From 340a323c8785c8b84bbf167803aa3896bbf33f11 Mon Sep 17 00:00:00 2001
From: Anirudh Buvanesh <39529765+anirudhb11@users.noreply.github.com>
Date: Thu, 21 Oct 2021 10:36:30 +0530
Subject: [PATCH] Add matrix exponentiation based Fibonacci numbers (#2616)

---
 MatrixExponentiation/Fibonacci.java | 74 +++++++++++++++++++++++++++++
 1 file changed, 74 insertions(+)
 create mode 100644 MatrixExponentiation/Fibonacci.java

diff --git a/MatrixExponentiation/Fibonacci.java b/MatrixExponentiation/Fibonacci.java
new file mode 100644
index 00000000..bdcc0681
--- /dev/null
+++ b/MatrixExponentiation/Fibonacci.java
@@ -0,0 +1,74 @@
+package 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();
+    }
+}