JavaAlgorithms/Maths/KeithNumber.java

package Maths;

import java.util.*;

class KeithNumber  
{  
    //user-defined function that checks if the given number is Keith or not  
    static boolean isKeith(int x)  
    {  
        //List stores all the digits of the X  
        ArrayList<Integer> terms=new ArrayList<Integer>();  
        //n denotes the number of digits   
        int temp = x, n = 0;   
        //executes until the condition becomes false  
        while (temp > 0)  
        {  
            //determines the last digit of the number and add it to the List      
            terms.add(temp%10);  
            //removes the last digit  
            temp = temp/10;  
            //increments the number of digits (n) by 1  
            n++;  
        }  
        //reverse the List  
        Collections.reverse(terms);  
        int next_term = 0, i = n;  
        //finds next term for the series  
        //loop executes until the condition returns true  
        while (next_term < x)  
        {  
            next_term = 0;  
            //next term is the sum of previous n terms (it depends on number of digits the number has)  
            for (int j=1; j<=n; j++)  
            next_term = next_term + terms.get(i-j);  
            terms.add(next_term);  
            i++;  
        }  
        //when the control comes out of the while loop, there will be two conditions:  
        //either next_term will be equal to x or greater than x  
        //if equal, the given number is Keith, else not  
        return (next_term == x);  
    }  
    //driver code  
    public static void main(String[] args)  
    {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        if (isKeith(n))  
            System.out.println("Yes, the given number is a Keith number.");  
        else  
            System.out.println("No, the given number is not a Keith number.");   
    }  
}