fibonacci numbers using matrix exponentiation

Author: gkcs

src/main/java/main/java/videos/FibonacciNumbers.java

@@ -0,0 +1,61 @@
+package main.java.videos;
+
+import java.util.Arrays;
+
+public class FibonacciNumbers {
+ public static void main(String[] args) {
+ final FibonacciFinder fibonacciFinder = new FibonacciFinder();
+ for (int i = 0; i < 15; i++) {
+ System.out.println(fibonacciFinder.fib(i));
+ }
+ }
+}
+
+class FibonacciFinder {
+ private final long[][][] exponents;
+
+ public FibonacciFinder() {
+ exponents = new long[64][2][2];
+ exponents[0] = new long[][]{{1, 1}, {1, 0}};
+ for (int i = 1; i < exponents.length; i++) {
+ exponents[i] = square(exponents[i - 1]);
+ }
+ }
+
+ private long[][] square(final long[][] matrix) {
+ return multiply(matrix, matrix);
+ }
+
+ private long[][] multiply(final long[][] matrix1, final long[][] matrix2) {
+ final long[][] result = new long[matrix1[0].length][matrix2.length];
+ for (int i = 0; i < matrix1.length; i++) {
+ for (int j = 0; j < matrix2[0].length; j++) {
+ for (int k = 0; k < matrix1[i].length; k++) {
+ result[i][j] += matrix1[i][k] * matrix2[k][j];
+ }
+ }
+ }
+ return result;
+ }
+
+ public long fib(int n) {
+ if (n < 0) {
+ throw new IllegalArgumentException();
+ } else if (n == 0 || n == 1) {
+ return 1;
+ } else {
+ final long[][] matrix = binaryExponentiation(n - 1);
+ return matrix[0][0] + matrix[0][1];
+ }
+ }
+
+ private long[][] binaryExponentiation(final int n) {
+ long[][] result = new long[][]{{1, 0}, {0, 1}};
+ for (int i = 31; i >= 0; i--) {
+ if ((n & (1 << i)) != 0) {
+ result = multiply(result, exponents[i]);
+ }
+ }
+ return result;
+ }
+}