WhatBaseIsThis.java

/**
 * In positional notation we know the position of a digit indicates the weight of that digit toward the
 * value of a number. For example, in the base 10 number 362 we know that 2 has the weight 100
 * , 6
 * has the weight 101
 * , and 3 has the weight 102
 * , yielding the value 3 × 102 + 6 × 101 + 2 × 100
 * , or just
 * 300 + 60 + 2. The same mechanism is used for numbers expressed in other bases. While most people
 * assume the numbers they encounter everyday are expressed using base 10, we know that other bases
 * are possible. In particular, the number 362 in base 9 or base 14 represents a totally different value than
 * 362 in base 10.
 * For this problem your program will presented with a sequence of pairs of integers. Let’s call the
 * members of a pair X and Y . What your program is to do is determine the smallest base for X and the
 * smallest base for Y (likely different from that for X) so that X and Y represent the same value.
 * Consider, for example, the integers 12 and 5. Certainly these are not equal if base 10 is used for
 * each. But suppose 12 was a base 3 number and 5 was a base 6 number? 12 base 3 = 1 × 3
 * 1 + 2 × 3
 * 0
 * ,
 * or 5 base 10, and certainly 5 in any base is equal to 5 base 10. So 12 and 5 can be equal, if you select
 * the right bases for each of them!
 * Input
 * On each line of the input data there will be a pair of integers, X and Y , separated by one or more blanks;
 * leading and trailing blanks may also appear on each line, are are to be ignored. The bases associated
 * with X and Y will be between 1 and 36 (inclusive), and as noted above, need not be the same for X and
 * Y . In representing these numbers the digits 0 through 9 have their usual decimal interpretations. The
 * uppercase alphabetic characters A through Z represent digits with values 10 through 35, respectively.
 * Output
 * For each pair of integers in the input display a message similar to those shown in the examples shown
 * below. Of course if the two integers cannot be equal regardless of the assumed base for each, then print
 * an appropriate message; a suitable illustration is given in the examples.
 * Sample Input
 * 12 5
 * 10 A
 * 12 34
 * 123 456
 * 1 2
 * 10 2
 * Sample Output
 * 12 (base 3) = 5 (base 6)
 * 10 (base 10) = A (base 11)
 * 12 (base 17) = 34 (base 5)
 * 123 is not equal to 456 in any base 2..36
 * 1 is not equal to 2 in any base 2..36
 * 10 (base 2) = 2 (base 3)
 */

//https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=&problem=279

import java.math.BigInteger;
import java.util.Scanner;

public class WhatBaseIsThis {

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		while (input.hasNext()) {
			String x = input.next();
			String y = input.next();
			boolean found = false;
			for (int i = 2; i < 37 && !found; i++) {
				BigInteger xConvertedToBase;
				try {
					xConvertedToBase = new BigInteger(x, i);
				} catch (Exception e) {
					continue;
				}
				for (int j = 2; j < 37; j++) {
					BigInteger yConvertedToBase;
					try {
						yConvertedToBase = new BigInteger(y, j);
					} catch (Exception e) {
						continue;
					}
					if (xConvertedToBase.equals(yConvertedToBase)) {
						System.out.println(x + " (base " + i + ") = " + y
								+ " (base " + j + ")");
						found = true;
						break;
					}
				}
			}
			if (!found) {
				System.out.println(x + " is not equal to " + y
						+ " in any base 2..36");
			}
		}
	}
}