Change project structure to a Maven Java project + Refactor (#2816)

src/main/java/com/thealgorithms/matrixexponentiation/Fibonacci.java

@@ -0,0 +1,76 @@
+package com.thealgorithms.matrixexponentiation;
+
+import java.util.Scanner;
+
+/**
+ * @author Anirudh Buvanesh (https://github.com/anirudhb11) For more information
+ * see https://www.geeksforgeeks.org/matrix-exponentiation/
+ *
+ */
+public class Fibonacci {
+
+    // Exponentiation matrix for Fibonacci sequence
+    private static final int[][] fibMatrix = {{1, 1}, {1, 0}};
+    private static final int[][] identityMatrix = {{1, 0}, {0, 1}};
+    //First 2 fibonacci numbers
+    private static final int[][] baseFibNumbers = {{1}, {0}};
+
+    /**
+     * Performs multiplication of 2 matrices
+     *
+     * @param matrix1
+     * @param matrix2
+     * @return The product of matrix1 and matrix2
+     */
+    private static int[][] matrixMultiplication(int[][] matrix1, int[][] matrix2) {
+        //Check if matrices passed can be multiplied
+        int rowsInMatrix1 = matrix1.length;
+        int columnsInMatrix1 = matrix1[0].length;
+
+        int rowsInMatrix2 = matrix2.length;
+        int columnsInMatrix2 = matrix2[0].length;
+
+        assert columnsInMatrix1 == rowsInMatrix2;
+        int[][] product = new int[rowsInMatrix1][columnsInMatrix2];
+        for (int rowIndex = 0; rowIndex < rowsInMatrix1; rowIndex++) {
+            for (int colIndex = 0; colIndex < columnsInMatrix2; colIndex++) {
+                int matrixEntry = 0;
+                for (int intermediateIndex = 0; intermediateIndex < columnsInMatrix1; intermediateIndex++) {
+                    matrixEntry += matrix1[rowIndex][intermediateIndex] * matrix2[intermediateIndex][colIndex];
+                }
+                product[rowIndex][colIndex] = matrixEntry;
+            }
+        }
+        return product;
+    }
+
+    /**
+     * Calculates the fibonacci number using matrix exponentiaition technique
+     *
+     * @param n The input n for which we have to determine the fibonacci number
+     * Outputs the nth * fibonacci number
+     * @return a 2 X 1 array as { {F_n+1}, {F_n} }
+     */
+    public static int[][] fib(int n) {
+        if (n == 0) {
+            return Fibonacci.identityMatrix;
+        } else {
+            int[][] cachedResult = fib(n / 2);
+            int[][] matrixExpResult = matrixMultiplication(cachedResult, cachedResult);
+            if (n % 2 == 0) {
+                return matrixExpResult;
+            } else {
+                return matrixMultiplication(Fibonacci.fibMatrix, matrixExpResult);
+            }
+        }
+    }
+
+    public static void main(String[] args) {
+        // Returns [0, 1, 1, 2, 3, 5 ..] for n = [0, 1, 2, 3, 4, 5.. ]
+        Scanner sc = new Scanner(System.in);
+        int n = sc.nextInt();
+        int[][] result = matrixMultiplication(fib(n), baseFibNumbers);
+        System.out.println("Fib(" + n + ") = " + result[1][0]);
+        sc.close();
+    }
+}