75 lines
2.7 KiB
Java
75 lines
2.7 KiB
Java
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package MatrixExponentiation;
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import java.util.Scanner;
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/** @author Anirudh Buvanesh (https://github.com/anirudhb11)
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* For more information see https://www.geeksforgeeks.org/matrix-exponentiation/
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* */
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public class Fibonacci {
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// Exponentiation matrix for Fibonacci sequence
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private static final int [][] fibMatrix = {{1,1}, {1,0}};
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private static final int [][] identityMatrix = {{1,0}, {0,1}};
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//First 2 fibonacci numbers
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private static final int [][] baseFibNumbers = {{1}, {0}};
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/**
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* Performs multiplication of 2 matrices
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* @param matrix1
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* @param matrix2
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* @return The product of matrix1 and matrix2
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*/
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private static int[][] matrixMultiplication(int[][] matrix1, int[][] matrix2){
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//Check if matrices passed can be multiplied
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int rowsInMatrix1 = matrix1.length;
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int columnsInMatrix1 = matrix1[0].length;
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int rowsInMatrix2 = matrix2.length;
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int columnsInMatrix2 = matrix2[0].length;
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assert columnsInMatrix1 == rowsInMatrix2;
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int [][] product = new int[rowsInMatrix1][columnsInMatrix2];
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for (int rowIndex = 0; rowIndex < rowsInMatrix1; rowIndex ++){
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for(int colIndex = 0; colIndex < columnsInMatrix2; colIndex++){
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int matrixEntry = 0;
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for(int intermediateIndex = 0; intermediateIndex < columnsInMatrix1; intermediateIndex++){
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matrixEntry += matrix1[rowIndex][intermediateIndex] * matrix2[intermediateIndex][colIndex];
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}
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product[rowIndex][colIndex] = matrixEntry;
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}
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}
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return product;
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}
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/**
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* Calculates the fibonacci number using matrix exponentiaition technique
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* @param n The input n for which we have to determine the fibonacci number Outputs the nth
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* * fibonacci number
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* @return a 2 X 1 array as { {F_n+1}, {F_n} }
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*/
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public static int[][] fib(int n){
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if(n == 0){
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return Fibonacci.identityMatrix;
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}
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else{
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int [][] cachedResult = fib(n/2);
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int [][] matrixExpResult = matrixMultiplication(cachedResult, cachedResult);
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if(n%2 == 0){
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return matrixExpResult;
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}
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else{
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return matrixMultiplication(Fibonacci.fibMatrix, matrixExpResult);
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}
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}
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}
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public static void main(String[] args) {
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// Returns [0, 1, 1, 2, 3, 5 ..] for n = [0, 1, 2, 3, 4, 5.. ]
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Scanner sc = new Scanner(System.in);
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int n = sc.nextInt();
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int [][] result = matrixMultiplication(fib(n), baseFibNumbers);
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System.out.println("Fib(" + n + ") = "+ result[1][0] );
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sc.close();
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}
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}
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