Algorithms - Discrete Mathematics - Diwali Lights

Diwali Lights

The following is the solution to Hacker Rank problem Diwali Lights using Java.  For solutions to other Hacker Rank Problem visit my page HackerRank, alternatively try searching for the problem in my blog.

The Approach I'm following is given below:

1. The problem is easy, if we have 2 bulbs atleast 1 bulb should be set at any time so there are 2²-1 possibilities eliminating the condition where all the bulbs are turned off.
2. So if we have N bulbs then we have 2^N-1 possibilities which is large  number to compute.
3. We can do this easily with Java's BigInteger , we can calculate the power using pow function.
4. Also we must note since this number is large we are asked to print the result mod 10⁵ we can also do this easily with Java's BigInteger mod function.

Score: 5/5

/**  *  */ import java.io.BufferedReader; import java.io.InputStreamReader; import java.math.BigInteger; /**  * @author Arun.G  *  */ public class Solution {        /**         * @param args         */        static BufferedReader in = new BufferedReader(new InputStreamReader(                      System.in));        public static BigInteger ExponentBySquare(long x, long n)     {               BigInteger big = BigInteger.valueOf(x)                    .pow((int)n)                    .subtract(BigInteger.ONE).mod(new BigInteger("100000"));                             return big;     }        public static void main(String[] args) throws NumberFormatException,                      Exception {                             int T = Integer.parseInt(in.readLine());                 for(int i=0;i<T;i++)           {           long noOfBulbs = Long.parseLong(in.readLine());           System.out.println(ExponentBySquare(2,noOfBulbs).toString());         }                 in.close();                                    } }

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