fibonacci matrix DP

Author: gkcs

src/main/java/main/java/dp/Fibonacci.java

@@ -0,0 +1,70 @@
+package main.java.dp;
+
+import java.util.Scanner;
+
+public class Fibonacci {
+ public static void main(String[] args) {
+ final Scanner scanner = new Scanner(System.in);
+ final int n = scanner.nextInt();
+ //Fib sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21
+ System.out.println(fibonacciDP(n));
+ System.out.println(fibonacciRecursive(n));
+ System.out.println(fibonacciMatrix(n));
+ }
+
+ private static long fibonacciRecursive(final int n) {
+ if (n < 2) {
+ if (n == 0) {
+ return 0;
+ } else {
+ return 1;
+ }
+ }
+ return fibonacciRecursive(n - 1) + fibonacciRecursive(n - 2);
+ }
+
+ private static long fibonacciDP(final int n) {
+ if (n < 2) {
+ if (n == 0) {
+ return 0;
+ } else {
+ return 1;
+ }
+ }
+ long first = 0, second = 1;
+ for (int i = 0; i < n; i++) {
+ final long temp = first;
+ first = second;
+ second = second + temp;
+ }
+ return first;
+ }
+
+ private static long fibonacciMatrix(int n) {
+ if (n < 2) {
+ if (n == 0) {
+ return 0;
+ } else {
+ return 1;
+ }
+ }
+ n--;
+ long product[][] = new long[][]{{1, 0}, {0, 1}}, M[][] = new long[][]{{1, 1}, {1, 0}};
+ while (n > 0) {
+ if ((n & 1) == 1) {
+ product = matrixMult(product, M);
+ }
+ M = matrixMult(M, M);
+ n = n >> 1;
+ }
+ return product[1][0] + product[1][1];
+ }
+
+ private static long[][] matrixMult(final long[][] first, final long[][] second) {
+ final long f00 = first[0][0] * second[0][0] + first[0][1] * second[1][0],
+ f01 = first[0][0] * second[0][1] + first[0][1] * second[1][1],
+ f10 = first[1][0] * second[0][0] + first[1][1] * second[1][0],
+ f11 = first[1][0] * second[0][1] + first[1][1] * second[1][1];
+ return new long[][]{{f00, f01}, {f10, f11}};
+ }
+}