SquareDigits

Problem Statement
    
***Note:  Please keep programs under 7000 characters in length.  Thank you

Class Name: SquareDigits
Method Name: smallestResult
Parameters: int
Returns: int

Define the function S(x) as the sum of the squares of the digits of x.  
For example: S(3)=3*3=9 and S(230)=2*2+3*3+0*0=13.

Define the set T(x) to be the set of unique numbers that are produced by
repeatedly applying S to x.  That is: S(x), S(S(x)), S(S(S(x))), etc...
For example, repeatedly applying S to 37:
S(37)=3*3+7*7=58. 
S(58)=5*5+8*8=89.
S(89)=145.
S(145)=42.
S(42)=20.
S(20)=4.
S(4)=16.
S(16)=37.
Note this sequence will repeat so we can stop calculating now and:
T(37)={58,89,145,42,20,4,16,37}.
However, note T(x) may not necessarily contain x. 

Implement a class SquareDigits, which contains a method smallestResult.  The
method takes an int, n, as a parameter and returns the smallest int, x, such
that T(x) contains n.

The method signature is (be sure your method is public):
int smallestResult(int n);

TopCoder will ensure n is non-negative and is between 0 and 199 inclusive.

Examples:
If n=0: S(0) = 0, so T(0)={0}, so the method should return 0.

If n=2: T(0) through T(10) do not contain the value 2.  If x=11, however:
S(11)=1*1+1*1=2, so T(11) contains 2, and the method should return 11.

If n=10: T(0) through T(6) do not contain 10.  If x=7:
S(7)=49.
S(49)=97.
S(97)=130.
S(130)=10.
S(10)=1.
and it starts to repeat...
so T(7) is {49,97,130,10,1}, which contains 10, and the method should return 7.

n=1 -> x=1
n=19 -> x=133
n=85 -> x=5
n=112 -> x=2666
Definition
    
Class:
SquareDigits
Method:
smallestResult
Parameters:
int
Returns:
int
Method signature:
int smallestResult(int param0)
(be sure your method is public)

package com.ibm.billyao.topcoder;

import java.util.ArrayList;
import java.util.List;

public class SquareDigits {

    public int smallestResult(int n) {
        if(n == 0 || n == 1) return n;

        List<Integer> vList = new ArrayList<Integer>();

        for(int i = 2; true; i++) {
            if(!vList.contains(i)) {
                int gen = i;
                while (true) {
                    gen = generate(gen);
                    if (gen == n) return i;

                    if(!vList.contains(gen)) {
                        vList.add(gen);
                    } else {
                        break;
                    }

                }
            }
        }
    }

    private int generate(int input) {
        int result = 0;
        
        while(true) {
            int val = input % 10;
            input = input / 10;
            result += val * val;
            if(input == 0) break;
        }
        
        return result;
    }
    
    public static void main(String[] args) {
        SquareDigits sd = new SquareDigits();
        
        System.out.println("0 : " + sd.generate(0));
        System.out.println("1 : " + sd.smallestResult(1));
        System.out.println("5 : " + sd.smallestResult(5));
        System.out.println("19 : " + sd.smallestResult(19));
        System.out.println("13 : " + sd.smallestResult(13));
        System.out.println("112 : " + sd.smallestResult(112));
        System.out.println("85 : " + sd.smallestResult(85));
    }
}