[Project Euler] Problem 25

The Fibonacci sequence is defined by the recurrence relation:

F_n = F_n1 + F_n2, where F₁ = 1 and F₂ = 1.

Hence the first 12 terms will be:

F₁ = 1
F₂ = 1
F₃ = 2
F₄ = 3
F₅ = 5
F₆ = 8
F₇ = 13
F₈ = 21
F₉ = 34
F₁₀ = 55
F₁₁ = 89
F₁₂ = 144

The 12th term, F₁₂, is the first term to contain three digits.

What is the first term in the Fibonacci sequence to contain 1000 digits?

这道题的思路很简单

我们编写一个“大数类”

重载加法运算符，编写方法判断最高位是否大于0

代码如下：

#include < iostream >
using namespace std;

class BigNumber
{
private :
int num[ 1000 ];

public :
BigNumber( int tmp)
{
for ( int i = 999 ; i >= 0 ; i -- )
{
num[i] = tmp % 10 ;
tmp /= 10 ;
}
}

public :
bool isThousand()
{
return num[ 0 ] > 0 ;
}


BigNumber operator + ( const BigNumber & bigNumber)
{
BigNumber sum( 0 );
int tmp;
int over = 0 ;
for ( int i = 999 ; i >= 0 ; i -- )
{
tmp = num[i] + bigNumber.num[i] + over;
sum.num[i] = tmp % 10 ;
over = tmp / 10 ;
}
return sum;
}

void print()
{
for ( int i = 0 ; i < 1000 ; i ++ )
{
cout << num[i];
}
cout << endl;
}
};

int main()
{
BigNumber A1( 1 );
BigNumber A2( 1 );
int i = 2 ;
while ( 1 )
{
i ++ ;
A1 = A1 + A2;
if (A1.isThousand())
{
break ;
}
i ++ ;
A2 = A1 + A2;
if (A2.isThousand())
{
break ;
}
}
cout << i << endl;
return 0 ;

}

我们看到第4782个数有1000位

恭喜成功晋级到Level 1 了。