Keith_Number.java

// In this section, we will learn what is Keith number and also create Java
// programs to check if the given number is Keith or not. The Keith number
// program frequently asked in Java coding test.

// Keith Number
// A positive n digit number X is called a Keith number (or repfigit number) if
// it is arranged in a special number sequence generated using its digits. The
// special sequence has first n terms as digits of x and other terms are
// recursively evaluated as the sum of previous n terms. For example, 197, 19,
// 742, 1537, etc.

import java.util.*;

class Keith_Number {
    // 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) {
        // calling the user-defined method inside the if statement and print the result
        // accordingly
        if (isKeith(19))
            System.out.println("Yes, the given number is a Keith number.");
        else
            System.out.println("No, the given number is not a Keith number.");
        if (isKeith(742))
            System.out.println("Yes, the given number is a Keith number.");
        else
            System.out.println("No, the given number is not a Keith number.");
        if (isKeith(4578))
            System.out.println("Yes, the given number is a Keith number.");
        else
            System.out.println("No, the given number is not a Keith number.");
    }
}