Thursday, 18 August 2016

Fibonacci Modified

Problem Statement
A series is defined in the following manner:
Given the nth and (n+1)th terms, the (n+2)th can be computed by the following relation
Tn+2 = (Tn+1)2 + Tn

So, if the first two terms of the series are 0 and 1:
the third term = 12 + 0 = 1
fourth term = 12 + 1 = 2
fifth term = 22 + 1 = 5
… And so on.

Given three integers A, B and N, such that the first two terms of the series (1st and 2nd terms) are A and B respectively, compute the Nth term of the series.
Input Format
You are given three space separated integers A, B and N on one line.
Input Constraints
0 <= A,B <= 2
3 <= N <= 20

Output Format
One integer.
This integer is the Nth term of the given series when the first two terms are A and B respectively.
Note
    Some output may even exceed the range of 64 bit integer.
Sample Input
0 1 5 

Sample Output
5

Explanation
The first two terms of the series are 0 and 1. The fifth term is 5. How we arrive at the fifth term, is explained step by step in the introductory sections.
Solution
 
import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {

    public static void main(String[] args) {
        /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */
        int i,n;
        BigInteger a,b;
        Scanner sc=new Scanner(System.in);
        a =  sc.nextBigInteger();
        b =  sc.nextBigInteger();
        n = sc.nextInt();
        BigInteger [] val = new BigInteger[n];
        val[0] = a;
        val[1] = b;
        for(i=2;i<n;i++){
            val[i]= (val[i-1].pow(2)).add(val[i-2]);
        }
        System.out.println(val[i-1]);
   
    }
}

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