[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>
usingnamespace 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;
    return0;

}

我们看到第4782个数有1000位

恭喜成功晋级到Level 1 了。