算法导论-3 divide-and-conquer-strassen-fibonacci-polynomial-multiplication

1、计算 x(实数) 的 n(整数) 次方 ，O(logn)

codes：

import java.util.Scanner;public class Power {public static double power(double x, int n){if(n==0)return 1;if(n%2==0){// evendouble temp= power(x,n/2);return temp*temp;}else{// odddouble temp=power(x,(n-1)/2);return temp*temp*x;}}public static void main(String[] args) {Scanner in=new Scanner(System.in);while(true){double x=in.nextDouble();int n=in.nextInt();System.out.println(power(x,n));System.out.println(Math.pow(x, n));}}}

 

2、求Fibonacci数，O(logN)，矩阵相乘

codes：

import java.util.Scanner;//矩阵class Matrix{//初始为基本矩阵public int [][] elem={{1,1},{1,0}};//矩阵相乘，修改本身public Matrix multiply(Matrix m2){int temp[][]=new int[2][2];temp[0][0]=elem[0][0]*m2.elem[0][0]+elem[0][1]*m2.elem[1][0];temp[0][1]=elem[0][0]*m2.elem[0][1]+elem[0][1]*m2.elem[1][1];temp[1][0]=elem[1][0]*m2.elem[0][0]+elem[1][1]*m2.elem[0][1];temp[1][1]=elem[1][0]*m2.elem[0][1]+elem[1][1]*m2.elem[1][1];for(int i=0;i<2;i++)for(int j=0;j<2;j++)elem[i][j]=temp[i][j];return this;}public String toString(){return elem[0][0]+" "+elem[0][1]+"/n"+elem[1][0]+" "+elem[1][1];}}public class Fibo {//通过矩阵相乘求Fibo O(logN)public static int LogNFibo(int n){if(n==0)return 0;Matrix m=power(n);return m.elem[0][1];}public static final Matrix base=new Matrix();public static Matrix power(int n){if(n==1){return new Matrix();}if(n%2==0){// evenMatrix temp=power(n/2);return temp.multiply(temp);}else{// oddMatrix temp=power((n-1)/2);return temp.multiply(temp).multiply(base);}}//自底向上法 O(n)public static int LinearFibo(int n){int []ans=new int[n+1];ans[0]=0;ans[1]=1;for(int i=2;i<=n;i++){ans[i]=ans[i-1]+ans[i-2];}return ans[n];}public static void main(String[] args) {Scanner in=new Scanner(System.in);while(in.hasNext()){int n=in.nextInt();System.out.println(LinearFibo(n));System.out.println(LogNFibo(n));}}}