Analysis: The trick is to map the Rational Number Tree to another complete binary tree as: 1 10 11 100 101 110 111 You can see in this tree, left child is to append 0 the end of parent node, right child is to append 1 to the parent node. And each binary number value just represents the position:(1, 10(2), 11(3), 100(4), 101(5)..)
Then, since left child is p/(p+q), right child is (p+q)/q, so:
1. when p/q is given, if p >q, it is the left child (0), if p
My solution: (Your opinion is highly appreciated)
package codeJam.google.com;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.math.BigInteger;
/**
* @author Zhenyi 2013 Dec 21, 2013 17:56:56 PM
*/
public class RationalNumberTree {
public static void main(String[] args) throws IOException {
BufferedReader in = new BufferedReader(new FileReader(
"C:/Users/Zhenyi/Downloads/B-small-practice.in"));
FileWriter out = new FileWriter(
"C:/Users/Zhenyi/Downloads/B-small-practice.out");
// BufferedReader in = new BufferedReader(new FileReader(
// "C:/Users/Zhenyi/Downloads/B-large-practice.in"));
// FileWriter out = new FileWriter(
// "C:/Users/Zhenyi/Downloads/B-large-practice.out");
Integer T = new Integer(in.readLine());
for (int cases = 1; cases <= T; cases++) {
String[] st = in.readLine().split("\\s");
Integer choice = new Integer(st[0]);
if (choice.equals(1)) {
// find p, q
BigInteger n = new BigInteger(st[1]);
BigInteger p = new BigInteger("1");
BigInteger q = new BigInteger("1");
int len = 0;
BigInteger[] bits = new BigInteger[65];
while (!n.equals(new BigInteger("0"))) {
bits[len] = n.mod(new BigInteger("2"));
n = n.divide(new BigInteger("2"));
len++;
}
if (len == 1) {
out.write("Case #" + cases + ": 1 1" + "\n");
} else {
for (int i = len - 2; i >= 0; i--) {
if (bits[i].equals(new BigInteger("0"))) {
q = q.add(p);
}
if (bits[i].equals(new BigInteger("1"))) {
p = p.add(q);
}
}
out.write("Case #" + cases + ": " + p + " " + q + "\n");
}
} else {
// find sequence
BigInteger n = new BigInteger("0");
BigInteger p = new BigInteger(st[1]);
BigInteger q = new BigInteger(st[2]);
BigInteger root = new BigInteger("1");
BigInteger[] bits = new BigInteger[65];
int len = 0;
while (!(p.equals(root) && q.equals(root))) {
if (p.subtract(q).signum() > 0) {
// right child
bits[len] = new BigInteger("1");
p = p.subtract(q);
} else {
// left child
bits[len] = new BigInteger("0");
q = q.subtract(p);
}
len++;
}
bits[len] = new BigInteger("1");
len++;
if (len == 1) {
out.write("Case #" + cases + ": 1" + "\n");
} else {
for (int i = len - 1; i >= 0; i--) {
n = n.multiply(new BigInteger("2")).add(bits[i]);
}
out.write("Case #" + cases + ": " + n + "\n");
}
}
}
in.close();
out.flush();
out.close();
}
}