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42.fib.c
76 lines (70 loc) · 1.44 KB
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42.fib.c
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#include<stdio.h>
int M[2][2]={{1,0},{0,1}};
int A[2][2]={{1,1},{1,0}};
int C[2][2]={{0,0},{0,0}};
int perfectSqr(float n);
void matM(int n);
void mul(int flag);
void main()
{
printf("%d\n",fib(2));//1,1,2,3,5,8,13,21,34
int n=9;
matM(n-1);
printf("%d th fibonacci no.. %d\n",n,M[0][0]);
printf("%d th fibonacci no.. %d\n",n,fib2(n));
printf("\nif %d is..perfect square...%d\n",120,perfectSqr(120.0));
printf("\nif %d is fbonacci no..%d\n",34,chkFib(34));
}
int fib(int n)
{
return n<=2?1:fib(n-1)+fib(n-2);
}
void matM(int n)
{
if(n>1)
{
matM(n/2);
mul(0);//m*m
}
if(n%2!=0)
mul(1);//m*{1,1,1,0}
}
void mul(int flag)
{
int i,j,k,t;
if(flag==0)//m*m
{
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{C[i][j]=0;
for(k=0;k<2;k++)
C[i][j]+=M[i][k]*M[k][j];
}
}
if(flag==1)
{
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{C[i][j]=0;
for(k=0;k<2;k++)
C[i][j]+=A[i][k]*M[k][j];
}
}
for(i=0;i<2;i++)
for(j=0;j<2;j++)
M[i][j]=C[i][j];
}
int perfectSqr(float n)
{
return ((int)sqrt(n))*((int)sqrt(n))==n?1:0;
}
int chkFib(int n)
{
return (perfectSqr(5*n*n+4)||perfectSqr(5*n*n-4))?1:0;
}
int fib2(int n)
{
float n1=pow(((1+sqrt(5))/2) , n);
float n2=pow(((1-sqrt(5))/2), n);
return ((n1-n2)/sqrt(5));
}