Being Code Expert: Diwali Lights

On the eve of Diwali, Hari is decorating his house with a serial light bulb set. The serial light bulb set has N bulbs placed sequentially on a string which is programmed to change patterns every second. If at least one bulb in the set is on at any given instant of time, how many different patterns of light can the serial light bulb set produce?

Note: Lighting two bulbs *-* is different from **-

Example:

Input:  n = 4
Output: 15

Approach

Java


public class DiwaliLights {
    public static void main(String[] args) {

        int n = 4;

        System.out.println(lights(n));

    }

    static long mod = 100000;

    static long power(long a, long n) {
        // Base Case
        if (n == 0)
            return 1;
        long res = power(a, n / 2) % mod;
        if (n % 2 == 1)
            return (res * res * a) % mod;
        else
            return (res * res) % mod;
    }

    static long lights(long n) {
        return (power(2, n) % mod - 1);
    }

}

C++

#include <bits/stdc++.h>
using namespace std;

#define mod 100000
long power(long a, long n)
{
    //Base Case
    if (n == 0)
        return 1;
    long res = power(a, n / 2) % mod;
    if (n & 1)
        return (res * res * a) % mod;
    else
        return (res * res) % mod;
}

long lights(long n)
{
    return (power(2, n) % mod - 1);
}

int main()
{

    int n = 4;

    cout << lights(n) << "\n";
    return 0;
}