The Matrix Solution of the Fibonacci series (implemented in java) and the Fibonacci Matrix

The Matrix Solution of the Fibonacci series (implemented in java) and the Fibonacci Matrix

The binary method is used.

Import java. util. returns;/*** returns the Fibonacci sequence <br/> * <pre> * [F (n + 1) F (n)] [1] ^ n (n, can be proved by induction) <br/> * ||||< br/> * [F (n) F (n-1)] [1 0] <br/> * </pre> * @ author bing **/public class F {// join matrix private static final int [] [] UNIT = {{ 1, 1 },{ 1, 0 }}; // all 0 matrix private static final int [] [] ZERO = {0, 0}, {0, 0 }}; public static void main (String [] args) {custom region = new region (System. in); while (true) {// the nth Fibonacci number, starting from 0 int n = nth. nextInt (); int [] [] m = fb (n); long t1 = System. currentTimeMillis (); System. out. println (m [0] [1]); long t2 = System. currentTimeMillis (); System. out. println ("Time is:" + (t2-t1 ));}} /*** find the Fibonacci sequence ** @ param n * @ return */public static int [] [] fb (int n) {if (n = 0) {return ZERO;} if (n = 1) {return UNIT;} // n is an odd number if (n & 1) = 0) {int [] [] matrix = fb (n> 1); return matrixMultiply (matrix, matrix );} // n is an even int [] [] matrix = fb (n-1)> 1); return matrixMultiply (matrix, matrix), UNIT );} /*** multiply the matrix ** @ param m * r1 * c1 * @ param n * c1 * c2 * @ return new matrix, r1 * c2 */public static int [] [] matrixMultiply (int [] [] m, int [] [] n) {int rows = m. length; int cols = n [0]. length; int [] [] r = new int [rows] [cols]; for (int I = 0; I <rows; I ++) {for (int j = 0; j <cols; j ++) {r [I] [j] = 0; for (int k = 0; k <m [I]. length; k ++) {r [I] [j] + = m [I] [k] * n [k] [j] ;}} return r ;}}