)
+		{
+			cout<<1<<"/"<<1<<endl;
+			continue;
+		}
+
+		divisor = gcd(a,b);
+		a /= divisor;
+		b /= divisor;
+
+		if (b == 1)
+		{
+			cout<<a<<"/"<<b<<endl;
+			continue;
+		}
+
+		den = 1;
+		if( (a%b) > (b>>1) )
+		{
+			nom = a/b + 1;
+		}
+		else
+			nom = a/b == 0?1:a/b;
+		cout<<nom<<"/"<<den<<endl;
+		for (den_next = 2; den_next < b; ++den_next)
+		{
+			prev = double(nom) /den;
+			next = double(a)/b;
+			prev = abs(next - prev);
+
+			nom_1 = (int)ceil(den_next * (next - prev)+0.00001);
+			nom_2 = (int)floor(den_next * (next + prev)-0.00001);
+
+			// nom_next = nom > den? den:nom;
+			nom_1 = nom_1 < 1?1:nom_1;
+			if (nom_2 < nom_1) continue;
+			// nom = nom_next;
+			den = den_next;
+			nom = nom_1;
+			cout<<nom<<"/"<<den<<endl;
+			
+		}
+		cout<<a<<"/"<<b<<endl;
+
+	}
+	return 0;
+}