// Pre:
// 1) a >= 0
// Constructively returns floor(a/2)
// Changes the remainder of a, possibly
Rational halfOf(Rational a) {
if(a.getLength() == 1 && a.getDigit(0) == 0)
return Rational ("0");
string c = "";
stringstream ss;
int curr = 0;
int i = a.getLength()-1;
int innerZeros = 0;
while(i >= 0) {
curr = 10*curr + a.getDigit(i);
if(curr/2 > 0 || innerZeros) {
innerZeros = 1;
ss.str(string());
ss << curr/2;
c += ss.str();
}
curr = curr%2;
i--;
}
Rational d (c);
if(a.getDigit(0)%2 == 1)
d.setRemainder(1);
return d;
}
// Pre:
// 1) a >= b
// Constructively returns a-b
Rational subtract(Rational a, Rational b) {
Rational c ("0");
int i = 0;
while(i < a.getLength()) {
if(a.getDigit(i) >= b.getDigit(i))
c.setDigit(i,a.getDigit(i)-b.getDigit(i));
else {
c.setDigit(i,a.getDigit(i)+10-b.getDigit(i));
a.setDigit(i+1,a.getDigit(i+1)-1);
}
i++;
}
while(i > 1 && c.getDigit(i-1) == 0)
i--;
c.setLength(i);
return c;
}
// Constructively returns a+b
Rational add(Rational a, Rational b) {
int max = ((a.getLength() > b.getLength()) ? a.getLength() : b.getLength());
int i = 0;
Rational c ("0");
c.setLength(max);
while(i < max) {
c.setDigit(i, c.getDigit(i) + a.getDigit(i) + b.getDigit(i));
if(c.getDigit(i) > 9) {
c.setDigit(i, c.getDigit(i)%10);
c.setDigit(i+1, c.getDigit(i+1)+1);
if(i == max-1)
c.setLength(c.getLength()+1);
}
i++;
}
return c;
}
