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?

 

 1 #include <iostream>
 2 using namespace std;
 3 
 4 class BigNumber
 5 {
 6 private:
 7     int num[1000];
 8 
 9 public:
10     BigNumber(int number)
11     {
12         for(int i=999; i>=0; i--)
13         {
14             num[i] = number % 10;
15             number /= 10;
16         }
17     }
18 
19     bool Contains1000Digits()
20     {
21         return num[0] > 0;
22     }
23 
24     BigNumber operator+(const BigNumber& bigNumber)
25     {
26         BigNumber sum(0);
27         int temp;
28         int over = 0;
29         for(int i=999; i>=0; i--)
30         {
31             temp = num[i]+bigNumber.num[i]+over;
32             sum.num[i] = temp % 10;
33             over = temp / 10;
34         }
35         return sum;
36     }
37 
38     void print()
39     {
40         for(int i=0; i<1000; i++)
41         {
42             cout << num[i];
43         }
44         cout << endl;
45     }
46 };
47 
48 int main()
49 {
50     BigNumber F1(1);
51     BigNumber F2(1);
52     int i=2;
53     while(true)
54     {
55         i++;
56         F1 = F1+F2;
57         if(F1.Contains1000Digits())
58         {
59             break;
60         }
61         i++;
62         F2=F1+F2;
63         if(F2.Contains1000Digits())
64         {
65             break;
66         }
67     }
68     cout << i << endl;
69     cin.get();
70     return 0;
71 }