calculate Fibonacci Num by using Dynamic plan method
/*
*filename: fibonacci.cpp
*date: 2006.10.1
*created: karl zheng
*description: MatrixMultiplication for calculate Fibonacci No. n,cost: logN
*/
#include <stdafx.h>
#include <stdio.h>
#include<iostream>
#include "string.h"
void MatrixMultiply2By2(int a[2][2],int b[2][2],int c[2][2])
{
//c[1][1]=a[1][1]*b[1][1]+a[1][2]*b[2][1]; //it's strange:out bound but no compiler error message
c[0][0]=a[0][0]*b[0][0]+a[0][1]*b[1][0];
c[0][1]=a[0][0]*b[1][0]+a[0][1]*b[1][1];
c[1][0]=a[1][0]*b[0][0]+a[1][1]*b[1][0];
c[1][1]=a[1][0]*b[0][1]+a[1][1]*b[1][1];
}
void MatrixMultiply2By2_n_times_Power(int a[2][2],int n,int c[2][2])
{
int temp[2][2];
if(1==n)
{
c[0][0]=a[0][0];
c[0][1]=a[0][1];
c[1][0]=a[1][0];
c[1][1]=a[1][1];
return;
};
if(2==n)
{
MatrixMultiply2By2(a,a,c);
return;
};
if(n%2) //n is odd
{
MatrixMultiply2By2_n_times_Power(a,n/2,temp);
MatrixMultiply2By2(temp,temp,c);
temp[0][0]=c[0][0];
temp[0][1]=c[0][1];
temp[1][0]=c[1][0];
temp[1][1]=c[1][1];
MatrixMultiply2By2(a,temp,c);
return;
}
else //n is even
{
MatrixMultiply2By2_n_times_Power(a,n/2,c);
temp[0][0]=c[0][0];
temp[0][1]=c[0][1];
temp[1][0]=c[1][0];
temp[1][1]=c[1][1];
MatrixMultiply2By2(temp,temp,c);
return;
}
}
int main(int argc,char *argv[])
{
//char t[2][3]={'a'};
int a[2][2]={{1,1},{1,0}};
int c[2][2]={{1,1},{1,0}};;
//MatrixMultiply2By2(a,a,c);
int n,n1;
using namespace std;
while(true){
cin>>n;
if(n<0)
{
cout<<" input Negative No.Error";
return 0;
};
if(0==n)
{
cout<<"Fibonacci("<<n<<")"<<a[1][1];
return 0;
};
MatrixMultiply2By2_n_times_Power(a,n,c);
cout<<"MatrixMultiplication for calculate Fibonacci No. n,cost: logN"<<endl;
cout<<"Fibonacci("<<n<<")="<<c[0][1];
//getch();
}
return 0;
}