70 lines
2.5 KiB
Java
70 lines
2.5 KiB
Java
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/*
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This is a Java Program to Implement Efficient O(log n) Fibonacci generator . This is a program to generate nth fibonacci number with O(log n) complexity.
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*/
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/**
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** Java Program to Implement Efficient O(log n) Fibonacci generator
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**/
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import java.util.Scanner;
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import java.math.BigInteger;
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/** Class FibonacciGenerator **/
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public class FibonacciGenerator
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{
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/** function to generate nth fibonacci number **/
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public void genFib(long n)
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{
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BigInteger arr1[][] = {{BigInteger.ONE, BigInteger.ONE}, {BigInteger.ONE, BigInteger.ZERO}};
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if (n == 0)
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System.out.println("\nFirst Fibonacci number = 0");
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else
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{
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power(arr1, n - 1);
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System.out.println("\n"+ n +" th Fibonacci number = "+ arr1[0][0]);
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}
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}
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/** function raise matrix to power n recursively **/
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private void power(BigInteger arr1[][], long n)
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{
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if (n == 0 || n == 1)
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return;
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BigInteger arr2[][] = {{BigInteger.ONE, BigInteger.ONE}, {BigInteger.ONE, BigInteger.ZERO}};
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power(arr1, n / 2);
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multiply(arr1, arr1);
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if (n % 2 != 0)
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multiply(arr1, arr2);
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}
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/** function to multiply two 2 d matrices **/
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private void multiply(BigInteger arr1[][], BigInteger arr2[][])
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{
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BigInteger x = (arr1[0][0].multiply(arr2[0][0])).add(arr1[0][1].multiply(arr2[1][0]));
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BigInteger y = (arr1[0][0].multiply(arr2[0][1])).add(arr1[0][1].multiply(arr2[1][1]));
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BigInteger z = (arr1[1][0].multiply(arr2[0][0])).add(arr1[1][1].multiply(arr2[1][0]));
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BigInteger w = (arr1[1][0].multiply(arr2[0][1])).add(arr1[1][1].multiply(arr2[1][1]));
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arr1[0][0] = x;
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arr1[0][1] = y;
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arr1[1][0] = z;
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arr1[1][1] = w;
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}
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/** Main function **/
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public static void main(String[] args)
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{
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Scanner scan = new Scanner(System.in);
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System.out.println("Efficient Fibonacci Generator\n");
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System.out.println("Enter number n to find nth fibonacci number\n");
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long n = scan.nextLong();
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FibonacciGenerator fg = new FibonacciGenerator();
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fg.genFib(n);
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}
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}
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/*
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Enter number n to find nth fibonacci number
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1000
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1000 th Fibonacci number = 43466557686937456435688527675040625802564660517371780
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40248172908953655541794905189040387984007925516929592259308032263477520968962323
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9873322471161642996440906533187938298969649928516003704476137795166849228875
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